## Problem Solving and Data Analysis

Problem Solving and Data Analysis includes using ratios, percentages, and proportional reasoning to solve problems in real-world situations, including science, social science, and other contexts. It also includes describing relationships shown graphically and analyzing statistical data.

This group of skills is really about being quantitatively literate and demonstrating a command of the math that resonates throughout college courses, career training programs, and everyday life.

Problem Solving and Data Analysis includes the following types of questions:

Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems.

Solve single- and multistep problems involving percentages.

Solve single- and multistep problems involving measurement quantities, units, and unit conversion.

Use scatterplot, linear, quadratic, or exponential models to describe how the variables are related.

Use the relationship between 2 variables to investigate key features of the graph.

Compare linear growth with exponential growth.

Use 2-way tables to summarize categorical data and relative frequencies and calculate conditional probability.

Make inferences about population parameters based on sample data.

Use statistics to investigate measures of center of data. Analyze shape, center, and spread.

Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods. The reports may consist of tables, graphs, or text summaries.

For tutorials and practice questions of all these types, go to Official SAT Practice on Khan Academy at satpractice.org.

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## Unit 9: Lesson 6

## Problem Solving and Data Analysis: lessons by skill

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## What are your chances of acceptance?

## Guide to SAT Math Problem Solving and Data Analysis + Practice Questions

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## What’s Covered:

Overview of sat math problem solving and data analysis, how will the sat impact my college chances.

- Strategies for Problem Solving and Data Analysis Questions
- Practice Questions for Problem Solving and Data Analysis

## Final Tips and Strategies

Here is the breakdown of each category:

Problem Solving and Data Analysis questions ask students to:

- Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems.
- Solve single- and multi-step problems involving percentages.
- Solve single- and multi-step problems involving measurement quantities, units, and unit conversion.
- Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related.
- Use the relationship between two variables to investigate key features of the graph.
- Compare linear growth with exponential growth.
- Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability.
- Make inferences about population parameters based on sample data.
- Use statistics to investigate measures of center of data and analyze shape, center, and spread.
- Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods.

## Strategies to Solve Problem Solving and Data Analysis Problems

## 10 Difficult Problem Solving and Data Analysis Questions

## 1. Measures of Central Tendency (Mean/Median/Mode)

## 2. Percent Increase

## 3. Analyzing Graphical Data

## 4. Inference

## 5. Proportions

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## 6. Scale Factors

If you wanted to be precise, you could set up an equation:

\(8 in\:\cdot\:\frac{50 coins}{3\frac{7}{8} in}\)

## 7. Line of Best Fit/Scatterplots

## 8. Geometric Applications of Proportions

Correct Answer: 5/18, .277, .278

## 9. Unit Conversions

\(\$62,400\:\cdot\:\frac{1 ounce}{\$20}\:\cdot\:\frac{1 pound}{16 ounces}\)

## 10. Probability

Here are some other articles that will help you prepare for the SAT Math section:

- 15 Hardest SAT Math Questions
- 30 SAT Math Formulas You Need to Know
- Guide to SAT Math Heart of Algebra + Practice Questions
- 5 Common SAT Math Mistakes to Avoid
- 5 Tips to Boost Your Math SAT Score

## Related CollegeVine Blog Posts

## Problem Solving and Data Analysis: SAT Math Tips & Practice

## Kickstart Your SAT Prep with Test Geek’s Free SAT Study Guide.

Welcome to the dark side, people. Welcome to Problem Solving and Data Analysis.

## Problem Solving and Data Analysis: What’s Included?

- Ratios, rates and proportions
- Percentages
- Measurement quantities and units
- Scatterplots
- The relationship between variables and graphs in a data context
- Linear vs. exponential growth
- Data tables
- Sample, population, inferences and other statistical survey topics
- Mean, median, mode and other related concepts

## Data Analysis: Statistics and Data Collection

Let’s start by defining a couple of key terms:

- Sample : The group of people being surveyed. In a presidential election survey, the sample is the survey respondents.
- Population : The group of people being described. In a United States presidential election survey, the population is all American voters.

So, we ask questions of a sample in order to learn something about the population .

