Statistics guides

Each guide answers one question the way you would ask it, then shows the work: formula, steps, worked example, and the interpretation language graders expect.

Describing data

How to calculate standard deviation by hand Mean vs median: which to use, and what skew does How to make a boxplot (five-number summary)How to find outliers: the 1.5 x IQR rule

The normal distribution and z-scores

How to find a z-score and read a z-table Empirical rule (68-95-99.7) and normal distribution

Probability distributions

How to find binomial probability (formula, examples)Binomial vs geometric: how to tell them apart

Sampling distributions

What is a sampling distribution? Mean and proportion Central limit theorem, explained simply Standard error vs standard deviation explained

Confidence intervals

How to Calculate a Confidence Interval (Mean, Proportion)What does 95% confidence actually mean?

Hypothesis testing

What Does a P-Value Mean? (Plain-English Guide)Null vs Alternative Hypothesis: How to Write Them Type I vs Type II Error and Statistical Power t-test vs z-test: when to use each One-proportion vs two-proportion z-test setup Chi-square test explained: 3 tests, one formula Which statistical test should I use? A decision guide

Regression and correlation

Least-squares regression line: find and interpret it How to interpret a residual plot (AP Stats)r vs r-squared: what is r squared and what r means Correlation vs causation, with real examples

Study design and the AP exam

Experiment vs observational study: what to conclude AP Statistics FRQ Tips: State, Plan, Do, Conclude How to read t-test, z, chi-square calculator output AP Statistics cram sheet: every formula and template

Foundations and comparisons

Parameter vs statistic: how to tell them apart Descriptive vs inferential statistics explained Categorical vs quantitative variables (with examples)Histogram vs bar graph: the difference that matters Simple random vs stratified vs cluster sampling Skewed left vs skewed right: what happens to the mean Mutually exclusive vs independent events Probability vs odds: how to convert between them

More

P(A|B) vs P(B|A): which conditional do I need?When a Confidence Interval and P-Value Disagree Does a bigger sample fix bias? Why size fails Does changing units change r or the regression slope?Does a regression line pass through the means?How to describe a completely randomized design How to tell which type of bias a survey has Pooled or not on a TI-84 two-sample t-test? Choose No How to find P(at least one) with the complement rule Can you do a t-test with n less than 30?What if a two-proportion confidence interval has 0?When can you multiply probabilities?Why 10 successes and 10 failures? Large Counts rule Why is df a decimal on a two-sample t-test?Why do we square the residuals in regression?