✍️ Free Response Questions (FRQs)
👆 Unit 1 - Exploring One-Variable Data
1.4Representing a Categorical Variable with Graphs
1.5Representing a Quantitative Variable with Graphs
1.6Describing the Distribution of a Quantitative Variable
1.7Summary Statistics for a Quantitative Variable
1.8Graphical Representations of Summary Statistics
1.9Comparing Distributions of a Quantitative Variable
✌️ Unit 2 - Exploring Two-Variable Data
2.0 Unit 2 Overview: Exploring Two-Variable Data
2.1Introducing Statistics: Are Variables Related?
2.2Representing Two Categorical Variables
2.3Statistics for Two Categorical Variables
2.4Representing the Relationship Between Two Quantitative Variables
2.8Least Squares Regression
🔎 Unit 3 - Collecting Data
3.5Introduction to Experimental Design
🎲 Unit 4 - Probability, Random Variables, and Probability Distributions
4.1Introducing Statistics: Random and Non-Random Patterns?
4.7Introduction to Random Variables and Probability Distributions
4.8Mean and Standard Deviation of Random Variables
4.9Combining Random Variables
4.11Parameters for a Binomial Distribution
📊 Unit 5 - Sampling Distributions
5.0Unit 5 Overview: Sampling Distributions
5.1Introducing Statistics: Why Is My Sample Not Like Yours?
5.4Biased and Unbiased Point Estimates
5.6Sampling Distributions for Differences in Sample Proportions
⚖️ Unit 6 - Inference for Categorical Data: Proportions
6.0Unit 6 Overview: Inference for Categorical Data: Proportions
6.1Introducing Statistics: Why Be Normal?
6.2Constructing a Confidence Interval for a Population Proportion
6.3Justifying a Claim Based on a Confidence Interval for a Population Proportion
6.4Setting Up a Test for a Population Proportion
6.6Concluding a Test for a Population Proportion
6.7Potential Errors When Performing Tests
6.8Confidence Intervals for the Difference of Two Proportions
6.9Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
6.10Setting Up a Test for the Difference of Two Population Proportions
😼 Unit 7 - Inference for Qualitative Data: Means
7.1Introducing Statistics: Should I Worry About Error?
7.2Constructing a Confidence Interval for a Population Mean
7.3Justifying a Claim About a Population Mean Based on a Confidence Interval
7.4Setting Up a Test for a Population Mean
7.5Carrying Out a Test for a Population Mean
7.6Confidence Intervals for the Difference of Two Means
7.7Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
7.8Setting Up a Test for the Difference of Two Population Means
7.9Carrying Out a Test for the Difference of Two Population Means
✳️ Unit 8 Inference for Categorical Data: Chi-Square
📈 Unit 9 - Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
Is AP Statistics Hard? Is AP Statistics Worth Taking?
Best Quizlet Decks for AP Statistics
⏱️ 2 min read
June 3, 2020
Lets look back at the two-way table from Unit 2.2.
Courtesy of Starnes, Daren S. and Tabor, Josh. The Practice of Statistics—For the AP Exam, 5th Edition. Cengage Publishing.
We can find more than just joint relative frequencies here as there’s also marginal relative frequencies and conditional relative frequencies. Marginal Relative Frequency
A marginal relative frequency is the relative frequency of all the people in a certain category. For example, the marginal relative frequency of a "50-50 chance” is 1416/4826 as from the right margin, we see that 1416 overall respondents gave that response.
On the other hand, the conditional relative frequency is the frequency that we have of a particular category given the fact that we know a subject is in another category. The category that we know is called the given, or independent category, while the other is called the dependent category, just like independent and dependent variables on graphs. For example, the conditional frequency for “50-50 chance given male” is 720/2459 because out of the 2459 males who responded, 720 of them said “50-50 chance.” When calculating a conditional relative frequency, our denominator (or total) is usually considerably smaller than that of overall total.
From a two-way table, we can use marginal and conditional relative frequencies to consider if two categorical variables are associated or not. To do this, see if two corresponding conditional relative frequencies across different categories are not the same. This is also the same as seeing if the conditional relative frequency is not the same as the marginal relative frequency for the dependent category. This makes it so that certain independent category values are more likely to yield a certain result than others. That is, we can predict behavior given the fact that we know that an individual falls under a certain category.
Using the two-way table above, we can determine that the variables "gender" and "opinion" are independent, or not associated, because the marginal relative frequency of being "50-50 chance" is roughly equal to the conditional relative frequency of being "50-50 chance given male".
🎥Watch: AP Stats - Probability: Two Way Tables, Independence, Tree Diagrams, etc
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