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1.1: Graphs for Discrete and for Continuous Data

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Basic Graph Types

In previous sections, you learned about discrete and continuous data and were introduced to categorical and numerical forms of displaying data. In later sections, you will learn how to display discrete and continuous data in both categorical and numerical displays, but in a way that allows you to compare sets of data. However, as a review, let's first go through the following examples.

Identifying Discrete and Continuous Data

Which of the following graphs represents discrete data? Which represents continuous data?

Remember that discrete data is represented by exact values that result from counting, as in the number of people in the households in your neighborhood. Continuous data is represented by a range of data that results from measuring. For example, taking the average temperatures for each month during a year is an example of continuous data. Also remember from an earlier Concept how you distinguished between these types of data when you graphed them.

The first graph shows discrete data. Remember that you know this because the data points are not joined. The second graph represents the average temperatures during the months in 2009. This data is continuous. You can easily tell this by looking at the graph and seeing the data points connected together.

Recognizing the Type of Data Graphs Represent

1. Which of the following graphs represent categorical, or qualitative, data? Which represent numerical, or quantitative, data?

2 newer terms used are the categorical and numerical data forms. Categorical data forms are just what the term suggests. These are data forms that are in categories and describe characteristics, or qualities, of a category. These data forms are more qualitative data and, therefore, are less numerical than they are descriptive. Graphs such as pie charts and bar graphs show descriptive data, or qualitative data. The top 2 graphs are examples of categorical data represented in these types of graphs.

Numerical data is quantitative data . Numerical data involves measuring or counting a numerical value. Therefore, when you talk about discrete and continuous data, you are talking about numerical data. Line graphs, frequency polygons, histograms, and stem-and-leaf plots all involve numerical data, or quantitative data, as is shown in the remaining graphs.

2. Does the following graph represent categorical or numerical data? Is the data discrete or continuous?

Box-and-whisker plots are considered numerical displays of data, as they are based on quantitative data (the mean and median), as well as the maximum (upper) and minimum (lower) values found in the data. Also, since a box-and-whisker plot analyzes individual data points, we know that the data must be discrete, and not continuous.

You will spend the next several sections learning about how to compare sets of categorical and numerical data, including data that is both discrete and continuous.

Points to Consider

• What is the difference between categorical and numerical data, and how does this relate to qualitative and quantitative data?

Give a graphical example of each of the following types of data. There are many possible examples, but one example for each type of data is shown below:

Discrete data

The graph shown above is a box-and-whisker plot. Remember that to create a box-and-whisker plot, you put the data in order and find the minimum, first quartile, median, third quartile, and maximum of the data set. Since a box-and-whisker plot analyzes individual data points to find these values, it represents discrete data.

Continuous data

The graph shown above is a broken-line graph. As you can see from the graph, there is no break in the line. In other words, you can choose any time between 8:45 am and 12:15 pm, even one involving a fraction of a second, and there will be a corresponding distance in km. Therefore, this broken line graph represents continuous data.

Numerical, or quantitative, data

The graph shown above is a histogram. The horizontal axis of the histogram represents the heights of students in inches. This means that the data being counted by the histogram are numbers, so the histogram represents numerical, or quantitative, data.

Categorical, or qualitative, data

The graph shown above is a pie chart. The slices of the pie represents homework, music, meals, sleep, school, and work, respectively. In other words, the data that the slices of the pie stand for are not numbers. Therefore, the pie chart represents categorical, or quantitative, data.

• In the table below, match the following types of graphs with the types of variables used to create the graphs.

Determine if each of the following graphs represents discrete or continuous data.

USGS, earthquake.usgs.gov/earthquak...troller-40240/

Determine if each of the following graphs represents numerical (quantitative) data or categorical (qualitative) data.

USGS - earthquake.usgs.gov/earthquak...ear/graphs.php

Review (Answers)

To view the Review answers, open this PDF file and look for section 8.1.

Additional Resources

PLIX: Play, Learn, Interact, Experience for Discrete vs. Continuous Data.

A list of student-submitted discussion questions for Basic Graph Types for Basic Graph Types Discussion Questions.

Lesson plans for Review of Basic Graph Types Lesson Plan.

Practice for Graphs for Discrete and for Continuous Data.

Real World application with Basic Graph Types.

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Home » Histogram – Types, Examples and Making Guide

Histogram – Types, Examples and Making Guide

Table of Contents

Definition:

Histogram is a graphical representation of the distribution of numerical data. It consists of a series of bars, where the height of each bar represents the frequency or relative frequency of the data within a particular interval or “bin.” The intervals, or bins, are typically specified on the x-axis, while the frequency or relative frequency is displayed on the y-axis. Histograms are commonly used in data analysis to visualize the distribution of a dataset, including information about its central tendency, spread, and skewness. They are particularly useful for identifying patterns and outliers in large datasets.

Parts of Histogram

The parts of a histogram include:

The x-axis, or horizontal axis, represents the range of values for the variable being measured. It is divided into intervals or bins, each of which represents a range of values.

The y-axis, or vertical axis, represents the frequency or relative frequency of the data within each interval or bin. The height of each bar represents the frequency or relative frequency of the data within that interval.

The bars in a histogram are vertical rectangles that represent the frequency or relative frequency of the data within each interval or bin. The width of the bars corresponds to the width of the interval or bin.

Intervals or bins

The intervals or bins represent the ranges of values that are grouped together in a histogram. They are typically of equal width and are specified on the x-axis.

The title of the histogram should provide a clear and concise description of the variable being measured and the purpose of the histogram.

If the histogram represents multiple groups or categories, a legend may be included to explain the meaning of each color or pattern used to represent the data.

The shape of the histogram can indicate whether the data is skewed to the left, right, or has a symmetrical distribution. This can be helpful in understanding the distribution of the data and making inferences about the population being measured.

Types of Histogram

Some common types of Histogram are as follows:

Probability Histogram

A probability histogram is a type of histogram that shows the probability density function of a continuous variable. The area under each bar in a probability histogram represents the probability of the data falling within that range.

Bimodal Histogram

A bimodal histogram is a type of histogram that shows two distinct peaks, indicating that the data has two modes or two different populations. Bimodal histograms can indicate that the data is a mixture of two different distributions or that there are two underlying processes contributing to the data.

Uniform Histogram

A uniform histogram is a type of histogram that shows that the data is evenly distributed over a given range. In a uniform histogram, all bars are approximately the same height, indicating that there is an equal probability of the data falling within any given range.

Symmetric Histogram

A symmetric histogram is a type of histogram that shows that the data is evenly distributed around a central value, resulting in a shape that is roughly symmetrical. In a symmetric histogram, the mean, median, and mode are all approximately equal. This means that the distribution of the data is balanced, with roughly the same number of values on either side of the central value. An example of a symmetric histogram is the normal distribution.

How to Make Histogram

Here are the general steps to make a histogram:

• Collect and organize the data: Collect the data you want to represent in the histogram. Group the data into intervals or bins, depending on the range and distribution of the data.
• Determine the range and interval width: Determine the minimum and maximum values of the data, and decide on an appropriate interval width or bin size. The bin size should be small enough to capture the variability in the data, but large enough to group similar values together.
• Draw the horizontal and vertical axes: Draw the horizontal axis and label it with the variable being measured. Draw the vertical axis and label it with the frequency or relative frequency of the data.
• Draw the bars : Draw rectangles above each interval or bin, with the height of the rectangle corresponding to the frequency or relative frequency of the data in that bin. The width of the rectangle should be equal to the bin size.
• Add titles and labels : Add a title to the histogram that describes the variable being measured and the range of the data. Label the x-axis and y-axis with appropriate units and titles.
• Fine-tune the histogram: Adjust the histogram as needed to improve its readability and visual appeal. This may include changing the bin size, adjusting the scale of the axes, or changing the colors and styles of the bars.
• Interpret the histogram: Analyze the shape, center, and spread of the data using the histogram. Look for patterns and trends, and draw conclusions based on the data.

Histogram Creating Guide

Here are the steps to create a histogram using a spreadsheet program like Microsoft Excel:

• Open a new spreadsheet and enter the data you want to use for the histogram.
• Create a column for the bins or intervals you want to use for the histogram. These bins should be evenly spaced and cover the entire range of your data.
• Select the data and the bin column, and then click on the “Insert” tab and select “Histogram” from the “Charts” section.
• Choose the desired histogram style and format for your chart. You can customize the colors, titles, axis labels, and other chart elements to suit your needs.
• Review the histogram and make any necessary adjustments. You may need to adjust the bin size, scale of the axis, or formatting of the bars to make the histogram more informative and visually appealing.
• Analyze the histogram and draw conclusions based on the data. Look for patterns, trends, and outliers in the data, and use the histogram to support your analysis and decision-making.

