Statistics Formulas Cheat Sheet

A quick reference guide for students. All essential formulas for descriptive statistics and probability in one place.

Bookmark this definitive statistics formulas cheat sheet for your next exam or homework assignment. From basic descriptive statistics to complex probability rules and linear regression, this quick reference guide provides the mathematical formulas you need to succeed. Use the links provided to instantly calculate these values using our free tools.

Measures of Central Tendency

Population Mean (μ) Calculate →

μ = (Σx) / N

Σx = sum of all values
N = number of values in population

Sample Mean (x̄) Calculate →

x̄ = (Σx) / n

n = number of values in sample

Measures of Variability

Sample Variance (s²) Calculate →

s² = Σ(x - x̄)² / (n - 1)

Use n – 1 (Bessel’s correction) for unbiased sample estimation.

Sample Standard Deviation (s) Calculate →

s = \sqrt[ Σ(x - x̄)² / (n - 1) ]

Range

Range = Max(x) - Min(x)

Measures of Position

Z-Score (Standard Score) Z-Score Table →

z = (x - μ) / σ

x = raw score
μ = population mean
σ = standard deviation

Percentile Rank Calculate →

P = (B / n) \times 100

B = number of values below x

Probability Basics

Basic Probability P(A)

P(A) = n(A) / n(S)

n(A) = number of favorable outcomes
n(S) = total possible outcomes

Addition Rule (OR)

P(A \cup B) = P(A) + P(B) - P(A \cap B)

Multiplication Rule (AND)

P(A \cap B) = P(A) \times P(B|A)

Correlation & Regression

Pearson Correlation Coefficient (r)

r = [ n(Σxy) - (Σx)(Σy) ] / \sqrt[ [nΣx²-(Σx)²][nΣy²-(Σy)²] ]

Range: -1 to +1. Measures linear relationship strength.

Linear Regression Equation

ŷ = b₀ + b₁x

b₁ = Slope = r(sy/sx)
b₀ = Y-Intercept = ȳ – b₁x̄

μ Population Mean

x̄ Sample Mean

σ Standard Deviation

Σ Summation

n Sample Size

N Population Size