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AP Statistics formula sheet (2026-27 course)
AP Statistics was revised for the 2026-27 school year. The geometric distribution, combining random variables, chi-square goodness-of-fit and inference for slope were removed, so they aren’t here. Correlation and regression are still taught, so r, r2 and the regression line are included.
One-variable data
| Mean | x̄ = Σx / n |
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| Standard deviation | s = √[Σ(x − x̄)2 / (n − 1)] |
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| IQR and outliers | IQR = Q3 − Q1; outlier below Q1 − 1.5·IQR or above Q3 + 1.5·IQR |
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| z-score | z = (x − mean) / SD |
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| Skew | right: mean > median; left: mean < median; skewed data: report median and IQR |
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Probability
| Complement | P(not A) = 1 − P(A) |
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| Addition rule | P(A or B) = P(A) + P(B) − P(A and B) |
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| Multiplication rule | P(A and B) = P(A)·P(B | A) |
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| Conditional | P(A | B) = P(A and B) / P(B) |
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| Mutually exclusive | P(A and B) = 0 |
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| Independent | P(A | B) = P(A) |
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Random variables
| Mean | μX = Σ x·P(x) |
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| Standard deviation | σX = √[Σ (x − μX)2·P(x)] |
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| Binomial | P(X = x) = nCx pˣ(1 − p)n−x; μ = np; σ = √[np(1 − p)] |
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| Normal | about 68%, 95% and 99.7% within 1, 2 and 3 SDs of the mean |
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Sampling distributions
| Sample proportion p̂ | mean p; SD √[p(1 − p)/n] |
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| Sample mean x̄ | mean μ; SD σ/√n |
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| Central Limit Theorem | x̄ is approximately normal when n ≥ 30 (or the population is normal) |
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Inference
| Test statistic | (statistic − parameter) / SE of the statistic |
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| Confidence interval | statistic ± (critical value)(SE of the statistic) |
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| Common z* | 90%: 1.645; 95%: 1.960; 99%: 2.576 |
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| SE of p̂ | √[p̂(1 − p̂)/n]; a one-proportion test uses p0: √[p0(1 − p0)/n] |
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| SE of p̂1 − p̂2 | √[p̂1(1 − p̂1)/n1 + p̂2(1 − p̂2)/n2] |
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| Pooled, for a test of p1 = p2 | p̂c = (n1p̂1 + n2p̂2)/(n1 + n2); SE = √[p̂c(1 − p̂c)(1/n1 + 1/n2)] |
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| SE of x̄ | s/√n, with df = n − 1 (paired data: use the differences) |
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| SE of x̄1 − x̄2 | √(s12/n1 + s22/n2) |
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Conditions
| Random | random sample or random assignment |
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| 10% condition | n ≤ 10% of the population when sampling without replacement |
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| Large counts (proportions) | successes and failures both at least 10 |
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| Means | n ≥ 30, a normal population, or a sample with no strong skew or outliers |
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| Chi-square | all expected counts at least 5 |
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Chi-square tests (homogeneity and independence)
| Statistic | χ2 = Σ (observed − expected)2 / expected |
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| Expected count | (row total)(column total) / table total |
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| Degrees of freedom | (rows − 1)(columns − 1) |
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| Which test | homogeneity: several groups, one variable; independence: one sample, two variables |
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Decisions and errors
| Decision | p-value ≤ α: reject H0 (convincing evidence for Ha); p-value > α: fail to reject H0 |
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| Type I error | rejecting a true H0; probability α |
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| Type II error | failing to reject a false H0 |
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| Power | 1 − P(Type II error); a bigger sample gives more power and a narrower interval |
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Regression
| Least-squares line | ŷ = a + bx |
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| Slope and intercept | b = r(sy/sx); a = ȳ − b·x̄ |
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| Residual | y − ŷ |
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| r and r2 | r: direction and strength of a linear relationship (−1 to 1); r2: share of the variation in y explained by the line |
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| Residual plot | no pattern means a line fits well; don’t extrapolate |
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Collecting data
| Sampling methods | simple random, stratified, cluster, systematic |
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| Bias | undercoverage, nonresponse, response, voluntary response, convenience |
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| Experiments | comparison, random assignment, replication, control; block similar units, then randomize within blocks |
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On the TI-84 Plus CE
| Summary stats | STAT ▸ CALC ▸ 1-Var Stats; LinReg(a+bx) for the line |
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| Show r and r2 | MODE ▸ Stat Diagnostics ON |
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| Tests and intervals | STAT ▸ TESTS: 1-PropZTest, 2-PropZTest, 1-PropZInt, 2-PropZInt, T-Test, 2-SampTTest, TInterval, 2-SampTInt, χ2-Test (observed counts in matrix [A]) |
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| Distributions | 2ND VARS (DISTR): normalcdf(lower, upper, μ, σ), invNorm(area to the left, μ, σ), tcdf(lower, upper, df), invT(area to the left, df), binompdf(n, p, x), binomcdf(n, p, x) |
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| At least x | P(X ≥ x) = 1 − binomcdf(n, p, x − 1) |
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| No lower or upper bound | use −1E99 or 1E99 (2ND , types the E) |
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What it looks like on the calculator
The calculator version is the same sheet in plain text with short lines, so it fits the screen. Square roots are written as sqrt( ), powers with ^ and Greek letters as words. On the calculator, search a word like “pooled” or “binomcdf” to jump straight to it. The notes are stored in Archive, so a RAM clear won’t erase them.
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Does this match the new AP Statistics course?
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