Examples of Histogram

Here are some examples of histograms:

• Height of Students in a Class: A histogram of the height of students in a class might show a normal distribution with a peak around the average height of the class.
• Daily Temperatures in a City: A histogram of daily temperatures in a city might show a bimodal distribution, with one peak around the average high temperature and another peak around the average low temperature.
• Ages of Employees in a Company: A histogram of the ages of employees in a company might show a slightly skewed distribution, with more employees in their 30s and 40s than in their 20s or 50s.
• Grades on a Test: A histogram of grades on a test might show a uniform distribution if all the students performed equally well, or a skewed distribution if there are a few high or low scores that are significantly different from the others.
• Housing Prices in a Neighborhood: A histogram of housing prices in a neighborhood might show a skewed distribution with a long tail on the high end, indicating that there are a few very expensive houses in the area.

Applications of Histogram

Histograms have many applications in various fields, including:

• Quality Control: Histograms are used in quality control to monitor the distribution of product characteristics, such as weight, dimensions, or color. By analyzing histograms, manufacturers can identify and correct problems with production processes and ensure that products meet quality standards.
• Market Research: Histograms are used in market research to analyze data on consumer preferences, behavior, and demographics. By analyzing histograms, marketers can identify trends and patterns in consumer data and use this information to develop targeted marketing strategies.
• Finance and Economics: Histograms are used in finance and economics to analyze data on stock prices, interest rates, and other financial variables. By analyzing histograms, analysts can identify trends and patterns in financial data and use this information to make investment decisions and develop economic models.
• Medical Research: Histograms are used in medical research to analyze data on patient characteristics, such as age, weight, and medical history. By analyzing histograms, researchers can identify risk factors for disease, track the progress of treatment, and identify patterns in health outcomes.
• Image Processing: Histograms are used in image processing to analyze and manipulate digital images. By analyzing histograms of image pixels, software can adjust image contrast, brightness, and color balance to enhance image quality and improve visual clarity.

When to use Histogram

They are particularly useful for:

• Identifying the shape of a distribution: Histograms can help you identify the shape of a distribution, including whether it is symmetric, skewed, or bimodal.
• Identifying central tendency: Histograms can help you identify the center of a distribution, including the mean, median, and mode.
• Identifying variability: Histograms can help you identify the range and spread of a distribution, including the minimum and maximum values, as well as the interquartile range and standard deviation.
• Identifying outliers: Histograms can help you identify outliers, or extreme values that are significantly different from the rest of the data.
• Comparing distributions: Histograms can help you compare the distributions of two or more variables to identify similarities and differences.

Purpose of Histogram

The purpose of a histogram is to visualize the distribution of a dataset. It provides a graphical representation of the frequency or proportion of data points that fall within each interval or bin of a continuous variable. Histograms can reveal patterns and trends in the data that may not be apparent from other methods of analysis, and can help you identify the shape, center, spread, and outliers of a distribution.

Histograms are particularly useful for identifying the following:

• The shape of a distribution: Histograms can help you identify whether a distribution is symmetric, skewed, bimodal, or uniform.
• The center of a distribution : Histograms can help you identify the mean, median, or mode of a distribution.
• The spread of a distribution : Histograms can help you identify the range, interquartile range, or standard deviation of a distribution.
• Outliers : Histograms can help you identify values that fall far outside the bulk of the distribution, which may be unusual or extreme.

Advantages of Histogram

Here are some advantages of using a histogram to analyze data:

• Easy to interpret: Histograms provide a visual representation of the data that is easy to understand and interpret. The bars in a histogram show the frequency or proportion of data points that fall within each interval or bin, making it easy to see the distribution of the data.
• Reveals patterns and trends: Histograms can reveal patterns and trends in the data that may not be apparent from other methods of analysis. By looking at the shape of the distribution, you can identify whether it is symmetric, skewed, bimodal, or uniform, which can provide insights into the underlying data.
• Identifies outliers: Histograms can help you identify outliers, or data points that fall far outside the bulk of the distribution. This can be useful for identifying unusual or extreme values that may require further investigation.
• Quantitative analysis: Histograms provide a quantitative analysis of the data that can be used to calculate measures such as the mean, median, mode, range, interquartile range, and standard deviation. This can help you gain a more precise understanding of the distribution of the data.
• Comparisons: Histograms can be used to compare the distribution of two or more variables, which can reveal similarities and differences in the data.

Limitation of Histogram

• Bin size: The shape of the histogram can be affected by the bin size or width, and choosing the appropriate bin size can be subjective. A small bin size can lead to a jagged or noisy histogram, while a large bin size can oversimplify the distribution and obscure important features.
• Outliers : Histograms can be affected by outliers, which are data points that fall far outside the bulk of the distribution. Outliers can skew the distribution and make it difficult to interpret the data.
• Noisy data: Histograms can be sensitive to noisy or incomplete data, which can affect the shape and interpretation of the distribution.
• Subjectivity : The interpretation of histograms can be subjective, and different analysts may choose different bin sizes or interpret the distribution differently.
• Limited to one variable: Histograms are limited to analyzing one variable at a time, which can make it difficult to identify relationships between variables.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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2: Graphical Representations of Data

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In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

• 2.1: Introduction In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
• 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends.  A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
• 2.3: Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
• 2.4: Using Excel to Create Graphs Using technology to create graphs will make the graphs faster to create, more precise, and give the ability to use larger amounts of data. This section focuses on using Excel to create graphs.
• 2.5: Graphs that Deceive It's common to see graphs displayed in a misleading manner in social media and other instances. This could be done purposefully to make a point, or it could be accidental. Either way, it's important to recognize these instances to ensure you are not misled.
• 2.E: Graphical Representations of Data (Exercises) These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

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17 Data Visualization Techniques All Professionals Should Know

• 17 Sep 2019

There’s a growing demand for business analytics and data expertise in the workforce. But you don’t need to be a professional analyst to benefit from data-related skills.

Becoming skilled at common data visualization techniques can help you reap the rewards of data-driven decision-making , including increased confidence and potential cost savings. Learning how to effectively visualize data could be the first step toward using data analytics and data science to your advantage to add value to your organization.

Several data visualization techniques can help you become more effective in your role. Here are 17 essential data visualization techniques all professionals should know, as well as tips to help you effectively present your data.

Access your free e-book today.

What Is Data Visualization?

Data visualization is the process of creating graphical representations of information. This process helps the presenter communicate data in a way that’s easy for the viewer to interpret and draw conclusions.

There are many different techniques and tools you can leverage to visualize data, so you want to know which ones to use and when. Here are some of the most important data visualization techniques all professionals should know.

Data Visualization Techniques

The type of data visualization technique you leverage will vary based on the type of data you’re working with, in addition to the story you’re telling with your data .

Here are some important data visualization techniques to know:

• Gantt Chart
• Box and Whisker Plot
• Waterfall Chart
• Scatter Plot
• Pictogram Chart
• Highlight Table
• Bullet Graph
• Choropleth Map
• Network Diagram
• Correlation Matrices

1. Pie Chart

Pie charts are one of the most common and basic data visualization techniques, used across a wide range of applications. Pie charts are ideal for illustrating proportions, or part-to-whole comparisons.

Because pie charts are relatively simple and easy to read, they’re best suited for audiences who might be unfamiliar with the information or are only interested in the key takeaways. For viewers who require a more thorough explanation of the data, pie charts fall short in their ability to display complex information.

2. Bar Chart

The classic bar chart , or bar graph, is another common and easy-to-use method of data visualization. In this type of visualization, one axis of the chart shows the categories being compared, and the other, a measured value. The length of the bar indicates how each group measures according to the value.

One drawback is that labeling and clarity can become problematic when there are too many categories included. Like pie charts, they can also be too simple for more complex data sets.

3. Histogram

Unlike bar charts, histograms illustrate the distribution of data over a continuous interval or defined period. These visualizations are helpful in identifying where values are concentrated, as well as where there are gaps or unusual values.

