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 handMean vs median: which to use, and what skew doesHow 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-tableEmpirical 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 proportionCentral limit theorem, explained simplyStandard 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 ThemType I vs Type II Error and Statistical Powert-test vs z-test: when to use eachOne-proportion vs two-proportion z-test setupChi-square test explained: 3 tests, one formulaWhich statistical test should I use? A decision guide

Regression and correlation

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

Study design and the AP exam

Experiment vs observational study: what to concludeAP Statistics FRQ Tips: State, Plan, Do, ConcludeHow to read t-test, z, chi-square calculator outputAP Statistics cram sheet: every formula and template

Foundations and comparisons

Parameter vs statistic: how to tell them apartDescriptive vs inferential statistics explainedCategorical vs quantitative variables (with examples)Histogram vs bar graph: the difference that mattersSimple random vs stratified vs cluster samplingSkewed left vs skewed right: what happens to the meanMutually exclusive vs independent eventsProbability vs odds: how to convert between them

More

AP Statistics Bell Ringers: 30 Five-Minute IdeasAP Statistics Discussion Questions, by TopicAP Statistics Exit Tickets, by UnitAP Statistics FRQ Format 2027: 4 Questions, 40 PointsAP Statistics pacing guide: 32 weeks, unit by unitAP Statistics Project Ideas for High SchoolAP Statistics Review Games Worth Class TimeWhat are the AP Statistics course practices?Emergency AP Statistics Sub Plans (No Prep)AP Statistics units 2027: all five, weightedbinompdf vs binomcdf: which one do I use?Can a data set have no mode? Yes, and here is whenCan expected value be impossible? Yes, and often isCan you generalize these results? (scope of inference)P(A|B) vs P(B|A): which conditional do I need?Conditions for inference: the complete checklistWhen a Confidence Interval and P-Value DisagreeConfidence interval vs hypothesis test: which to useDescriptive Statistics Classroom Activity (40 Min)Does a bigger sample fix bias? Why size failsDoes changing units change r or the regression slope?Does a correlation of 0 mean no relationship?Does a regression line pass through the means?First Day of AP Statistics: A Complete PlanHow Many Decimal Places in Statistics?How many topics are in AP Statistics? 55How many units are in AP Statistics? FiveHow to check if two events are independentHow to choose a sampling methodHow to Choose a Significance Level (Alpha)How to compare two distributionsHow to describe a completely randomized designHow to describe a distribution (and get full credit)How to describe the shape of a distributionHow to design an experiment and describe itHow to find expected value (step by step)How to find p-hat (the sample proportion)How to find Q1 and Q3 by handHow to find the correlation coefficient r by handHow to find sample size for a margin of errorHow to find standard deviation on TI-84: Sx vs sigma-xHow to find the mode (and when it is useful)How to find the weighted mean (with GPA example)How to tell which type of bias a survey hasHow to interpret a confidence interval for a meanHow to Interpret a Confidence Interval for a ProportionHow to interpret the slope of a regression lineHow to interpret the y-intercept of a regression lineHow to Know What the Null Hypothesis IsHow to predict y from x with a regression lineHow to pace the AP Statistics examHow to read a normal probability plotHow to read and make a stemplot (stem-and-leaf)How to read a two-way table: joint, marginal, conditionalHow to run a t-test on the TI-84 and read the outputHow to design and run a simulation (5 steps)How to study for AP Statistics: a real planHow to tell if a situation is binomial: 4 checksHow to use a tree diagram for probabilityHow to use a Venn diagram in probabilityHow to write a hypothesis test conclusionIs a higher standard deviation better? It dependsIs AP Statistics hard? An honest answerIs chi-square goodness of fit on the AP exam?Is expected value the same as the mean?Is inference still on the AP Statistics exam?Is the AP Statistics exam digital?Is the geometric distribution on the AP Stats exam?How to use normalcdf and invNorm on the TI-84One-Proportion Z-Test, Step by Step (Worked Example)One-sample t-test, step by stepPooled or not on a TI-84 two-sample t-test? Choose NoHow to find P(at least one) with the complement ruleSampling Distribution Slider: A 40-Minute LessonShould I use old AP Statistics review books?Statistical vs practical significance explainedCan you do a t-test with n less than 30?What if a two-proportion confidence interval has 0?The uniform distribution, explainedWhat are degrees of freedom?What changed in AP Statistics for 2027What does a negative z-score mean?What does percentile mean? Definition and examplesWhat does standard deviation actually mean?What is a Bernoulli trial? One trial, two outcomesWhat is a bimodal distribution? Two peaks, explainedWhat is a cluster sample? (with examples)What is a density curve? Area equals proportionWhat is a good AP Statistics score?What Is a Good P-Value? There Is No Such ThingWhat is a good r-squared value? It dependsWhat is a randomization test? Shuffle and countWhat is a resistant statistic? Median vs meanWhat is a standardized test statistic?What is cumulative relative frequency?Mean absolute deviation (MAD): formula and examplesWhat is on the AP Statistics exam in 2027?What is selection bias? Direction, not just the labelWhat is statistics actually used for?What is the normal approximation to the binomial?What makes a statistical procedure robust?What was removed from AP StatisticsWhen can you multiply probabilities?When to use a paired t-testWhy 10 successes and 10 failures? Large Counts ruleWhy divide by n - 1 for sample standard deviation?Why Do We Assume the Null Hypothesis Is True?Why is df a decimal on a two-sample t-test?Why Is My Confidence Interval So Wide?Why the median is not affected by outliersWhy variance is in squared units (and SD is not)Why do we square the residuals in regression?