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AP®︎/College Statistics
Course: ap®︎/college statistics > unit 4.
- Z-score introduction
Calculating z-scores
- Comparing with z-scores
- Z-scores-problem
- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi
Helping math teachers bring statistics to life
Modeling Distributions of Data
Chapter 2 Lesson Plans
Chapter 10 Chapter 11
Ap exam review.
Day 1: Lesson 2.1 - Percentiles Day 2: Lesson 2.1 - z-scores & Transforming Data Day 3: Quiz 2.1 Day 4: Lesson 2.2 - Density Curves, 68-95-99.7 Rule Day 5: Lesson 2.2 - Normal Distribution Calculations Day 6: Lesson 2.2 - Assessing Normality Day 7: Quiz 2.2 Day 8: Chapter 2 Review Day 9: Chapter 2 Test
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Factors and multiples, 19.8k plays, 4th - 5th , 285.8k plays, kg - 1st .
AP Stats 2.1 Practice
9th - 10th grade, mathematics.
9 questions
Introducing new Paper mode
No student devices needed. Know more
Find the Z-score.
Standard Deviation: 3.1
- 2. Multiple Choice Edit 5 minutes 1 pt If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall? -5 -2 2 5
- 3. Multiple Choice Edit 5 minutes 1 pt A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test? 82 88 100 118
The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.
If I tell you that you scored at the 55th percentile on your final exam, you would know:
55% of the class scored the same or worse than you did
You earned a 55% on the exam
You failed the exam
45% of the class scored worse than you did
- 6. Multiple Choice Edit 30 seconds 1 pt The 75th percentile is also know as the median third quartile 1st quartile` interquartile range
What is the percentile rank of 74 in the following group of 15 data values? 35, 65, 68, 100, 23, 69, 74, 70, 61, 90, 85, 55, 30, 65, 80
Joanne's score on a test gives her a Z-score is -1.50. What does this mean?
Joanne didn't take the test yet.
Joanne's test score is 1.50 standard deviations below the average test score.
Joanne did better than 1.50 times her peers.
Joanne's test score, on average, was 1.5 points lower than the other test scores.
More practice: At a recent invitational, Emmett threw the shotput 43.5 feet with an invite mean of 41 and a SD of 3.
Reese ran the 800 in 2 minutes, 1 second with the mean being 2 minutes 46 seconds and SD of 15 seconds.
What were their Z-scores and who performed better?
Emmett's Z-score was +0.83, Reese's was -3.00. Emmett did better because his Z-score is higher.
Emmett's Z-score was +0.83, Reese's was -3.00 but Reese did better because in track, lower times are better to have
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*All solutions and teacher notes in blue*
AP Statistics Handout Key: Lesson 2.1 Topics: percentiles, cumulative relative frequency , standardized scores (z-scores)
Lesson 2.1 Guided Notes
Percentiles
Percentile: the percent of data less than or equal to a certain data value.
At what percentile is the person who makes a salary of $43,000? Show your work. 29, 32, 34, 34, 34, 34, 35, 35, 39, 43, 67, 185 10/12 ≈ 83% → The salary of $43,000 is at the 83rd percentile of salaries.
For a large dataset…
1) What percentile is Q1? 2) What percentile is the median ? 3) What percentile is Q3? Q1 is at the 25th percentile Q2 is at the 50th percentile Q3 is at the 75th percentile
Whose score is more impressive? Why?
Guy Fieri’s score is relatively more impressive because he tied or outscored 69% of those who took the ACT, while Mr. Young-Saver only tied or outscored 45% of those who took the SAT.
Note: Percentiles based on 2019-2020 exam year
Material adapted from the Skew The Script curriculum (skewthescript.org)
Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License (https://creativecommons.org/licenses/by-nc-sa/4.0) 2
Cumulative Relative Frequency 1) Is 18 a good ACT score? A score of 18 is at or above 40% of ACT test takers. So, it’s an ok score.
2) You are applying for an elite college and want to score in the top quartile of test takers. What score do you need? You would need a score of 24 (Q3) or higher to be in the top 25%
Standardized Scores (Z-Scores)
Z-Scores (also called standardized scores): measures how many standard deviations a data point is above/below the mean .
푑푎푡푎 푝표푖푛푡 − 푚푒푎푛 푥푖 − μ 푧 = | z = 푠푡푎푛푑푎푟푑 푑푒푣푖푎푡푖표푛 휎
Variation Matters:
In which league (A or B) is this player relatively
“better?” Why?
This player is relatively better in League A because there is less variation in League A – therefore, there
are fewer players who score more than him. Because he is more standard deviations above the mean in League A, he is more “unusually good” in that league.
Standardization: A point’s location in the distribution depends on both distance from the center and the distribution’s spread or variation.
Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License (https://creativecommons.org/licenses/by-nc-sa/4.0) 3
Data Source: Stats based on NBA data from Kaggle Standardized: Who Was the Best? database: kaggle.com/drgilermo/nba-players-stats Show all z-score calculations below:
Q: Who was the G.O.A.T?