Histograms are especially useful for showing the frequency of a particular occurrence. For instance, if you’d like to show how many clicks your website received each day over the last week, you can use a histogram. From this visualization, you can quickly determine which days your website saw the greatest and fewest number of clicks.

4. Gantt Chart

Gantt charts are particularly common in project management, as they’re useful in illustrating a project timeline or progression of tasks. In this type of chart, tasks to be performed are listed on the vertical axis and time intervals on the horizontal axis. Horizontal bars in the body of the chart represent the duration of each activity.

Utilizing Gantt charts to display timelines can be incredibly helpful, and enable team members to keep track of every aspect of a project. Even if you’re not a project management professional, familiarizing yourself with Gantt charts can help you stay organized.

5. Heat Map

A heat map is a type of visualization used to show differences in data through variations in color. These charts use color to communicate values in a way that makes it easy for the viewer to quickly identify trends. Having a clear legend is necessary in order for a user to successfully read and interpret a heatmap.

There are many possible applications of heat maps. For example, if you want to analyze which time of day a retail store makes the most sales, you can use a heat map that shows the day of the week on the vertical axis and time of day on the horizontal axis. Then, by shading in the matrix with colors that correspond to the number of sales at each time of day, you can identify trends in the data that allow you to determine the exact times your store experiences the most sales.

6. A Box and Whisker Plot

A box and whisker plot , or box plot, provides a visual summary of data through its quartiles. First, a box is drawn from the first quartile to the third of the data set. A line within the box represents the median. “Whiskers,” or lines, are then drawn extending from the box to the minimum (lower extreme) and maximum (upper extreme). Outliers are represented by individual points that are in-line with the whiskers.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted.

7. Waterfall Chart

A waterfall chart is a visual representation that illustrates how a value changes as it’s influenced by different factors, such as time. The main goal of this chart is to show the viewer how a value has grown or declined over a defined period. For example, waterfall charts are popular for showing spending or earnings over time.

8. Area Chart

An area chart , or area graph, is a variation on a basic line graph in which the area underneath the line is shaded to represent the total value of each data point. When several data series must be compared on the same graph, stacked area charts are used.

This method of data visualization is useful for showing changes in one or more quantities over time, as well as showing how each quantity combines to make up the whole. Stacked area charts are effective in showing part-to-whole comparisons.

9. Scatter Plot

Another technique commonly used to display data is a scatter plot . A scatter plot displays data for two variables as represented by points plotted against the horizontal and vertical axis. This type of data visualization is useful in illustrating the relationships that exist between variables and can be used to identify trends or correlations in data.

Scatter plots are most effective for fairly large data sets, since it’s often easier to identify trends when there are more data points present. Additionally, the closer the data points are grouped together, the stronger the correlation or trend tends to be.

10. Pictogram Chart

Pictogram charts , or pictograph charts, are particularly useful for presenting simple data in a more visual and engaging way. These charts use icons to visualize data, with each icon representing a different value or category. For example, data about time might be represented by icons of clocks or watches. Each icon can correspond to either a single unit or a set number of units (for example, each icon represents 100 units).

In addition to making the data more engaging, pictogram charts are helpful in situations where language or cultural differences might be a barrier to the audience’s understanding of the data.

11. Timeline

Timelines are the most effective way to visualize a sequence of events in chronological order. They’re typically linear, with key events outlined along the axis. Timelines are used to communicate time-related information and display historical data.

Timelines allow you to highlight the most important events that occurred, or need to occur in the future, and make it easy for the viewer to identify any patterns appearing within the selected time period. While timelines are often relatively simple linear visualizations, they can be made more visually appealing by adding images, colors, fonts, and decorative shapes.

12. Highlight Table

A highlight table is a more engaging alternative to traditional tables. By highlighting cells in the table with color, you can make it easier for viewers to quickly spot trends and patterns in the data. These visualizations are useful for comparing categorical data.

Depending on the data visualization tool you’re using, you may be able to add conditional formatting rules to the table that automatically color cells that meet specified conditions. For instance, when using a highlight table to visualize a company’s sales data, you may color cells red if the sales data is below the goal, or green if sales were above the goal. Unlike a heat map, the colors in a highlight table are discrete and represent a single meaning or value.

13. Bullet Graph

A bullet graph is a variation of a bar graph that can act as an alternative to dashboard gauges to represent performance data. The main use for a bullet graph is to inform the viewer of how a business is performing in comparison to benchmarks that are in place for key business metrics.

In a bullet graph, the darker horizontal bar in the middle of the chart represents the actual value, while the vertical line represents a comparative value, or target. If the horizontal bar passes the vertical line, the target for that metric has been surpassed. Additionally, the segmented colored sections behind the horizontal bar represent range scores, such as “poor,” “fair,” or “good.”

14. Choropleth Maps

A choropleth map uses color, shading, and other patterns to visualize numerical values across geographic regions. These visualizations use a progression of color (or shading) on a spectrum to distinguish high values from low.

Choropleth maps allow viewers to see how a variable changes from one region to the next. A potential downside to this type of visualization is that the exact numerical values aren’t easily accessible because the colors represent a range of values. Some data visualization tools, however, allow you to add interactivity to your map so the exact values are accessible.

15. Word Cloud

A word cloud , or tag cloud, is a visual representation of text data in which the size of the word is proportional to its frequency. The more often a specific word appears in a dataset, the larger it appears in the visualization. In addition to size, words often appear bolder or follow a specific color scheme depending on their frequency.

Word clouds are often used on websites and blogs to identify significant keywords and compare differences in textual data between two sources. They are also useful when analyzing qualitative datasets, such as the specific words consumers used to describe a product.

16. Network Diagram

Network diagrams are a type of data visualization that represent relationships between qualitative data points. These visualizations are composed of nodes and links, also called edges. Nodes are singular data points that are connected to other nodes through edges, which show the relationship between multiple nodes.

There are many use cases for network diagrams, including depicting social networks, highlighting the relationships between employees at an organization, or visualizing product sales across geographic regions.

17. Correlation Matrix

A correlation matrix is a table that shows correlation coefficients between variables. Each cell represents the relationship between two variables, and a color scale is used to communicate whether the variables are correlated and to what extent.

Correlation matrices are useful to summarize and find patterns in large data sets. In business, a correlation matrix might be used to analyze how different data points about a specific product might be related, such as price, advertising spend, launch date, etc.

Other Data Visualization Options

While the examples listed above are some of the most commonly used techniques, there are many other ways you can visualize data to become a more effective communicator. Some other data visualization options include:

• Bubble clouds
• Circle views
• Dendrograms
• Dot distribution maps
• Open-high-low-close charts
• Polar areas
• Radial trees
• Ring Charts
• Sankey diagram
• Span charts
• Streamgraphs
• Wedge stack graphs
• Violin plots

Tips For Creating Effective Visualizations

Creating effective data visualizations requires more than just knowing how to choose the best technique for your needs. There are several considerations you should take into account to maximize your effectiveness when it comes to presenting data.

Related : What to Keep in Mind When Creating Data Visualizations in Excel

One of the most important steps is to evaluate your audience. For example, if you’re presenting financial data to a team that works in an unrelated department, you’ll want to choose a fairly simple illustration. On the other hand, if you’re presenting financial data to a team of finance experts, it’s likely you can safely include more complex information.

Another helpful tip is to avoid unnecessary distractions. Although visual elements like animation can be a great way to add interest, they can also distract from the key points the illustration is trying to convey and hinder the viewer’s ability to quickly understand the information.

Finally, be mindful of the colors you utilize, as well as your overall design. While it’s important that your graphs or charts are visually appealing, there are more practical reasons you might choose one color palette over another. For instance, using low contrast colors can make it difficult for your audience to discern differences between data points. Using colors that are too bold, however, can make the illustration overwhelming or distracting for the viewer.

Related : Bad Data Visualization: 5 Examples of Misleading Data

Visuals to Interpret and Share Information

No matter your role or title within an organization, data visualization is a skill that’s important for all professionals. Being able to effectively present complex data through easy-to-understand visual representations is invaluable when it comes to communicating information with members both inside and outside your business.

There’s no shortage in how data visualization can be applied in the real world. Data is playing an increasingly important role in the marketplace today, and data literacy is the first step in understanding how analytics can be used in business.

Are you interested in improving your analytical skills? Learn more about Business Analytics , our eight-week online course that can help you use data to generate insights and tackle business decisions.

