Statistics Basics > AP Statistics Formulas

This is a list of all the AP Statistics Formulas you’re likely to encounter on the test. Your AP Statistics teacher should have given you a formula sheet to study but if you’ve lost it, you’ll be given one at the exam so there’s no need to memorize the formulas. You *do* need to know how to use the formulas, so click on any formula in this list and you’ll find a step-by-step article explaining how to use that particular formula.

The most important thing to remember about these formulas is that in most of the questions for the test, *you won’t actually use the actual formulas!* Why? For the vast majority of questions, you’ll be using your TI-83 Graphing Calculator. Probably the best advice you can get for the AP statistics test is to not concentrate on these AP statistics formulas but rather, learn what the symbols mean and learn how to input them into your calculator.

### AP Statistics Formulas: Descriptive Statistics

Note: The Σ in these formulas is summation notation (it means to “add up”).

- Sample mean formula = x = ( Σ x
_{i}) / n - Sample standard deviation formula = s = sqrt [ Σ ( x
_{i}– x )^{2}/ ( n – 1 ) ] - Pooled sample standard error formula (two samples) = SE
_{pooled}= sqrt [ (n_{1}– 1) * s_{1}^{2}+ (n_{2}– 1) * s_{2}^{2}] / (n_{1}+ n_{2}– 2) ]

### AP Statistics Formulas: Probability (Addition and Multiplication Rules, Expected Value and Variance of Random Variables)

- Addition Rule: P(A ∪ B) = P(A) + P(B)- P(A ∩ B)
- Multiplication Rule: P(A ∩ B) = P(A) P(B|A)
- Expected value formula = E(X) = μ
_{x}= Σ [ x_{i}* P(x_{i}) ] - Formula for Variance of X (discrete random variable) = σ
^{2}= Σ(x_{i}-μ)^{2}

### AP Statistics Formulas: Linear Regression equations, slope and correlation coefficients

- Linear regression equation: ŷ = b
_{0}+ b_{1}x - Regression coefficient = b
_{1}= Σ [ (x_{i}– x)(y_{i}– y) ] / Σ [ (x_{i}– x)^{2}] or b_{1}= r * (s_{y}/ s_{x}) - Regression slope intercept = b
_{0}= y – b_{1}* x - Sample correlation coefficient = r = [ 1 / (n – 1) ] * Σ { [ (x
_{i}– x) / s_{x}] * [ (y_{i}– y) / s_{y}] } - Standard error of regression slope = s
_{b1}= sqrt [ Σ(y_{i}– ŷ_{i})^{2}/ (n – 2) ] / sqrt [ Σ(x_{i}– x)^{2}]

### AP Statistics Formulas: Binomial Distributions and Proportions

- Binomial distribution formula: P(X = x) = b(
*x*;*n, P*) =_{n}C_{x}* P^{x}* (1 – P)^{n – x}=_{n}C_{x}* P^{x}* Q^{n – x} - Formula for binomial distribution Mean = μ
_{x}= n * P - Standard deviation of binomial distribution formula = σ
_{x}= sqrt[*n***P** ( 1 –*P*) ] - Mean of sampling distribution of the proportion = μ
_{p}= P - Standard deviation of sampling distribution of the proportion = σ
_{p}= sqrt[p*q) / n ]

### AP Statistics Formulas: Inferential Statistics (Confidence Intervals, Chi-Square)

- Standardized test statistic general formula = (Statistic – Parameter) / (Standard deviation of statistic)
- Confidence interval general formula: Sample statistic
__+__Critical value * Standard error of statistic - Chi-square statistic = Χ
^{2}=

Σ[ (Observed – Expected)^{2}/ Expected ]

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## References

Princeton Review AP Statistics Prep, 2021: 4 Practice Tests + Complete Content Review + Strategies & Techniques (College Test Preparation).