A good sample has three features:

- Randomly selected: Any population has outliers in it. There are probably a thousand people in America who particularly enjoy wearing matching outfits with their dog and only talking in bark. But those people are kind of weird, and if we only asked them who they were voting for, our sample probably wouldn’t be reflective of all of America.
- Large enough to represent the population: You don’t need to get too into the details here, but you can’t accurately describe a big group by asking six people. You can, however, describe a class of 400 students by asking 80 kids, and you can describe a country of 300 million by asking a thousand. Normally, sample size issues will be glaring (if they exist).
- Part of the population: If you want to learn something about how America is going to vote, don’t poll Canadians and definitely don’t poll the French.

There are a few caveats that should come with any survey results:

- Samples tell us what is likely, not what is necessary. I’m not going to get too into things like confidence intervals because those concepts are beyond the scope of the SAT. But surveys are ultimately just telling us what is very likely to be true, not what is guaranteed to be true. For example, every presidential election survey comes with a “margin of error” disclaimer. That is telling that the results are not a concrete number but are instead likely to fall within a certain range.
- Different samples might yield different results, even if they are both done correctly. This follows directly from the first point. If surveys are totally precise, we shouldn’t expect them to give us exactly the same results every time.
- Correlation doesn’t equal causation. For example, a recent study showed that a rooster crows every single morning. Also, get this, the sun rises every single morning, typically right after the roosters crow. Better correlation doesn’t exist. But is all of this crowing actually causing the sun to rise? Of course not. They are perfectly correlated, but that’s not the same thing as causation.

## Statistics and Data Collection Practice

Let’s take a look at a practice problem:

- A: Can we say that the entire studenty body must have the same preference as the sample? Of course not.
- B: Must a second sample yield exactly the same results as the first? Of course not.
- C: This is just an incorrect interpretation of the survey itself. The university didn’t ask students what they use, it asked what they prefer. Those are two different things, so this can’t be the right answer.
- D : This is all we have left, so that’s our answer.

## Problem Solving and Data Analysis Basics: Mean, Median and Mode

Mean, median and mode on the SAT math section tends to only require two things:

- Basic concept understanding (calculate the mean or median given a data set)
- An understanding of how mean, median and mode vary when things change

- Mean is the average of a set of numbers. Add them up to get the sum, and then divide the sum by the number of numbers you have.
- Median is the middle number when the numbers are sorted from least to greatest. In the set 1, 2, 5, the median is 2.
- Mode is the number that occurs most frequently. In the set 1, 2, 2, 5, 6, the mode is 2.

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Let’s take a look at that sort of question:

Running through the answer chocies:

- A: Can we calculate the mean if we don’t know exactly what the last number is? No, so this can’t be our answer.
- B: Can we calculate the median if we don’t know exactly what the last number is? Yes, we can. The median doesn’t depend on the outside numbers. In this case, our median is 12, so this is the right answer.
- C: We can’t calculate the mean, so this can’t be right.
- D: B is correct, so this is incorrect.

## Visual Representations of Data

These questions often present a scatterplot followed by several questions. Here’s an example:

## Models: The Scary Side of Problem Solving and Data Analysis

But watch what happens when we put it into a model:

## Problem Solving & Data Analysis: Final Thoughts

## SAT Math Complex Numbers & Imaginary Numbers

Must know equations for the sat [free formula study guide], you may also like.

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## 6 SAT Math Problem Solving and Data Analysis Concepts to Master

Problem Solving and Data Analysis is worth 29 percent of your SAT Math score.

Key concepts to master include ratios, percentages and lines of best fit. (Getty Images)

Below, we provide an overview of the test's six sections:

3. Unit conversion and unit rate

## Ace the SAT's Passport to Advanced Math

5. Relationships between variables

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## SAT Math : Data Analysis

## Example Question #2 : Venn Diagrams

## Example Question #3 : Venn Diagrams

## Example Question #4 : Venn Diagrams

## Example Question #5 : Venn Diagrams

First, it is given that S=450.

Setting them equal to each other we get A+C=B+C.

Subtract C from both sides to get A=B; so the same number of students take art only and gym only.

Since A=B we can use substitution to get 2A+C=800.