This post was updated on January 20, 2022. It was originally published on September 17, 2019.

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9.2: Presenting Quantitative Data Graphically

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• Page ID 59977

• Darlene Diaz
• Santiago Canyon College via ASCCC Open Educational Resources Initiative

Quantitative, or numerical, data can also be summarized into frequency tables.

Example \(\PageIndex{1}\)

A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are

19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0

These scores could be summarized into a frequency table by grouping like values:

Using this table, it would be possible to create a standard bar chart from this summary, like we did for categorical data:

However, since the scores are numerical values, this chart doesn’t really make sense; the first and second bars are five values apart, while the later bars are only one value apart. It would be more correct to treat the horizontal axis as a number line. This type of graph is called a histogram .

Definition: Histogram

A histogram is a graphical representation of quantitative data. The horizontal axis is a number line.

Example \(\PageIndex{2}\)

For the values above, a histogram would look like:

Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.

If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals .

Definition: Class Intervals

Class intervals are groupings of the data. In general, we define class intervals so that

• Each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
• Each interval has a lower limit and an upper limit , e.g., for interval 120-129, 120 is the lower limit and 129 is the upper limit.
• The class width is the difference between two consecutive lower limits.
• The class width is the same for every interval in the frequency table.
• We have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.

Example \(\PageIndex{3}\)

Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of \(263-121 = 142\). We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Oftentimes, we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.

Notice, the class width is 15 since \(150-135 = 15\), \(165-150 = 15\), and so on.

A histogram of this data would look like:

In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.

Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.

Try It Now 3

The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.

$140 $160 $160 $165 $180 $220 $235 $240 $250 $260 $280 $285

$285 $285 $290 $300 $300 $305 $310 $310 $315 $315 $320 $320

$330 $340 $345 $350 $355 $360 $360 $380 $395 $420 $460 $460

When collecting data to compare two groups, it is desirable to create a graph that compares quantities.

Example \(\PageIndex{4}\)

The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.

One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.

Definition: Frequency Polygon

An alternative representation is a frequency polygon. A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. The midpoint of an interval is

\[\dfrac{\text{lower limit}_2 - \text{lower limit}_1}{2} \nonumber \]

Typically, the points are connected with straight lines to emphasize the distribution of the data.

Example \(\PageIndex{5}\)

This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.

Numerical Summaries of Data

It is often desirable to use a few numbers to summarize a distribution. One important aspect of a distribution is where its center is located. Measures of central tendency are discussed first. A second aspect of a distribution is how spread out it is. In other words, how much the data in the distribution vary from one another. The second section describes measures of variability

Types of Graphs and Charts And Their Uses

If you are wondering what are the different types of graphs and charts ,   their uses and names, this page summarizes them with examples and pictures.

Although it is hard to tell what are all the types of graphs, this page consists all of the common types of statistical graphs and charts (and their meanings) widely used in any science.

1. Line Graphs

A line chart graphically displays data that changes continuously over time. Each line graph consists of points that connect data to show a trend (continuous change). Line graphs have an x-axis and a y-axis. In the most cases, time is distributed on the horizontal axis.

Uses of line graphs:

• When you want  to show trends . For example, how house prices have increased over time.
• When you want  to make predictions based on a data history over time.
• When comparing  two or more different variables, situations, and information over a given period of time.

The following line graph shows annual sales of a particular business company for the period of six consecutive years:

Note: the above example is with 1 line. However, one line chart can compare multiple trends by several distributing lines.

2. Bar Charts

Bar charts represent categorical data with rectangular bars (to understand what is categorical data see categorical data examples ). Bar graphs are among the most popular types of graphs and charts in economics, statistics, marketing, and visualization in digital customer experience . They are commonly used to compare several categories of data.

Each rectangular bar has length and height proportional to the values that they represent.

One axis of the bar chart presents the categories being compared. The other axis shows a measured value.

Bar Charts Uses:

• When you want to display data that are grouped into nominal or ordinal categories (see nominal vs ordinal data ).
• To compare data among different categories.
• Bar charts can also show large   data changes over time.
• Bar charts are ideal for visualizing the distribution of data when we have more than three categories.

The bar chart below represents the total sum of sales for Product A and Product B over three years.

The bars are 2 types: vertical or horizontal. It doesn’t matter which kind you will use. The above one is a vertical type.

3. Pie Charts

When it comes to statistical types of graphs and charts, the pie chart (or the circle chart) has a crucial place and meaning. It displays data and statistics in an easy-to-understand ‘pie-slice’ format and illustrates numerical proportion.

Each pie slice is relative to the size of a particular category in a given group as a whole. To say it in another way, the pie chart brakes down a group into smaller pieces. It shows part-whole relationships.

To make a pie chart, you need a list of categorical variables and numerical variables.

Pie Chart Uses:

• When you want to create and represent the composition of something.
• It is very useful for displaying nominal or ordinal categories of data.
• To show percentage or proportional data.
• When comparing areas of growth within a business such as profit.
• Pie charts work best for displaying data for 3 to 7 categories.

The pie chart below represents the proportion of types of transportation used by 1000 students to go to their school.

Pie charts are widely used by data-driven marketers for displaying marketing data.

4. Histogram

A histogram shows continuous data in ordered rectangular columns (to understand what is continuous data see our post discrete vs continuous data ). Usually, there are no gaps between the columns.

The histogram displays a frequency distribution (shape) of a data set. At first glance, histograms look alike to bar graphs. However, there is a key difference between them. Bar Chart represents categorical data and histogram represent continuous data.

Histogram Uses:

• When the data is continuous .
• When you want to represent the shape of the data’s distribution .
• When you want to see whether the outputs of two or more processes are different.
• To summarize large data sets graphically.
• To communicate the data distribution quickly to others.

The histogram below represents per capita income for five age groups.

Histograms are very widely used in statistics, business, and economics.

5. Scatter plot

The scatter plot is an X-Y diagram that shows a relationship between two variables. It is used to plot data points on a vertical and a horizontal axis. The purpose is to show how much one variable affects another.

Usually, when there is a relationship between 2 variables, the first one is called independent. The second variable is called dependent because its values depend on the first variable.

Scatter plots also help you predict the behavior of one variable (dependent) based on the measure of the other variable (independent).

Scatter plot uses:

• When trying to find out whether there is a relationship between 2 variables .
• To predict  the behavior of dependent variable based on the measure of the independent variable.
• When having paired numerical data.
• When working with  root cause analysis tools  to identify the potential for problems.
• When you just want to visualize the correlation between 2 large datasets without regard to time .

The below Scatter plot presents data for 7 online stores, their monthly e-commerce sales, and online advertising costs for the last year.

The orange line you see in the plot is called “line of best fit” or a “trend line”. This line is used to help us make predictions that are based on past data.

The Scatter plots are used widely in data science and statistics. They are a great tool for visualizing linear regression models .

More examples and explanation for scatter plots you can see in our post what does a scatter plot show and simple linear regression examples .

6. Venn Chart

Venn Diagram (also called primary diagram, set diagram or logic diagrams) uses overlapping circles to visualize the logical relationships between two or more group of items.

Venn Diagram is one of the types of graphs and charts used in scientific and engineering presentations, in computer applications, in maths, and in statistics.

The basic structure of the Venn diagram is usually overlapping circles. The items in the overlapping section have specific common characteristics. Items in the outer portions of the circles do not have common traits.

Venn Chart Uses:

• When you want to compare and contrast groups of things.
• To categorize or group items.
• To illustrate logical relationships from various datasets.
• To identify all the possible relationships between collections of datasets.

The following science example of Venn diagram compares the features of birds and bats.

7. Area Charts 

Area Chart Uses:

• When you want to show trends , rather than express specific values.
• To show a simple comparison of the trend of data sets over the period of time.
• To display the magnitude of a change.
• To compare a small number of categories.

The area chart has 2 variants: a variant with data plots overlapping each other and a variant with data plots stacked on top of each other (known as stacked area chart – as the shown in the following example).

The area chart below shows quarterly sales for product categories A and B for the last year.

This area chart shows you a quick comparison of the trend in the quarterly sales of Product A and Product B over the period of the last year.

8. Spline Chart

The Spline Chart is one of the most widespread types of graphs and charts used in statistics. It is a form of the line chart that represent smooth curves through the different data points.

Spline charts possess all the characteristics of a line chart except that spline charts have a fitted curved line to join the data points. In comparison, line charts connect data points with straight lines.

