Statistics & Probability Calculators

Compute sample (n−1) and population (n) standard deviation from a list of numbers.

Sample (n−1) and population (n) variance — the square of standard deviation.

Find the value at the kth percentile in a dataset (linear interpolation).

z = (x − μ) / σ — how many standard deviations a value is above or below the mean.

t = (x̄ − μ₀) / (s/√n) — for testing a sample mean against a hypothesized population mean.

IQR = Q3 − Q1 — the middle 50% spread, robust to outliers.

CV = σ / μ — relative variability as a percentage. Useful for comparing spread across different scales.

GM = (x₁ · x₂ · ... · xₙ)^(1/n). Right "average" for ratios, growth rates, multiplicative quantities.

C(n, r) = n! / (r!(n−r)!). Number of ways to choose r items from n where order doesn't matter.

P(n, r) = n! / (n−r)!. Number of ways to arrange r items from n where order matters.

Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.

CI = mean ± z × (σ/√n). 90 / 95 / 99 % standard intervals.

Compute probability density and cumulative probability at x for given μ, σ.

P(X = k) = C(n,k) p^k (1−p)^(n−k). Probability of exactly k successes in n trials.

r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² Σ(yᵢ−ȳ)²). Linear correlation [−1, 1].

Test whether two means differ. t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂).

z = (x̄ − μ) / (σ/√n). Compare sample mean to known population.

χ² = Σ(O−E)²/E. Test if observed frequencies match expected.

F = MS_between / MS_within. Test if 3+ group means differ.

y = mx + b via least squares. Returns m, b, r², SE.

n = (z × σ / E)². Required sample size for given margin E at confidence z.

Paste a list of numbers to get the mean, median, mode, range, count, and sum — the core measures of central tendency.

Compute sample and population standard deviation and variance from a pasted list of numbers, with the mean and formulas shown.

Find Q1, Q2 (median), Q3, the interquartile range, and outliers using the 1.5×IQR rule from a pasted dataset.

Build a confidence interval for a population mean from the sample mean, standard deviation, size, and confidence level using the t-distribution.

Compute the posterior probability P(A|B) from the prior P(A), the evidence P(B), and the likelihood P(B|A).

Compute P(A and B), P(A or B), and P(A|B) for two events, whether they are independent or dependent.

Find the probability that at least two people in a group share a birthday — the famous, counterintuitive birthday problem.

Run a chi-square goodness-of-fit test from observed and expected frequencies — get the χ² statistic, degrees of freedom, and p-value.

Fit a least-squares line to paired X and Y data — get the slope, intercept, equation, correlation, and R².

Compute Pearson’s r for two paired data columns, with R² and a plain-language interpretation of strength and direction.

Find the optimal number of histogram bins and bin width by three rules — Sturges, Scott, and Freedman-Diaconis — from your data.

Enter a 2×2 payoff matrix to find each player’s dominant strategy, the Nash equilibrium, and whether it is a true prisoner’s dilemma.