## Example Question #6 : Venn Diagrams

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

1 and 48; 2 and 24; 3 and 16; 4 and 12; 6 and 8

Therefore the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Now we can write P = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}.

Next, we need to find the factors of 90.

1 and 90; 2 and 45; 3 and 30; 5 and 18; 6 and 15; 9 and 10

Then the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Thus, Q = {1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90}.

1 and 56; 2 and 28; 4 and 14; 7 and 8

Set R = {1, 2, 4, 7, 8, 14, 28, 56}

Now, we need to find set T, which is P U (Q ∩ R).

Lastly, we must find P U (Q ∩ R).

{1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

Therefore, T = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}.

## Example Question #215 : Data Analysis

We can draw a Venn diagram to see these two sets of students.

## Example Question #8 : How To Interpret Venn Diagrams

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## Choose Your Test

Sat / act prep online guides and tips, problem solving and data analysis: key sat math concepts.

SAT Math is divided intro three domains:

## Basic Information

You will receive a subscore on a scale of 1-15 on this domain.

There will be both multiple choice and grid-in questions.

## General Concepts

You’ll be working with a lot of numbers.

## Real-World Applications

## Data and Statistics

## Specific Skills

In fact, let’s hope these skills aren’t all that new!

## Statistical Analysis

Another tidbit of interest you should know is that randomization combats bias .

## Mathematical Models

- You might take a loan at 9%, but if it compounds monthly, you’re really taking a loan at $(1+.09/12)^12 – 1 = 9.38%$ at the end of the year.
- On the other hand, you might make a deposit that accrues interest at a rate of 5%, but it compounds quarterly, so you’re really getting $(1+.05/4)^4 – 1 = 5.095%$ at the end of the year.

Math and money are very closely linked.

## Ratios, Proportions, Units, and Percentages

Take a look at this pair of problems:

Agriculture/natural resources — $373,904/488,106=.766$

Education — $2,164,607/3,008,036=.7196$

Highways and transportation — $1,468,482/1,773,893=.8278$

Public safety — $263,463/464,233=.5675$

Out of these, the closest to human resources ($4,051,050/5,921,379=.6841$), is (B).

For mutually exclusive events: P(A or B) = P(A) + P(B).

Let’s take a look at this problem:

Math and gambling are closely linked, too. It’s all about that probability.

This domain of the test is calculation-heavy, although there are some theoretical questions.

These questions compose almost a third of the test . They cover, roughly:

Your answers will be scored to yield one of three subscores for the Math section.

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## IMAGES

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The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

Data analysis seems abstract and complicated, but it delivers answers to real world problems, especially for businesses. By taking qualitative factors, data analysis can help businesses develop action plans, make marketing and sales decisio...

Questions about Problem Solving and Data Analysis on the SAT Math section? We explain the subscore and different types of questions to help you excel. SAT Math SAT Math is divided intro three domains: It's a good idea to get really familia...

The Problem Solving and Data Analysis questions on the SAT Math. Test assess your ability to use your understanding of math and your.

Problem Solving and Data Analysis includes using ratios, percentages, and proportional reasoning to solve problems in real-world situations

SAT Math questions fall into different categories called "domains." One of these domains is Problem Solving and Data Analysis.

The lessons here will walk you through each skill on the SAT within the "Problem Solving and Data Analysis" domain. Every lesson provides background

The Problem Solving and Data Analysis section tests students' ability to solve real-world problems using mathematical understanding and skills.

In this video, part 3 of 4, we cover the Problem Solving and Data Analysis. Watch carefully to understand all of the critical concepts in

College Board created the Problem Solving and Data Analysis questions to test your ability to use your math understanding to solve

DRILL Problem Solving and Data Analysis Test 1. Page of. 1 3. No Calculator = none. With Calculator = all. Also Used as Analysis in History/Social Studies.

The SAT Math Problem Solving and Data Analysis subsection is a significant area of focus on the college entrance exam.

Since A=B we can use substitution to get 2A+C=800. Finally you can solve the system of equations using the method of your choice (substitution or elimination)

Questions about Problem Solving and Data Analysis on the SAT Math section? We explain the subscore and different types of questions to help