Spline Chart   Uses:

• When you want to plot data that requires the usage of curve-fitting such as a product lifecycle chart or an impulse-response chart.
• Spline charts are often used in designing Pareto charts .
• Spline chart also is often used for data modeling by when you have limited number of data points and estimating the intervening values.

The following spline chart example shows sales of a company through several months of a year:

9. Box and Whisker Chart

A box and whisker chart is a statistical graph for displaying sets of numerical data through their quartiles. It displays a frequency distribution of the data.

The box and whisker chart helps you to display the spread and skewness for a given set of data using the five number summary principle: minimum, maximum, median, lower and upper quartiles. The ‘five-number summary’ principle allows providing a statistical summary for a particular set of numbers. It shows you the range (minimum and maximum numbers), the spread (upper and lower quartiles), and the center (median) for the set of data numbers.

A very simple figure of a box and whisker plot you can see below:

Box and Whisker Chart Uses:

• When you want to observe the upper, lower quartiles, mean, median, deviations, etc. for a large set of data.
• When you want to see a quick view of the dataset distribution .
• When you have multiple data sets that come from independent sources and relate to each other in some way.
• When you need to compare data from different categories.

The table and box-and-whisker plots below shows test scores for Maths and Literature for the same class.

Box and Whisker charts have applications in many scientific areas and types of analysis such as statistical analysis, test results analysis, marketing analysis, data analysis, and etc.

10. Bubble Chart

Bubble charts are super useful types of graphs for making a comparison of the relationships between data in 3 numeric-data dimensions: the Y-axis data, the X-axis data, and data depicting the bubble size.

Bubble charts are very similar to XY Scatter plots but the bubble chart adds more functionality – a third dimension of data that can be extremely valuable.

Both axes (X and Y) of a bubble chart are numeric.

Bubble Chart Uses:

• When you have to display three or four dimensions of data.
• When you want to compare and display the relationships between categorized circles, by the use of proportions.

The bubble chart below shows the relationship between Cost (X-Axis), Profit (Y-Axis), and Probability of Success (%) (Bubble Size).

11. Pictographs

The pictograph or a pictogram is one of the more visually appealing types of graphs and charts that display numerical information with the use of icons or picture symbols to represent data sets.

They are very easy to read statistical way of data visualization. A pictogram shows the frequency of data as images or symbols. Each image/symbol may represent one or more units of a given dataset.

Pictograph Uses:

• When your audience prefers and understands better displays that include icons and illustrations. Fun can promote learning.
• It’s habitual for infographics to use of a pictogram.
• When you want to compare two points  in an emotionally powerful way.

The following pictographic represents the number of computers sold by a business company for the period from January to March.

The pictographic example above shows that in January are sold 20 computers (4×5 = 20), in February are sold 30 computers (6×5 = 30) and in March are sold 15 computers.

12. Dot Plot

Dot plot or dot graph is just one of the many types of graphs and charts to organize statistical data. It uses dots to represent data. A Dot Plot is used for relatively small sets of data and the values fall into a number of discrete categories.

If a value appears more than one time, the dots are ordered one above the other. That way the column height of dots shows the frequency for that value.

Dot Plot Uses:

• To plot frequency counts when you have a small number of categories .
• Dot plots are very useful when the variable is quantitative or categorical .
• Dot graphs are also used for univariate data (data with only one variable that you can measure).

Suppose you have a class of 26 students. They are asked to tell their favorite color. The dot plot below represents their choices:

It is obvious that blue is the most preferred color by the students in this class.

13. Radar Chart

A radar chart is one of the most modern types of graphs and charts – ideal for multiple comparisons. Radar charts use a circular display with several different quantitative axes looking like spokes on a wheel. Each axis shows a quantity for a different categorical value.

Radar charts are also known as spider charts, web charts, star plots, irregular polygons, polar charts, cobweb charts or Kiviat diagram.

Radar Chart has many applications nowadays in statistics, maths, business, sports analysis, data intelligence, and etc.

Radar Chart Uses:

• When you want to observe which variables have similar values or whether there are any outliers amongst each variable.
• To represent  multiple comparisons .
• When you want to see which variables are scoring low or high within a dataset. This makes radar chart ideal for displaying performance .

For example, we can compare employee’s performance with the scale of 1-8 on subjects such as Punctuality, Problem-solving, Meeting Deadlines, Marketing Knowledge, Communications. A point that is closer to the center on an axis shows a lower value and a worse performance.

It is obvious that Jane has a better performance than Samanta.

14. Pyramid Graph

When it comes to easy to understand and good looking types of graphs and charts, pyramid graph has a top place.

A pyramid graph is a chart in a pyramid shape or triangle shape. These types of charts are best for data that is organized in some kind of hierarchy. The levels show a progressive order.

Pyramid Graph Uses:

• When you want to indicate a hierarchy level among the topics or other types of data.
• Pyramid graph is often used to represent progressive orders such as: “older to newer”, “more important to least important”, “specific to least specific”‘ and etc.
• When you have a proportional or interconnected relationship between data sets.

A classic pyramid graph example is the healthy food pyramid that shows fats, oils, and sugar (at the top) should be eaten less than many other foods such as vegetables and fruits (at the bottom of the pyramid).

Conclusion:

You might know that choosing the right type of chart is some kind of tricky business.

Anyway, you have a wide choice of types of graphs and charts. Used in the right way, they are a powerful weapon to help you make your reports and presentations both professional and clear.

What are your favorite types of graphs and charts? Share your thoughts on the field below.

About The Author

Silvia Valcheva

Silvia Valcheva is a digital marketer with over a decade of experience creating content for the tech industry. She has a strong passion for writing about emerging software and technologies such as big data, AI (Artificial Intelligence), IoT (Internet of Things), process automation, etc.

I have learned a lot from your presentation. Very informative

Nicely described different graphs, I learned a lot.

very useful. exiting

I love this. I learned a lot.

Very good representation of date. I would suggest an addition of “stem and leaf” diagrams.

I have only one thing to say and that is this is the best representation of every graphs and charts I have ever seen 😀

Very well described. Great learning article for beginners on Charts.

Really helpful thanks

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• Math Article

Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

Thanks very much for the information

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Introduction to Graphs

Table of Contents

15 December 2020                 

Read time: 6 minutes

Introduction

What are graphs?

What are the different types of data?

What are the different types of graphical representations?

The graph is nothing but an organized representation of data. It helps us to understand the data. Data are the numerical information collected through observation.

The word data came from the Latin word Datum which means “something given”

After a research question is developed, data is being collected continuously through observation. Then it is organized, summarized, classified, and then represented graphically.

Differences between Data and information: Data is the raw fact without any add on but the information is the meaning derived from data.

Introduction to Graphs-PDF

The graph is nothing but an organized representation of data. It helps us to understand the data. Data are the numerical information collected through observation. Here is a downloadable PDF to explore more.

• Line and Bar Graphs Application
• Graphs in Mathematics & Statistics

What are the different Types of Data?

There are two types of Data :

Quantitative

The data which are statistical or numerical are known as Quantitive data. Quantitive data is generated through. Quantitative data is also known as Structured data. Experiments, Tests, Surveys, Market Report.

Quantitive data is again divided into Continuous data and Discrete data.

Continuous Data

Continuous data is the data which can have any value. That means Continuous data can give infinite outcomes so it should be grouped before representing on a graph.

• The speed of a vehicle as it passes a checkpoint
• The mass of a cooking apple
• The time taken by a volunteer to perform a task

Discrete Data

Discrete data can have certain values. That means only a finite number can be categorized as discrete data.

• Numbers of cars sold at a dealership during a given month
• Number of houses in certain block
• Number of fish caught on a fishing trip
• Number of complaints received at the office of airline on a given day
• Number of customers who visit at bank during any given hour
• Number of heads obtained in three tosses of a coin

Differences between Discrete and Continuous data

• Numerical data could be either discrete or continuous
• Continuous data can take any numerical value (within a range); For example, weight, height, etc.
• There can be an infinite number of possible values in continuous data
• Discrete data can take only certain values by finite ‘jumps’, i.e., it ‘jumps’ from one value to another but does not take any intermediate value between them (For example, number of students in the class)

Qualitative

Data that deals with description or quality instead of numbers are known as Quantitative data. Qualitative data is also known as unstructured data. Because this type of data is loosely compact and can’t be analyzed conventionally.

