AP® Statistics

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Unit 1: Exploring categorical data

About this unit.

This unit covers methods for dealing with data that falls into categories. Learn how to use bar graphs, Venn diagrams, and two-way tables to see patterns and relationships in categorical data.

The language of variation: Variables

  • Identifying individuals, variables and categorical variables in a data set (Opens a modal)
  • Individuals, variables, and categorical & quantitative data Get 3 of 4 questions to level up!

Representing a categorical variable with graphs

  • Creating a bar graph (Opens a modal)
  • Reading bar graphs: movies (Opens a modal)
  • Reading bar charts: comparing two sets of data (Opens a modal)
  • Read bar graphs Get 5 of 7 questions to level up!

Representing two categorical variables

  • Two-way frequency tables and Venn diagrams (Opens a modal)
  • Two-way relative frequency tables (Opens a modal)
  • Interpreting two-way tables (Opens a modal)
  • Mosaic plots and segmented bar charts (Opens a modal)
  • Analyzing mosaic plots (Opens a modal)
  • Read two-way frequency tables Get 3 of 4 questions to level up!
  • Create two-way frequency tables Get 3 of 4 questions to level up!
  • Analyze two-way frequency tables Get 3 of 4 questions to level up!
  • Interpret two-way tables Get 3 of 4 questions to level up!
  • Mosaic plots Get 3 of 4 questions to level up!

Statistics for two categorical variables

  • Marginal and conditional distributions (Opens a modal)
  • Conditional distributions and relationships (Opens a modal)
  • Identify marginal and conditional distributions Get 3 of 4 questions to level up!
  • Marginal distributions Get 3 of 4 questions to level up!
  • Conditional distributions Get 3 of 4 questions to level up!

ap statistics 1.1 homework answers

  • AP Statistics Syllabus
  • AP Statistics PowerPoints
  • AP Statistics Additional Notes

AP Statistics Answers

Unit 1 answers.

  • Homework Unit 1 – 1st part
  • Homework Unit 1 – 2nd part
  • Homework Unit 1 – 3rd part

Unit 2 Answers

  • Unit 2 Homework – Part 1
  • Unit 2 Homework – Part 2
  • Unit 2 Homework – Part 3
  • Unit 2 Homework – Part 4

Unit 3 Answers

  • Chapter 5, Section 1
  • Chapter 5, Section 2
  • Chapter 5, Section 3
  • Chapter 5 answers

Unit 4 Answers

  • Go to google classroom

Unit 5 Answers

  • TRM-Section 8.1 Full Solutions
  • TRM-Section 8.2 Full Solutions
  • TRM-Section 8.3 Full Solutions

Unit 6 Answers

  • Homework Unit 6 – 2019-2020

Unit 7 Answers

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ap statistics 1.1 homework answers

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đź“Š AP Statistics

đź“Ś exam date: may 7, 2024.

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AP Stats Unit 1 Study Guides

Unit 1 – exploring one-variable data.

Unit 1 Overview: Exploring One-Variable Data

Josh Argo

written by Josh Argo

Introducing Statistics: What Can We Learn from Data?

written by Lusine Ghazaryan

The Language of Variation: Variables

Representing a Categorical Variable with Tables

Representing a Categorical Variable with Graphs

Representing a Quantitative Variable with Graphs

Describing the Distribution of a Quantitative Variable

Summary Statistics for a Quantitative Variable

Graphical Representations of Summary Statistics

Comparing Distributions of a Quantitative Variable

The Normal Distribution

Additional Resources

Study tools.

Download AP Statistics Cheat Sheet PDF Cram Chart

AP Statistics Cheat Sheet PDF & Formula Review Chart

Athena_Codes

written by Athena_Codes

2024 AP Statistics Exam Guide

16 min read

A Q

written by A Q

Frequently Asked Questions

How Do I Self-Study AP Statistics?

Harrison Burnside

written by Harrison Burnside

What Are the Best Quizlet Decks for AP Statistics?

11 min read

What Are the Best AP Statistics Textbooks and Prep Books?

Is AP Statistics Hard? Is AP Statistics Worth Taking?

How Can I Get a 5 in AP Statistics?

What is bias?

