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Statistics

Statistics for a first (AP-aligned) course: describing data, probability, random variables, the normal distribution, confidence intervals, hypothesis tests, and regression. The exercises build statistical judgment — choosing the right procedure, running it, and saying what the result actually means.

1,030 exercises58 sections

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Sections

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Sampling and Data

85

1.1 Definitions of Statistics, Probability, and Key Terms16

1.2 Data, Sampling, and Variation in Data and Sampling46

1.3 Frequency, Frequency Tables, and Levels of Measurement14

1.4 Experimental Design and Ethics9

Descriptive Statistics

83

2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs9

2.2 Histograms, Frequency Polygons, and Time Series Graphs5

2.3 Measures of the Location of the Data26

2.5 Measures of the Center of the Data15

2.6 Skewness and the Mean, Median, and Mode5

2.7 Measures of the Spread of the Data22

Probability Topics

129

3.1 Terminology24

3.2 Independent and Mutually Exclusive Events27

3.3 Two Basic Rules of Probability39

3.4 Contingency Tables23

3.5 Tree and Venn Diagrams16

Discrete Random Variables

130

4.1 Probability Distribution Function (PDF) for a Discrete Random Variable14

4.2 Mean or Expected Value and Standard Deviation22

4.3 Binomial Distribution (Optional)31

4.4 Geometric Distribution (Optional)17

4.5 Hypergeometric Distribution (Optional)17

4.6 Poisson Distribution (Optional)28

4.7 Discrete Distribution (Playing Card Experiment)1

Continuous Random Variables

53

5.1 Continuous Probability Functions5

5.2 The Uniform Distribution22

5.3 The Exponential Distribution (Optional)26

The Normal Distribution

67

6.1 The Standard Normal Distribution38

6.2 Using the Normal Distribution29

The Central Limit Theorem

69

7.1 The Central Limit Theorem for Sample Means (Averages)17

7.2 The Central Limit Theorem for Sums (Optional)22

7.3 Using the Central Limit Theorem30

Confidence Intervals

80

8.1 A Single Population Mean Using the Normal Distribution28

8.2 A Single Population Mean Using the Student's t-Distribution18

8.3 A Population Proportion34

Hypothesis Testing with One Sample

71

9.1 Null and Alternative Hypotheses11

9.2 Outcomes and the Type I and Type II Errors12

9.3 Distribution Needed for Hypothesis Testing7

9.4 Rare Events, the Sample, and the Decision and Conclusion9

9.5 Additional Information and Full Hypothesis Test Examples32

Hypothesis Testing with Two Samples

84

10.1 Two Population Means with Unknown Standard Deviations33

10.2 Two Population Means with Known Standard Deviations11

10.3 Comparing Two Independent Population Proportions21

10.4 Matched or Paired Samples (Optional)19

The Chi-Square Distribution

79

11.1 Facts About the Chi-Square Distribution4

11.2 Goodness-of-Fit Test19

11.3 Test of Independence23

11.4 Test for Homogeneity11

11.5 Comparison of the Chi-Square Tests5

11.6 Test of a Single Variance17

Linear Regression and Correlation

58

12.1 Linear Equations12

12.2 The Regression Equation8

12.3 Testing the Significance of the Correlation Coefficient (Optional)5

12.4 Prediction (Optional)18

12.5 Outliers15

F Distribution and One-way Anova

42

13.1 One-Way ANOVA5

13.2 The F Distribution and the F Ratio10

13.3 Facts About the F Distribution15

13.4 Test of Two Variances12

Adapted from Statistics © 2022 Rice University. Licensed under CC BY 4.0. Source: Statistics. Imported at revision 7dea80a.