Different Types of Graphical Representations

There are many types of graph we can use to represent data. They are as follows,

A bar graph or chart is a way to represent data by rectangular column or bar. The heights or length of the bar is proportional to the values.

A line graph is a type of graph where the information or data is plotted as some dots which are known as markers and then they are added to each other by a straight line.

The line graph is normally used to represent the data that changes over time.

A histogram graph is a graph where the information is represented along with the height of the rectangular bar. Though it does look like a bar graph, there is a fundamental difference between them. With the histogram, each column represents a range of quantitative data when a bar graph represents categorical variables.

The other name of the pie chart is a circle graph. It is a circular chart where numerical information represents as slices or in fractional form or percentage where the whole circle is 100%.

• Stem and leaf plot

The stem and leaf plot is a way to represents quantitative data according to frequency ranges or frequency distribution.

In the stem and leaf plot, each data is split into stem and leaf, which is 32 will be split into 3 stems and 2 leaves.

Frequency table: Frequency means the number of occurrences of an event. A frequency distribution table is a graph or chart which shows the frequency of events. It is denoted as ‘f’ .

Pictograph or Pictogram is the earliest way to represents data in a pictorial form or by using symbols or images. And each image represents a particular number of things.

According to the above-mentioned Pictograph, the number of Appels sold on Monday is 6x2=12.

• Scatter diagrams

Scatter diagram or scatter plot is a way of graphical representation by using cartesian coordinates of two variables. The plot shows the relationship between two variables. Below there is a data table as well as a Scattergram as per the given data.

What is the meaning of Graphical representation?

Graphical representation is a way to represent and analyze quantitive data. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables.

Principles of graphical representation

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin.

On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value.

When X-axis and y-axis intersected each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV.

The location on the coordinate plane is known as the ordered pair and it is written as (x,y). That means the first value will be on the x-axis and the second one is on the y-axis. When we will plot any coordinate, we always have to start counting from the origin and have to move along the x-axis, if it is positive then to the right side, and if it is negative then to the left side. Then from the x-axis, we have to plot the y’s value, which means we have to move up for positive value or down if the value is negative along with the y-axis.

In the following graph, 1st ordered pair (2,3) where both the values of x and y are positive and it is on quadrant I. 2nd ordered pair (-3,1), here the value of x is negative and value of y is positive and it is in quadrant II. 3rd ordered pair (-1.5, -2.5), here the value of x as well as y both are Negative and in quadrant III.

Methods of representing a frequency distribution

There are four methods to represent a frequency distribution graphically. These are,

• Smoothed Frequency graph
• Cumulative frequency graph or Ogive.
• Pie diagram.

Advantages and Disadvantages of Graphical representation of data

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represents it graphically.

You may also like:

• Graphing a Quadratic Function
• Empirical Relationship Between Mean, Median, and Mode

Not only in mathematics but almost in every field the graph is a very important way to store, analyze, and represents information. After any research work or after any survey the next step is to organize the observation or information and plotting them on a graph paper or plane. The visual representation of information makes the understanding of crucial components or trends easier.

A huge amount of data can be store or analyze in a small space.

The graphical representation of data helps to decide by following the trend.

A complete Idea: Graphical representation constitutes a clear and comprehensive idea in the minds of the audience. Reading a large number (say hundreds) of pages may not help to make a decision. Anyone can get a clear idea just by looking into the graph or design.

Graphs are a very conceptual topic, so it is essential to get a complete understanding of the concept. Graphs are great visual aids and help explain numerous things better, they are important in everyday life. Get better at graphs with us, sign up for a free trial . 

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Frequently Asked Questions (FAQs)

What is data.

Data are characteristics or information, usually numerical, that are collected through observation.

How do you differentiate between data and information?

Data is the raw fact without any add on but the information is the meaning derived from data.

What are the types of data?

There are two types of Data:

What are the ways to represent data?

Tables, charts and graphs are all ways of representing data , and they can be used for two broad purposes. The first is to support the collection, organisation and analysis of data as part of the process of a scientific study.

- Tables, charts and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organisation and analysis of data as part of the process of a scientific study.

What are the different types of graphs?

Different types of graphs include:

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Scales of Measurement and Presentation of Statistical Data

Prabhaker mishra.

Department of Biostatistics and Health Informatics, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India

Uttam Singh

Anshul gupta.

1 Department of Haematology, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India

Measurement scale is an important part of data collection, analysis, and presentation. In the data collection and data analysis, statistical tools differ from one data type to another. There are four types of variables, namely nominal, ordinal, discrete, and continuous, and their nature and application are different. Graphs are a common method to visually present and illustrate relationships in the data. There are several statistical diagrams available to present data sets. However, their use depends on our objectives and data types. We should use the appropriate diagram for the data set, which is very useful for easily and quickly communicating summaries and findings to the audience. In the present study, statistical data type and its presentation, which are used in the field of biomedical research, have been discussed.

Introduction

Statistics is a branch of mathematics dealing with the collection, analysis, presentation, interpretation, and conclusion of data, while biostatistics is a branch of statistics, where statistical techniques are used on biomedical data to reach a final conclusion.[ 1 ] Measurement scale (data type) is an important part of data collection, analysis, and presentation. In the data collection, the type of questionnaire and the data recording tool differ according to the data types. Similarly, in the data analysis, statistical tests/methods differ from one data type to another.

Data presentation is an important step to communicate our information and findings to the audience and readers in an effective way. If done properly, they not only reduce word count but also convey an important message in a meaningful way so that the readers can grasp it easily.[ 2 ] There are various tabulation and graphical methods used to present the data, which are not possible without proper knowledge of data types.

The objective of this paper is to discuss the statistical data type (Section A) and its presentation (Section B), which is an important part of biomedical research.

Scales of measurement

As data are the heart of the statistics, and at the time of data analysis and presentation, many people are confused about what type of statistical tools to be used on a set of data and the relevant forms of presentation or data display. Its decision is taken by looking the types of data and the objectives of the research.

Data are a collection of facts such as values or measurements. It can be numbers, words, measurements, observations, or even just descriptions of things. Basically, data are two types: constant and variable. Constant is a situation/value that does not change, while a characteristic, number, or quantity that increases or decreases over time or takes different values in different situations is called variable. Due to unchangeable property, constant is not used and only variable is used for summary measures and analysis.[ 1 , 3 , 4 ]

Types of variables

There are four types of variables: nominal, ordinal, discrete, and continuous. The first two are called qualitative data and the last two are quantitative data. The first two (nominal and ordinal) are assessed in terms of words or attributes called qualitative data, whereas discrete and continuous variables are part of the quantitative data.[ 5 ]

Qualitative variable

Qualitative variable (also called categorical variable) shows the quality or properties of the data. It is represented by a name, a symbol, or a number code. These scales are mutually exclusive (no overlap) and none of them have any numerical significance. It is two types: nominal and ordinal.

Nominal variable : Nominal data are simply names or properties having two or more categories, and there is no intrinsic ordering to the categories, i.e., data have no natural ranking or ordering. For example, gender (male and female) and marital status (married/unmarried) have two categories, but these categories have no natural order or ranking.

Ordinal variable : An ordinal variable is similar to a nominal variable. The difference between the two is that there is a clear ordering in the data, i.e., ordinal data, unlike nominal data, have some order. For example, ordinal scales are seen in questions that call for ratings of quality (very good, good, fair, poor, very poor), agreement (strongly agree, agree, disagree, strongly disagree), economic status (low, medium, and high), etc. All the ranking data including Likert scales, Bristol stool scale, and all the other scales which are ranked between 0 and 10 are also called ordinal data.

Quantitative variable

Quantitative variable is the data that show some quantity through numerical value. Quantitative data are the numeric variables (e.g., how many, how much, or how often). Age, blood pressure, body temperature, hemoglobin level, and serum creatinine level are some examples of quantitative data. It is also called metric data. It is two types: discrete and continuous.

Discrete variable : Discrete variable is the quantitative data, but its values cannot be expressed or presented in the form of a decimal; for example, number of males, number of females, number of patients, and family size cannot expressed in decimal in meaningful way.

Continuous data : Data are measured in values and can be quantified and presented in decimals. Age, height, weight, body mass index, serum creatinine, heart rate, systolic blood pressure, and diastolic blood pressure are some examples.