Exam Skills

Score Higher on AP Statistics 2024: MCQ Tips from Students

Score Higher on AP Statistics 2024: FRQ Tips from Students

AP Statistics Free Response Questions

John Le

written by John Le

AP Statistics Free Response Help - FRQ

AP Stats Mixed Units Practice FRQ #4 & Feedback

Jerry Kosoff

written by Jerry Kosoff

AP Stats Unit 7 FRQ Practice Prompt (#1) Answers & Feedback

12 min read

AP Cram Sessions 2021

AP Statistics Cram Unit 1: Exploring One Variable Data

slides by Josh Argo

🌶️ AP Stats Cram Review: Unit 1: Exploring One Variable Data

streamed by Josh Argo

AP Statistics Cram Unit 2: Exploring Two Variable Data

🌶️ AP Stats Cram Review: Unit 2: Exploring Two Variable Data

AP Statistics Cram Unit 3: Collecting Data

🌶️ AP Stats Cram Review: Unit 3: Collecting Data

Live Cram Sessions 2020

Unit 1 - Exploring One-Variable Data Slides

slides by Jerry Kosoff

Unit 1 - Exploring One-Variable Data

streamed by Jerry Kosoff

Unit 2 Cram Slides (AP Stats)

Unit 2 - Exploring Two-Variable Data

Unit 3 Cram Slides

Unit 3 - Collecting Data

Previous Exam Prep

Analyzing Categorical Data - Slides

Shane Durkan

slides by Shane Durkan

Analyzing Categorical Data

streamed by Shane Durkan

Sampling Methods and Sources of Bias - Slides

Sampling Methods and Sources of Bias

Displaying Quantitative Data with Graphs

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AIDS patients.

The average length of time (in months) AIDS patients live after treatment.

X = the length of time (in months) AIDS patients live after treatment

  • 823,088 823,856 823,088 823,856
  • quantitative discrete
  • quantitative continuous
  • In both years, underwater earthquakes produced massive tsunamis.

simple random

values for X , such as 3, 4, 11, and so on

No, we do not have enough information to make such a claim.

Take a simple random sample from each group. One way is by assigning a number to each patient and using a random number generator to randomly select patients.

This would be convenience sampling and is not random.

Yes, the sample size of 150 would be large enough to reflect a population of one school.

Even though the specific data support each researcher’s conclusions, the different results suggest that more data need to be collected before the researchers can reach a conclusion.

There is not enough information given to judge if either one is correct or incorrect.

The software program seems to work because the second study shows that more patients improve while using the software than not. Even though the difference is not as large as that in the first study, the results from the second study are likely more reliable and still show improvement.

Yes, because we cannot tell if the improvement was due to the software or the exercise; the data is confounded, and a reliable conclusion cannot be drawn. New studies should be performed.

No, even though the sample is large enough, the fact that the sample consists of volunteers makes it a self-selected sample, which is not reliable.

No, even though the sample is a large portion of the population, two responses are not enough to justify any conclusions. Because the population is so small, it would be better to include everyone in the population to get the most accurate data.

  • Inmates may not feel comfortable refusing participation, or may feel obligated to take advantage of the promised benefits. They may not feel truly free to refuse participation.
  • Parents can provide consent on behalf of their children, but children are not competent to provide consent for themselves.
  • All risks and benefits must be clearly outlined. Study participants must be informed of relevant aspects of the study in order to give appropriate consent.
  • all children who take ski or snowboard lessons
  • a group of these children
  • the population mean age of children who take their first snowboard lesson
  • the sample mean age of children who take their first snowboard lesson
  • X = the age of one child who takes his or her first ski or snowboard lesson
  • values for X , such as 3, 7, and so on
  • the clients of the insurance companies
  • a group of the clients
  • the mean health costs of the clients
  • the mean health costs of the sample
  • X = the health costs of one client
  • values for X , such as 34, 9, 82, and so on
  • all the clients of this counselor
  • a group of clients of this marriage counselor
  • the proportion of all her clients who stay married
  • the proportion of the sample of the counselor’s clients who stay married
  • X = the number of couples who stay married
  • all people (maybe in a certain geographic area, such as the United States)
  • a group of the people
  • the proportion of all people who will buy the product
  • the proportion of the sample who will buy the product
  • X = the number of people who will buy it
  • buy, not buy

quantitative discrete, 150

qualitative, Oakland A’s

quantitative discrete, 11,234 students

qualitative, Crest

quantitative continuous, 47.3 years

  • The survey was conducted using six similar flights. The survey would not be a true representation of the entire population of air travelers. Conducting the survey on a holiday weekend will not produce representative results.
  • Conduct the survey during different times of the year. Conduct the survey using flights to and from various locations. Conduct the survey on different days of the week.

