Statistics | Index

Statistics is the science of collecting data, describing it and drawing conclusions from it when chance is involved.

The course covers one- and two-variable data, sampling and experiments, probability, random variables, normal and sampling distributions, confidence intervals and hypothesis tests.

It’s for AP Statistics students and college intro statistics students.

What to know first: Algebra 2, especially graphs, linear equations and logarithms. You don’t need calculus. The binomial distribution uses combinations from Precalculus, Unit 7. Basic data displays and averages are in Pre-Algebra, Unit 7.

Lessons for this course are coming soon. The list below shows every planned lesson in teaching order.

Units in this course

Unit 1: One-Variable Data

  1. Categorical and Quantitative Variables (coming soon) — tell the two kinds of variables apart and choose a graph for each
  2. Bar Graphs and Pie Charts (coming soon) — display and compare categorical data
  3. Stem-and-Leaf Plots (coming soon) — display quantitative data with stems and leaves
  4. Describing a Distribution (coming soon) — describe shape, center, spread and unusual features in context
  5. Standard Deviation (coming soon) — measure spread with the standard deviation and variance
  6. Outliers and the 1.5 × IQR Rule (coming soon) — use the interquartile range to decide which values are outliers
  7. Percentiles and Z-Scores (coming soon) — describe where a value falls with percentiles and z-scores
  8. Transforming Data (coming soon) — see how adding or multiplying every value changes the center and spread
  9. Comparing Distributions (coming soon) — compare two or more data sets by shape, center and spread

Also see: Mean, Median, Mode and Range, Dot Plots and Histograms and Box Plots (Pre-Algebra, Unit 7).

Unit 2: Two-Variable Data and Regression

  1. Correlation Coefficient (coming soon) — find and interpret r, the strength and direction of a linear relationship
  2. Least-Squares Regression Line (coming soon) — find and interpret the slope and y-intercept of the regression line
  3. Residuals and Residual Plots (coming soon) — use residuals to decide whether a linear model fits
  4. Coefficient of Determination (coming soon) — interpret r² as the share of the variation that the model explains
  5. Influential Points (coming soon) — see how outliers and high-leverage points change a regression line
  6. Transformations to Achieve Linearity (coming soon) — use logs and powers to straighten curved data

Also see: Two-Way Tables, Scatter Plots and Correlation and Line of Best Fit (Algebra 1, Unit 10).

Unit 3: Sampling and Experiments

  1. Sampling Methods (coming soon) — simple random, stratified, cluster and systematic samples
  2. Sampling Bias (coming soon) — undercoverage, nonresponse, response bias and voluntary response
  3. Observational Studies and Experiments (coming soon) — tell them apart and know when you can claim cause and effect
  4. Experimental Design (coming soon) — treatments, control groups, random assignment and blinding
  5. Block Designs and Matched Pairs (coming soon) — reduce variation by grouping similar subjects

Unit 4: Probability

  1. Probability Simulations (coming soon) — estimate probabilities by simulating random events
  2. Probability Rules (coming soon) — sample spaces, the complement rule and the law of large numbers
  3. Addition Rule and Mutually Exclusive Events (coming soon) — find the probability that one event or another happens
  4. Conditional Probability (coming soon) — find the probability of an event when you know another event happened
  5. Independent Events (coming soon) — test for independence and use the multiplication rule
  6. Bayes’ Theorem (coming soon) — reverse a conditional probability with a tree diagram or Bayes’ formula

Also see: Probability (Pre-Algebra, Unit 7), and permutations and combinations in Precalculus, Unit 7.

Unit 5: Random Variables, Binomial and Geometric Distributions

  1. Discrete Random Variables (coming soon) — probability distributions for random variables with countable values
  2. Expected Value (coming soon) — find the mean and standard deviation of a random variable
  3. Combining Random Variables (coming soon) — find the mean and standard deviation of sums and differences
  4. Binomial Distribution (coming soon) — find binomial probabilities, the mean and the standard deviation
  5. Geometric Distribution (coming soon) — find the probability that the first success happens on a given trial

Unit 6: Normal Distributions

  1. Density Curves (coming soon) — use the area under a curve to describe a distribution
  2. Normal Distribution (coming soon) — the shape and parameters of the bell curve
  3. Empirical Rule (coming soon) — use the 68-95-99.7 rule for normal distributions
  4. Standard Normal Distribution (coming soon) — find areas under the standard normal curve with z-scores
  5. Normal Probability Calculations (coming soon) — find probabilities and cutoff values for any normal distribution
  6. Normal Probability Plots (coming soon) — decide whether data are close to normal
  7. Normal Approximation to the Binomial (coming soon) — use a normal curve to estimate binomial probabilities

Unit 7: Sampling Distributions

  1. Sampling Distributions (coming soon) — how a statistic varies from sample to sample, and what bias and variability mean
  2. Central Limit Theorem (coming soon) — why the distribution of sample means is close to normal for large samples, whatever the population’s shape
  3. Sampling Distribution of a Sample Proportion (coming soon) — the center, spread and shape of the distribution of sample proportions
  4. Sampling Distribution of a Sample Mean (coming soon) — the center, spread and shape of the distribution of sample means
  5. Sampling Distributions for Differences (coming soon) — the distribution of a difference in two proportions or two means

Unit 8: Confidence Intervals

  1. Confidence Intervals (coming soon) — what a confidence interval and a confidence level mean
  2. Confidence Interval for a Proportion (coming soon) — build and interpret a one-proportion z-interval
  3. Margin of Error (coming soon) — find the margin of error and the sample size you need
  4. t-Distribution (coming soon) — when and why to use t instead of z
  5. Confidence Interval for a Mean (coming soon) — build and interpret a one-sample t-interval
  6. Confidence Interval for a Difference in Proportions (coming soon) — estimate the difference between two population proportions
  7. Confidence Interval for a Difference in Means (coming soon) — build and interpret a two-sample t-interval

Unit 9: Hypothesis Tests

  1. Hypothesis Testing (coming soon) — null and alternative hypotheses and the logic of a significance test
  2. P-Values (coming soon) — what a p-value means and how to compare it with a significance level
  3. One-Proportion z-Test (coming soon) — test a claim about one population proportion
  4. Type I and Type II Errors (coming soon) — the two ways a test can be wrong, and what power means
  5. Two-Proportion z-Test (coming soon) — test whether two population proportions differ
  6. One-Sample t-Test (coming soon) — test a claim about one population mean
  7. Paired t-Test (coming soon) — test the mean difference in matched pairs data
  8. Two-Sample t-Test (coming soon) — test whether two population means differ

Unit 10: Chi-Square and Regression Inference

  1. Chi-Square Goodness-of-Fit Test (coming soon) — test whether data fit a claimed distribution
  2. Chi-Square Test for Independence (coming soon) — test for an association in a two-way table, plus the test for homogeneity
  3. Inference for Regression Slope (coming soon) — build a confidence interval and run a t-test for the slope of a regression line

For Teachers: Standards Alignment

Lessons follow the revised AP Statistics course framework (first exam in May 2027). They also follow a typical college intro statistics course. A few topics are no longer in AP Statistics but are still common in college courses: transformations to achieve linearity, combining random variables, the geometric distribution, the chi-square goodness-of-fit test and inference for regression slope. Lessons also cover the Common Core statistics standards (S-ID, S-IC, S-CP and S-MD). Each lesson with a calculation works the formula by hand first, then shows the same problem on a TI-84 and in Desmos.

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