Home/ Statistics & Probability

Category

Statistics & Probability

Statistics and probability formulas and calculators for descriptive statistics, distributions, and probabilistic reasoning used to analyze data and uncertainty. Includes mean, variance, hypothesis testing, and distribution equations.

29Formulas
2Subcategories
Updated Jul 2026
All (29) Descriptive Statistics (17) Probability Distributions (12)

Probability Distributions

One-Sample t-Statistic

t = (x̄ - μ0) / (s/√n)

Probability Distributions

Chi-Square Test Statistic

χ² = Σ((O - E)² / E)

Probability Distributions

Standard Error of the Mean

SE = σ / √n

Probability Distributions

Margin of Error

ME = z * (σ/√n)

Probability Distributions

Confidence Interval for the Mean

CI = x̄ ± z*(σ/√n)

Probability Distributions

Conditional Probability

P(A|B) = P(A∩B) / P(B)

Probability Distributions

Variance of a Discrete Random Variable

Var(X) = E(X²) - [E(X)]²

Probability Distributions

Expected Value (Discrete Random Variable)

E(X) = Σ(xᵢ * P(xᵢ))

Probability Distributions

Normal Distribution Probability Density

f(x) = (1/(σ√(2π))) * e^(-(x-μ)²/(2σ²))

Probability Distributions

Poisson Probability

P(X=k) = (λ^k * e^-λ) / k!

Descriptive Statistics

Harmonic Mean

HM = n / Σ(1/xᵢ)

Descriptive Statistics

Geometric Mean

GM = (x1*x2*...*xn)^(1/n)

Descriptive Statistics

Weighted Mean

x̄w = Σ(wᵢ*xᵢ) / Σwᵢ

Descriptive Statistics

Coefficient of Determination (R²)

R² = 1 - (SS_res / SS_tot)

Descriptive Statistics

Pearson Correlation Coefficient

r = Cov(X,Y) / (σX * σY)

Descriptive Statistics

Covariance

Cov(X,Y) = Σ(xᵢ-x̄)(yᵢ-ȳ) / n

Descriptive Statistics

Skewness (Pearson's Coefficient)

Sk = 3*(x̄ - Median) / s

Descriptive Statistics

Percentile Rank

PR = (Number of values below x / Total number of values) * 100

Descriptive Statistics

Z-Score

z = (x - μ) / σ

Descriptive Statistics

Interquartile Range (IQR)

IQR = Q3 - Q1

Descriptive Statistics

Sample Variance

s² = Σ(xᵢ-x̄)² / (n-1)

Descriptive Statistics

Population Variance

σ² = Σ(xᵢ-μ)² / N

Descriptive Statistics

Range (Statistics)

Range = Max - Min

Descriptive Statistics

Median

Median = middle value (sorted data), or average of two middle values

Descriptive Statistics

Arithmetic Mean

x̄ = Σx / n

Probability Distributions

Binomial Probability

P(X=k) = C(n,k)pᵏ(1−p)ⁿ⁻ᵏ

Probability Distributions

Bayes' Theorem

P(A|B) = P(B|A)P(A) / P(B)

Descriptive Statistics

Coefficient of Variation

CV = σ / μ × 100%

Descriptive Statistics

Standard Deviation

σ = √(Σ(xᵢ−μ)² / N)