Explain your answer based on the z-scores you calculate:
30.1 ppg 30.1 ppg 27.1 ppg Michael Jordan’s PPG was 3.6 Mean (휇) ppg standard deviations above the in their era: 10.8 ppg 8.7 ppg 8.4 ppg mean for his era, making him
the most unusually high scorer Stdv (휎) ppg among these three legends. in their era: 7.0 ppg 5.9 ppg 5.5 ppg
30.1−10.8 30.1−8.7 27.1−8.4 Z-Score: = 2.8 = 3.6 = 3.4 7.0 5.9 5.5 (show work )
Standardized: Players who were not the best…
Calculate Adam Morrison’s z-score for PPG…
While with the Lakers, he averaged 2.2 PPG. (League: µ = 8.4 ppg, σ = 5.5 ppg)
basketball.com - ퟐ. ퟐ − 8.4 z = = −ퟏ. ퟏ 5.5
Photo: opencourt Photo: Adam Morrison’s scoring rate was 1.1 standard deviations Adam Morrison below the league average in his era.
Positive and Negative Z-Scores Positive Z-Score: The number of standard
data value > mean → positive deviations above the mean.
data value < mean → negative Negative Z-Score: The number of standard deviations below the mean. 푑푎푡푎 푝표푖푛푡 − 푚푒푎푛 푧 = 푠푡푎푛푑푎푟푑 푑푒푣푖푎푡푖표푛
Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License (https://creativecommons.org/licenses/by-nc-sa/4.0) 4 Recommended discussion norms: skewthescript.org/discussion-norms Lesson 2.1 Discussion
Note: All data is from 2020 season and earlier
Shots per game: 22.5 22.9 19.6
% shots made: 54.0% 49.7% 50.4%
Discussion: Given these additional statistics, do you believe Jordan is still the G.O.A.T at scoring? Why or why not? What other stats may be helpful in determining who was the best?
Example arguments, against Michael Jordan:
• Scoring isn’t just about points – it’s about efficiency . Whenever you take a shot, you’re taking away the opportunity for your teammate to take that shot. So, you better make your shots often. Even though Jordan got many points, he also shot and missed a lot (he had the lowest “make” percentage of the three players). The other players were more efficient.
Example arguments, in favor of Michael Jordan:
• The 3-point line wasn’t added to the NBA until after Wilt retired. So, many players of his era (including Wilt) shot close to the rim. Because of this, they had high shooting percentages. Comparing shooting percentages across the 2 vs. 3 point eras may be flawed. • LeBron plays alongside other superstars, so the defense is not solely focused on him. Jordan played with good teammates, but not many superstars. So, the defense focused mainly on him. Despite this, Jordan’s shooting percent is less than 1% shy of LeBron’s. That’s impressive.
Teacher note: Ultimately, this sort of statistical question of “who was best” is somewhat subjective. Do you choose to look at total points? At efficiency? At strength of defense? At “clutch” moments? Expert sports statisticians debate these metrics. Ultimately, there is no single “correct” answer.
Lesson 2.1 Practice
Teachers: We recommend providing additional practice exercises from your AP Stats textbook or from prior AP Stats exams. The following textbook sections and AP exam questions are aligned to the content covered in this lesson.
• The Practice of Statistics (AP Edition), 4th-6th editions: section 2.1 • Stats: Modeling the World (AP Edition), 4th & 5th editions: ch 3 & 5, 3rd edition: ch 4 & 6 • Statistics: Learning from Data (AP Edition), 2nd edition: section 3.5 • AP Exam Free Response Questions (FRQs): 2011 Q1 (parts b & c), 2019 Q6 (parts d & e)
Handout key by statistics student Greyson Zuniga
Lessons made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License (https://creativecommons.org/licenses/by-nc-sa/4.0)
IMAGES
VIDEO
COMMENTS
AP Statistics. 2.1 Homework Worksheet. Percentiles and Z-score. Please show all work on a separate piece of paper. 1. Shoes. How many pairs of shoes do students have? ... Jorge's score on Exam 1 in his statistics class was at the 64th percentile of the scores for all students. His score falls. a) between the minimum and the first quartile. b ...
All Part 2 Lessons. AP Statistics lesson 2.1, from the Skew The Script curriculum. Covers percentiles and z-scores through the comparison of SAT/ACT scores and NBA scoring legends.
AP Statistics Handout Key: Lesson 2.1 Topics: percentiles, cumulative relative frequency, standardized scores (z-scores) Lesson 2.1 Guided Notes Percentiles Percentile: the percent of data less than or equal to a certain data value. Below are the yearly salaries of employees at a company (in thousands of $). At what percentile is the
Handout and lesson materials: https://skewthescript.org/2-1Relevant topics: Who was the NBA's best scorer?Statistics topics: percentiles, cumulative frequenc...
Measuring Position: z-Scores z-score = standardized value of x Formula: Example: Mr. Pryor's second period consists of 25 students. The mean grade on the first exam was 80, the median was also 80, and the standard deviation was 6.07. Find the standardized scores (z-scores) for each of the following students. Interpret each value in context.