The variables such as heart rate, platelet count, respiration rate, systolic blood pressure, and diastolic blood pressure are in fact discrete (measuring in complete number) but are considered continuous because of large number of possible values. Only those variables which can take a small number of values, say, <10, are generally considered discrete.[ 6 , 7 ] Summary is that if discrete variables values are at least 10 or more, then discrete variables can be considered as continuous variable and we analyze them as per the methods applicable on continuous data.

Data presentation

Data presentation plays a crucial role in research. The researchers can convince their research to the reader by the effective data presentation. Basically, there are two types of data presentation: numerical and graphical.

Numerical presentation

There are various types of numerical presentation of the data including arranging them into ascending order, descending order, and classification of the data in the tabular form.

Graphical presentation

Graphs are a common method to visually illustrate relationships in the data. A chart, also called a graph, is a graphical representation of the data, in which the data are represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart. Graphs enable us in studying the cause-and-effect relationship between two variables. Graphs help measure the extent of change in one variable when another variable changes by a certain amount.[ 8 , 9 ]

There are various types of graphical presentation given below.[ 10 , 11 ]

A bar graph is the presentation of data using rectangular bars, with heights or lengths proportional to the values that they represent. The reader can easily compare the quantity by observing the length of the bar. In bar graph, the bars may be plotted either horizontally or vertically. In the x-axis, use categorical variable, while in y-axis, use numerical values. Bar graph is three types: simple, adjacent, and cumulative. The last two are also called multiple bar graph. In simple bar graph, maximum two variables (one categorical and one quantitative) are used, while in multiple bar diagram, maximum three variables (two categorical and one quantitative) are used. Multiple bar graphs are useful when a researcher wants to compare figures of two or more different data [Figure ​ [Figure1a 1a and ​ andb b ].

(a) Simple bar graph showing mean age between sex, (b and c) multiple bar graph and line graph showing mean age and BMI between sex, (d) sex distribution of the data, (e) histogram showing nature of the BMI distribution, (f) error bar graph showing mean BMI as per sex, (g) box plot showing age distribution as per sex, (h) scatter diagram showing linear relationship between age and BMI, (i) Bland–Altman plot showing relationship between SBP difference and their average values, (j) Forest plot showing relative risk and associated confidence intervals observed from five different studies for the exposure group as compared to nonexposure group. BMI: Body mass index, SBP: Systolic blood pressure

It is alternative graph of the bar graph. A line graph is a kind of graph which represents data in a way that a series of points are to be connected by segments of straight lines. Difference between bar and line graph is that bar represented by rectangle while line graph showing by line, although both used for the same purpose [ Figure 1c ].

A pie chart is defined as a graph which contains a circle and is divided into sectors. The arc lengths of the sectors are proportional to the numerical value they represent. It is used only for the categorical data [ Figure 1d ].

Histogram and frequency polygon

A histogram represents the frequency distribution of a continuous variable whose areas are proportional to the corresponding frequencies. A histogram is quite similar to the bar graph and both are made up of rectangular bars. The difference is that there is no gap between any two bars in the histogram. The histogram is used to check the normal distribution of continuous data and have only one continuous variable, and no categorical variables are used to plot it, while in bar graph, we have required at least two variables including one quantitative and one categorical variables. Frequency polygons serve the same purpose as histograms but are particularly helpful for comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions. When the midpoints of tops of the rectangular bars in histogram are joined together, the frequency polygon is made [ Figure 1e ].

Error bars are graphical representations of the variability of data and used on graph to indicate the error or uncertainty (standard deviation/standard error/confidence interval) in a reported measurement (mean). They give a general idea of how precise a measurement is or conversely, how far from the reported value [ Figure 1f ].

Box plots characterize a sample using the minimum, 25 th , 50 th , and 75 th percentiles, maximum values. The interquartile range (IQR = Q3 − Q1, where Q1 is first quartile or 25 th percentile while Q3 is third quartile or 75 th percentile) which covers the central 50% of the data. Quartiles are insensitive to outliers and preserve information about the center and spread (variation). If a data point is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, it is viewed as being too far from the central values (median), which are called outliers [ Figure 1g ].

Scatter plot

A scatter plot (also called scatter diagram) is a graph in which the values of two quantitative variables are plotted along two axes, the pattern of the resulting points revealing any correlation present between variables for a set of data. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation. If the data points make a straight line going from the origin out to high x- and y-values, then the variables are said to have a positive correlation. If the line goes from a high value on the y-axis down to a high value on the x-axis, the variables have a negative correlation. In case no trend was shown, it is called no correlation [ Figure 1h ].

Bland–Altman plot

A Bland–Altman plot (difference plot) is a method of data plotting used in analyzing the agreement between two different assays. In the Bland–Altman plot, the differences (between the two methods) are plotted against the averages of the two methods. Alternatively, we can choose to plot the differences (between the two methods) against one of the two methods, if this is a reference method of both methods [ Figure 1i ].

Forest plot

A forest plot, also known as a blobbogram, is a graphical display of estimated results from a number of scientific studies addressing the same question, along with the overall results. It is a graphical representation of a meta-analysis. It is usually accompanied by a table listing references (author and date) of the studies with their estimated result included in the meta-analysis[ 12 ] [ Figure 1j ].

Other graphical methods

Besides above, there are some other graphical methods, used in the research studies, although they are less popular including stem and leaf plot, area chart, polar plot, youden plot, and high-low graph.

Relationship between Scales of Measurement, Statistical Methods, and Graphical Presentation of Statistical Data

Statistical methods are varying according to the scales of measurements. For example, when the data are a continuous variable, then we can use the parametric methods (including t -test, ANOVA test, linear regression, and Pearson correlation). When the data are a discrete variable/qualitative variable, we cannot use parametric testing and only nonparametric methods (including Mann–Whitney U-test, Kruskal–Wallis H-test, Wilcoxon test, Friedman test, Chi-square test, logistic regression, and Spearman correlation) are used. Similarly, graphical methods are varying according to the scales of measurements. For example, histogram, error bar graph, scatter plot, boxplot, and Bland–Altman graph can be drawn for continuous variables, but not for qualitative variables. In contrast, the pie chart is a graph that is only for qualitative data. There are many diagrams those are used for either categorical variable(s) or mix of the categorical and quantitative variables including bar graph and line graph. In brief, it is not possible to use appropriate statistical method and graphical presentation without proper knowledge of the concepts and properties of data types.

Conclusions

Data type is an important concept of statistics, which should be understand to implement statistical tools correctly. Proper knowledge of data types is necessary to analyze data sets with appropriate statistical methods. This not only enhances our ability to decide its summary measures but helps us to analyze data sets with proper statistical methods. There are several statistical diagrams available to display summaries and finding of data sets. There are several statistical diagrams available to display summaries and finding of data sets, although their use depends on our objectives and data types. We should use appropriate diagrams for our data sets, which is very much useful to communicate the summary and findings to the viewers with easily and quickly.

Financial support and sponsorship

Conflicts of interest.

There are no conflicts of interest.

Acknowledgment

We would like to express their deep and sincere gratitude to Dr. Prabhat Tiwari, Professor, Department of Anaesthesiology, Sanjay Gandhi Postgraduate Institute of Medical Sciences, Lucknow, for his encouragement to write this article. His critical reviews and suggestions were very useful for improvement in the article

Six Sigma Study Guide

Study notes and guides for Six Sigma certification tests

Graphical Analysis

Posted by Ted Hessing

What is Graphical Analysis?

Graphical analysis is one of the best ways to analyze problems in Six Sigma projects. It is an effective way to visualize data patterns and provides key insights into the data.

Generally, in any manufacturing or business process, Six Sigma teams deal with a vast amount of data, and it is impossible to convey the information effectively with the raw data. Thus, it is recommended to segregate and plot the data to analyze the problems. 

The graphical analysis creates pictures of the data, which will help to understand the patterns and the correlation between process parameters. Often graphical analysis is the starting point for any problem-solving method.

Graphical tools are readily available in Excel and statistical software such as Minitab, and they are very easy to use and can quickly plot graphs.

Walkthrough of Graphical Analysis Tools

Different graphical tools depict different data features such as trend, frequency, dispersion, and distribution shape. Below are a few graphical analysis tools.

Box-and-Whisker Plot

Box-and-Whisker plot , also known as a Box and Whisker plot, is a pictorial representation of continuous data. Box plots show the Max, Min, median, interquartile range Q1, Q3, and outlier data.