Answers will vary. Sample Answer: You could use a systematic sampling method. Stop the tenth person as they leave one of the buildings on campus at 9:50 in the morning. Then stop the tenth person as they leave a different building on campus at 1:50 in the afternoon.

Answers will vary. Sample Answer: Many people will not respond to mail surveys. If they do respond to the surveys, you can’t be sure who is responding. In addition, mailing lists can be incomplete.

convenience cluster stratified systematic simple random

  • qualitative

Causality: The fact that two variables are related does not guarantee that one variable is influencing the other. We cannot assume that crime rate impacts education level or that education level impacts crime rate.

Confounding: There are many factors that define a community other than education level and crime rate. Communities with high crime rates and high education levels may have other lurking variables that distinguish them from communities with lower crime rates and lower education levels. Because we cannot isolate these variables of interest, we cannot draw valid conclusions about the connection between education and crime. Possible lurking variables include police expenditures, unemployment levels, region, average age, and size.

  • Possible reasons: increased use of caller id, decreased use of landlines, increased use of private numbers, voice mail, privacy managers, hectic nature of personal schedules, decreased willingness to be interviewed
  • When a large number of people refuse to participate, then the sample may not have the same characteristics of the population. Perhaps the majority of people willing to participate are doing so because they feel strongly about the subject of the survey.

The sum of the travel times is 1,173.1. Divide the sum by 50 to calculate the mean value: 23.462. Because each state’s travel time was measured to the nearest tenth, round this calculation to the nearest hundredth: 23.46.

Explanatory variable: amount of sleep Response variable: performance measured in assigned tasks Treatments: normal sleep and 27 hours of total sleep deprivation Experimental Units: 19 professional drivers Lurking variables: none – all drivers participated in both treatments Random assignment: treatments were assigned in random order; this eliminated the effect of any “learning” that may take place during the first experimental session Control/Placebo: completing the experimental session under normal sleep conditions Blinding: researchers evaluating subjects’ performance must not know which treatment is being applied at the time

You cannot assume that the numbers of complaints reflect the quality of the airlines. The airlines shown with the greatest number of complaints are the ones with the most passengers. You must consider the appropriateness of methods for presenting data; in this case displaying totals is misleading.

Answers will vary. Sample answer: The sample is not representative of the population of all college textbooks. Two reasons why it is not representative are that he only sampled seven subjects and he only investigated one textbook in each subject. There are several possible sources of bias in the study. The seven subjects that he investigated are all in mathematics and the sciences; there are many subjects in the humanities, social sciences, and other subject areas, (for example: literature, art, history, psychology, sociology, business) that he did not investigate at all. It may be that different subject areas exhibit different patterns of textbook availability, but his sample would not detect such results.

He also looked only at the most popular textbook in each of the subjects he investigated. The availability of the most popular textbooks may differ from the availability of other textbooks in one of two ways:

  • the most popular textbooks may be more readily available online, because more new copies are printed, and more students nationwide are selling back their used copies OR
  • the most popular textbooks may be harder to find available online, because more student demand exhausts the supply more quickly.

In reality, many college students do not use the most popular textbook in their subject, and this study gives no useful information about the situation for those less popular textbooks.

He could improve this study by:

  • expanding the selection of subjects he investigates so that it is more representative of all subjects studied by college students, and
  • expanding the selection of textbooks he investigates within each subject to include a mixed representation of both the most popular and less popular textbooks.

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Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction
  • Authors: Barbara Illowsky, Susan Dean
  • Publisher/website: OpenStax
  • Book title: Introductory Statistics
  • Publication date: Sep 19, 2013
  • Location: Houston, Texas
  • Book URL: https://openstax.org/books/introductory-statistics/pages/1-introduction
  • Section URL: https://openstax.org/books/introductory-statistics/pages/1-solutions

© Jun 23, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

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