AP Statistics Chapter 2 Multiple Choice Questions. 7 terms. Jordyn_Vu. Preview. AP STATS TEST. 5 terms. joserod2021. Preview. AP stats 2.1 and 2.2 quiz. 13 terms. lflewell. ... percentiles z scores. cumulative relative frequency graph displays. the cumulative relative frequency of each class of a frequency distribution.
This unit takes our understanding of distributions to the next level. We'll measure the position of data within a distribution using percentiles and z-scores, we'll learn what happens when we transform data, we'll study how to model distributions with density curves, and we'll look at one of the most important families of distributions called Normal distributions.
Study with Quizlet and memorize flashcards containing terms like Measuring percentile, z score formula, Median and more. Scheduled maintenance: September 20, 2023 from 02:00 AM to 03:00 AM hello quizlet
AP Statistics Chapter 2. 2.1 Describing Location in a Distribution. Measures of Relative Standing and Density Curves. Z score, percentiles, read all the examples from the textbook section 1. 2.2 Normal Distributions. symmetric, single peaked, bell-shaped curves that play a large role in statistics. has a mean μ (mu) and a standard deviation σ ...
Standard Normal distribution. The standard normal distribution is the normal distribution with mean of 0 and standard deviation of 1. The standard normal table. Table A is a table of a real under the standard Normal curve. The table entry for each value z is the area under the curve to the left of z. Four step problems for Normal distributions.
Calculating z-scores. The grades on a geometry midterm at Springer are roughly symmetric with μ = 73 and σ = 3.0 . Umaima scored 72 on the exam. Find the z-score for Umaima's exam grade. Round to two decimal places. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.
This video is part of a series intended to help my AP Statistics students learn the basics of exploratory quantitative analysis. These videos align with the ...
View 2.1 AP z socre (1).pdf from STATISTICS STAT 3309 at Strayer University. AP Statistics 2.1 Homework Worksheet Percentiles and Z-score Please show all work on a separate piece of paper 1. Shoes.
Enhanced Document Preview: Name:_____ AP Stats/ _____ Date: _____ Date Due:_____ AP Statistics 2.1 Homework Worksheet Percentiles and Z-score Please show all work on a separate piece of paper. 1. Shoes. How many pairs of shoes do students have? Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school: Female 50 26 26 31 57 ...
Students should work in groups (or pairs) on page 1. By the end of the page, they will write a formula for a z-score. For now, we prefer to use words rather than symbols: z-score = (value - mean) / SD. We don't want students to have to wrestle with mu vs xbar and sigma vs s. We will save that discussion for Chapter 7.
Divides the area under the curve in half. Adding a constant (a) to all values in a data set. Measures of center change. Measures of spread do not change. Multiplying all the values in a data set by (b) Measures of center change. Measures of spread change. Study with Quizlet and memorize flashcards containing terms like pth percentile ...
Day 1: Lesson 2.1 - Percentiles Day 2: Lesson 2.1 - z-scores & Transforming Data Day 3: Quiz 2.1 Day 4: Lesson 2.2 - Density Curves, 68-95-99.7 Rule Day 5: Lesson 2.2 - Normal Distribution Calculations Day 6: Lesson 2.2 - Assessing Normality Day 7: Quiz 2.2 Day 8: Chapter 2 Review Day 9: Chapter 2 Test
2.3 - The Empirical Rule. Statistical Concepts Covered. Normal Curves. Empirical Rule (68-95-99.7) Data Validity. Relevant Topics Covered. Race & "Intelligence".
Joanne's test score, on average, was 1.5 points lower than the other test scores. 9. Multiple Choice. Edit. 15 minutes. 1 pt. More practice: At a recent invitational, Emmett threw the shotput 43.5 feet with an invite mean of 41 and a SD of 3. Reese ran the 800 in 2 minutes, 1 second with the mean being 2 minutes 46 seconds and SD of 15 seconds.
1. always plot data. 2. look for pattern (SOCS) 3. 5# summary for center and spread. 4. overall pattern of large #'s will be a smooth curve. Density curve. describes the overall pattern of distribution. -always ON or ABOVE the x-axis. -area exactly underneath 1. -an approximation.
What Is a Percentile Rank Score? The Multivariate Percentile Power Method Transformation; Unit 9 - ONE Sample Inference SOLUTIONS Suppose We Assume; Chapter 2 Full Solutions; Five Things You Should Know About Quantile Regression; Z-Scores & Percentiles; Explaining Normal Quantile-Quantile Plots Through Animation: the Water-Filling Analogy
z = (x - mean) / (standard deviation) Effect of Adding (or Subtracting) a Constant. Adding the number a (either positive, zero, or negative) to each observation: 1) adds a to measures of center and location (mean, median, quartiles, percentiles), but. 2) does NOT change the shape of the distribution or measures of spread (range, IQR, standard ...
2022 AP Score Distributions. See how students performed on each AP Exam for the exams administered in 2022. PDF. 4.42 KB. 2023 AP score distribution tables show the percentages of 1s, 2s, 3s, 4s, and 5s for each AP subject for all AP students.