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AP Statistics Formula Sheet 2026 — Complete Reference Guide

The AP Statistics exam provides a formula sheet during the test. But knowing which formulas are given vs. which you must memorize — and how to use them quickly — is what separates a 3 from a 5.

What's on the AP Stats Formula Sheet (Provided on Exam Day)

The College Board provides a reference sheet with formulas organized into three sections: Descriptive Statistics, Probability, and Inferential Statistics.

Section I: Descriptive Statistics

Sample mean: $$\bar{x} = \frac{\sum x_i}{n}$$

Sample standard deviation: $$s_x = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$$

Standardized score (z-score): $$z = \frac{x - \mu}{\sigma}$$

Simple linear regression line: $$\hat{y} = a + bx$$

Slope: $$b = r \cdot \frac{s_y}{s_x}$$

Intercept: $$a = \bar{y} - b\bar{x}$$

Residual: $$\text{residual} = y - \hat{y} = y - (a + bx)$$

Section II: Probability

Addition rule: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Multiplication rule: $$P(A \cap B) = P(A) \cdot P(B|A)$$

Conditional probability: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Mean of a discrete random variable: $$\mu_X = \sum x_i \cdot P(x_i)$$

Variance of a discrete random variable: $$\sigma_X^2 = \sum (x_i - \mu_X)^2 \cdot P(x_i)$$

If X has a binomial distribution:

$$\mu_X = np$$

$$\sigma_X = \sqrt{np(1-p)}$$

$$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$

If $\bar{x}$ is the mean of a random sample of size n:

$$\mu_{\bar{x}} = \mu$$

$$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$

Section III: Inferential Statistics

Standardized test statistic: $$\text{statistic} = \frac{\text{estimate} - \text{parameter}}{\text{standard error of estimate}}$$

Confidence interval: $$\text{estimate} \pm (t^* \text{ or } z^*) \cdot SE$$

Standard Errors

Parameter Standard Error
$\hat{p}$ (sample proportion) $\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$
$\bar{x}$ (sample mean) $\dfrac{s}{\sqrt{n}}$
$\hat{p}_1 - \hat{p}_2$ $\sqrt{\dfrac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \dfrac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$
$\bar{x}_1 - \bar{x}_2$ $\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}$
$b$ (regression slope) $\dfrac{s}{\sqrt{\sum(x_i - \bar{x})^2}}$

Chi-square statistic: $$\chi^2 = \sum \frac{(O - E)^2}{E}$$

What's NOT on the Formula Sheet (Must Memorize)

These are commonly tested but not provided on the AP Stats exam:

Formula/Concept What You Need to Know
IQR rule for outliers Q1 - 1.5×IQR and Q3 + 1.5×IQR
Large counts condition np ≥ 10 and n(1-p) ≥ 10
10% condition n ≤ 10% of population
Normal/Large sample condition n ≥ 30 or population is normal
Degrees of freedom (t-test) df = n - 1 (one sample); conservative: min(n₁-1, n₂-1)
Chi-square df (rows - 1)(columns - 1) for two-way table
Coefficient of determination r² = fraction of variation in y explained by x

Key Distributions Tested

Normal Distribution

t-Distribution

Binomial Distribution

Chi-Square Distribution

Inference Procedures Quick Reference

Test Use When Formula
z-test for proportion 1 proportion, σ known $z = \dfrac{\hat{p} - p_0}{\sqrt{p_0(1-p_0)/n}}$
t-test for mean 1 mean, σ unknown $t = \dfrac{\bar{x} - \mu_0}{s/\sqrt{n}}$
2-proportion z-test Compare 2 proportions Use pooled $\hat{p}$ for H₀: p₁=p₂
2-sample t-test Compare 2 means Use unpooled SE
Paired t-test Matched pairs t-test on differences $d_i = x_{1i} - x_{2i}$
Chi-square GOF 1 categorical var vs. model df = k - 1
Chi-square homogeneity Compare distributions df = (r-1)(c-1)
Chi-square association 2 categorical vars df = (r-1)(c-1)
t-test for slope Linear relationship exists? $t = b/SE_b$, df = n-2

Conditions Checklist (Every Test/Interval)

You must state and verify three conditions for every inference procedure:

1. Random — data from a random sample or randomized experiment

2. Normal / Large Counts

3. Independence (10% condition) — n ≤ 10% of population size

Missing conditions = automatic point deduction on FRQ.

AP Stats Formula Sheet Tips

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