Run charts , also known as Time Series Plots, are line graphs of data plotted over time. They help to identify the pattern of the data in the time series. Because they don’t use control limits, we cannot judge whether the process is stable or not. However, run chat shows how the process is behaving. The advantage of the run chart is that it identifies the special cause(s) in a process.

Scatter Diagram

Scatter diagrams , also known as Correlation Charts or XY Graphs, plot the relationship between two continuous variables. These can include the independent variable on the x-axis and the dependent variable on the y-axis.

A Histogram is the graphical representation of a frequency distribution. It is in the form of a rectangle with class intervals as the base and the corresponding frequencies as the height. Particularly, there are no gaps between any two successive rectangles.

Normal Probability Plot

The Normal Probability Plot is a graphical method to assess whether the data set follows a normal distribution or not. This includes identifying outliers, skewness, etc. Furthermore, the Normal Probability Plot is one example of a Quantile-Quantile (Q-Q) plot.

Pareto Chart

A Pareto Chart is also known as the 80-20 rule. It is a combination of a bar chart and a line chart. The actual data is in descending order and uses a bar chart and cumulative data in ascending order on a line graph.

A Bar Chart displays the frequency on one axis and the values of the categorical variable on the other axis. In a bar graph, bars of uniform widths are drawn with various heights. However, the height of the bars represents the frequency of the corresponding observation.

Why Use Graphical Analysis Tools

Six Sigma teams apply a wide range of graphical tools in each phase of DMAIC.

The main purpose of the Define Phase is to define the problem, identify customer requirements, and also summarize the project plan.

The project team uses various six sigma tools in the Define Phase like SIPOC (Supplier-Input-Process-Output-Customer), Process maps, value stream mapping, Project charter, SWOT analysis, and Voice of Customer .

The Six Sigma team uses graphical analysis tools. For example, they use a Bar Chart to understand a process trend, revenue loss, etc. Then, they use a Run chart to monitor customer complaints or defects over a period of time. Similarly, A Box Plot graphically represents the voice of the customer (pictorially depicts customer satisfaction with various attributes).

Measure the process performance. In fact, the main purpose of the measure phase is to collect the data that covers the project scope and also to determine what  data distribution  you are working with.

The project team uses various Six Sigma tools like a process flow chart, Gage R&R, Pareto Chart, and a process capability analysis in the measure phase.

Graphical tools like the Pareto Chart are used to analyze the frequency of problems and identify the majority (80%) of issues. Similarly, the Process Capability Analysis is used to assess the ability of the process to perform according to the specification.

The main purpose of Analyze phase is to understand the root cause of the problem. Furthermore, to identify the opportunity for improvement.

The project team uses various Six Sigma tools like Root cause analysis , Failure Mode Effects Analysis (FMEA) , Cause and effects diagram , 5 Why analysis , and hypothesis testing .

Above all Six Sigma team uses most of the graphical tools in Analyze phase. Few examples like a Histogram , Scatter Diagram , Multi-Vari Chart, Time Series Chart, Normal Probability Plot , etc.

The main purpose of Improve phase is to eliminate the root causes and implement the improvements. Additionally, design the action plan to monitor the improvements.

The project team uses various Six Sigma tools like Design of Experiments (DOE) , Poka-Yoke , Solution Selection Matrix, Kaizen Events, and Segments of a population for a  pilot test.

Graphical tools like Bar Charts and Run charts are used to monitor process performance (reduction of defects, rework, etc.).

The main purpose of the control phase is to validate that post-improvement samples follow the designed and expected results.

The project team uses various Six Sigma tools including Control Plan , 5S , and particularly statistical control charts for monitoring process behavior.

In fact, graphical tools like statistical control charts (I-MR chart, u-chart, p-chart, and c-chart) help to monitor progress and to make necessary adjustments.

How to Pick Which Tool to Use?

The selection of graphical tools depends on the type of data and the project’s objective. The picture below helps identify the right graphical tools based on the scenario. However, statistical analysis is required before drawing any conclusions.

How to Understand what the tools are telling you?

Often, the biggest challenge for Six Sigma teams is to understand the graph and make conclusions. In fact, it is difficult to understand the message from the graph right away. The Six Sigma team has to take time to interpret the graphs.

Each graph provides different messages like trend, frequency, dispersion, and distribution shape.

• Box-and-Whisker plot is to understand the difference between the groups, outliers in the process, and maximum and minimum values. Is there any difference between the subgroup’s median?
• A Histogram is used to understand the shape of the distribution. Is it symmetrical or skewed?
• Scatter diagram s are to understand the relationship between two continuous variables. Is there any correlation between factors?
• Time series plots are to understand the trend over time. Is the process stable over time?
• Pareto Charts are to understand the frequency of the problem as well as their cumulative impact.

Graphical Analysis Videos

How to graph data using MiniTab

Helpful graphical analysis links.

• https://www.sixsigmadaily.com/tools-six-sigma-analysis-phase/
• https://study.com/academy/lesson/six-sigma-statistical-tools-analysis.html

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Statistics and Research Methods in Psychology with Excel pp 135–160 Cite as

Graphical Presentation of Data

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Graphs are used to showcase relationships between different variables in a pictorial form. Different types of graphs including bar diagram, histogram, line diagram, cumulative frequency curve, pie diagram and ogive have been discussed with illustrations in the chapters. The procedure of identifying linear and curvilinear relationships on the basis of equation has been discussed. The objective-type and multiple-choice questions provide readers enough practice to understand the basic concepts of developing a graph.

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In today’s world of the internet and connectivity, there is a lot of data available and some or the other method is needed for looking at large data, the patterns, and trends in it. There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting the numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics . The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, astrostatistics, and so on. There are two ways of representing data, 

• Pictorial Representation through graphs.

They say, “A picture is worth the thousand words”.  It’s always better to represent data in graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in form of visuals as Human beings process data better in visual form than any other form. Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time. Let’s look at some of them in detail. 

Types of Graphical Representations

Comparison between different items is best shown with graphs, it becomes easier to compare the crux out of the data pertaining to different items. Let’s look at all the different types of graphical representations briefly: 

Line Graphs

A line graph is used to show how the value of particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data predicting further trends. 

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars. 

Histograms 

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range. 

Line Plot 

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point. 

Stem and Leaf Plot 

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4).  

Box and Whisker Plot 

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data. 

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole. 

Graphical Representations used in Maths

Graphs in maths are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths: 

• Value-Based or Time Series Graphs

Frequency Based

Value-based or time series graphs .

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values. 

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study. 

Example: Frequency Polygon, Histograms.

Principles of Graphical Representations

All types of graphical representations require some rule/principles which are to be followed. These are some algebraic principles. When we plot a graph, there is an origin, and we have our two axes. These two axes divide the plane into four parts called quadrants. The horizontal one is usually called the x-axis and the other one is called the y-axis. The origin is the point where these two axes intersect. The thing we need to keep in mind about the values of the variable on the x-axis is that positive values need to be on the right side of the origin and negative values should be on the left side of the origin. Similarly, for the variable on the y-axis, we need to make sure that the positive values of this variable should be above the x-axis and negative values of this variable must be below the y-axis. 

Advantages and Disadvantages of using Graphical System

Advantages: 

• It gives us a summary of the data which is easier to look at and analyze.
• It saves time.
• We can compare and study more than one variable at a time.

Disadvantage: 

It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data. 

General Rules for Graphical Representation of Data

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs: 

• Whenever possible, the data source must be mentioned for the viewer.
• Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
• The measurement Unit should be mentioned in the top right corner of the graph.
• The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
• Last but not the least, a suitable title should be chosen.

Frequency Polygon

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval. 

Sample Problems

Question 1: What are different types of frequency-based plots? 

Answer: 

Types of frequency based plots:  Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels. 

Draw a bar graph for the following data. 

Solution: 

Steps:  Put each of the channels on the x-axis The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following data 

Steps:  Put each of the x-axis row value on the x-axis joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data: 

Steps:  Draw the class intervals on the x-axis and frequencies on the y-axis. Calculate the mid point of each class interval. Class Interval Mid Point Frequency 0-3 1.5 3 3-6 4.5 4 6-9 7.5 2 9-12 10.5 6 Now join the mid points of the intervals and their corresponding frequencies on the graph.  This graph shows both the histogram and frequency polygon for the given distribution.

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Which graph is used to represent data in continuous elements? A. Bar B. pie C. histogram D. Frequency curve

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