Statistics calculators

Mean, median, mode, range, geometric mean and more from any list of numbers — with a labeled bar chart.

Compute a weighted average of value/weight pairs, with steps, a comparison to the simple mean and a diagram of each weight's contribution.

Population and sample standard deviation with variance, frequency table, confidence intervals and step-by-step working.

MAD with a transparent per-value deviation table and a number-line diagram showing each point's distance from the mean — plus MAD vs standard deviation explained and show/hide step-by-step working.

Find the sample size for a survey — or the margin of error for a given sample — with confidence level, population proportion and finite-population correction.

Arithmetic, geometric and Fibonacci sequences on one page — nth term, sum, full term list and a small line plot of the first terms.

All standard summary statistics in one place — count, sum, mean, median, mode, range, geometric mean, plus population and sample variance and standard deviation, with a bar chart and mean/median overlay.

Two-event probabilities, solver for unknowns, series of independent events, and normal-distribution probability with a shaded bell curve.

Compute posterior probability P(A|B) from a prior, likelihood and false-positive rate — with a natural-frequency population grid, medical-test preset and full step-by-step working.

Two-proportion z-test for A/B tests: control vs. variant conversion rates, relative uplift, p-value, and a bar chart with 95% confidence intervals so you can see interval overlap at a glance. Selectable 90/95/99% confidence and full step-by-step working.

Convert between raw scores, Z-scores and normal probabilities — with a live standard-normal CDF, bell-curve visuals and a two-Z-score area tool that replaces static Z-tables.

Confidence interval for the population mean with margin of error — auto-switches to the Student t-distribution for small samples (n < 30), with an error-bar visual and step-by-step working.

Pearson's r from two paired data sets, with plain-language strength, a scatter plot with best-fit trend line and full step-by-step working.

Spearman's ρ from two paired data sets with correct tie-adjusted (average) ranks — Pearson-on-ranks method so results stay right when ties are present. Full ranking table, rank-vs-rank scatter plot with best-fit line and show/hide step-by-step working.

Full diagnostic-test 2×2 calculator: sensitivity, specificity, PPV, NPV, accuracy and likelihood ratios (LR+, LR−) with a color-coded TP/FP/FN/TN table, Bayes-based PPV/NPV recomputation at any disease prevalence and show/hide step-by-step working.

Sample and population covariance from two paired data sets, with correlation r reported alongside, a quadrant-shaded scatter plot showing which points push cov up or down, and full step-by-step working.

Least-squares regression line y = m·x + b with slope, intercept, r, R², a scatter plot with the fitted line and residuals, and predictions for any X.

Multiple linear regression with any number of predictors — per-coefficient standard errors, t-statistics and p-values, R² and Adjusted R², overall F-test, a standardised-coefficient bar chart and a residuals-vs-predicted diagnostic plot. Powered by matrix algebra (β = (XᵀX)⁻¹Xᵀy) with show/hide step-by-step working.

Compute quartiles (Q1, Q2, Q3) and IQR, or find any percentile of a data set using linear interpolation, with a box-plot visual and automatic outlier flagging.

Minimum, Q1, median, Q3 and maximum from any list of numbers — with IQR, a labeled box plot and show/hide step-by-step working. Uses the exclusive quartile method so numbers match the Percentile & Quartile Calculator.

Find outliers in a data set using Tukey's 1.5×IQR rule — separates mild and extreme (3×IQR) outliers, with a box plot and step-by-step working.

CV (σ / mean × 100%) for a single dataset or side-by-side for two datasets on different scales, with population/sample toggle, comparison bar chart and step-by-step working.

Sample skewness (G₁) and sample excess kurtosis (G₂) with plain-language classification, a histogram plus distribution-shape overlay and full step-by-step working.

One-sample, two-sample independent (Student's or Welch's) and paired t-tests from raw data or summary stats — with exact p-values from the t-distribution, a shaded rejection-region diagram and full step-by-step working.

Convert any Z, T, chi-square or F test statistic into an exact p-value — with one- or two-tailed support, a shaded distribution diagram and a plain-language significance verdict at your chosen α.

Chi-square goodness-of-fit test and test of independence on an editable contingency table — with expected frequencies, exact p-values, critical values and a plain-language reject / fail-to-reject verdict.

One-way ANOVA on 3+ groups of raw data — full summary table (SS, df, MS, F, p), exact p-value from the F-distribution, shaded F-curve diagram, α-based verdict and a post-hoc note when the result is significant.

Two-sample F-test for equal variances — from raw data or summary stats (s², n). Get F = larger/smaller variance, degrees of freedom, exact F-distribution p-value, critical value, shaded F-curve diagram and a plain-language reject / fail-to-reject verdict.

Find critical values for Z, t, χ² and F distributions at any α, with left / right / two-tailed support. Shows both cutoffs for two-tailed tests, a shaded rejection-region diagram and links to the matching hypothesis-test calculators.

Margin of error for a proportion (survey / poll) and for a mean — with confidence level, optional finite-population correction, auto Z/t switch, ± result, full confidence interval and a shaded normal-curve diagram.

Standard error of the mean (s/√n), of a proportion (√(p(1−p)/n)) and of the difference between two independent means — with a sampling-distribution diagram and show/hide step-by-step working.

df for one-sample, pooled and Welch's t-tests, paired t-tests, chi-square goodness-of-fit and independence, one-way ANOVA and simple linear regression — with a t-distribution diagram and show/hide step-by-step working.

Exact binomial probabilities — P(X = k), P(X ≤ k), P(X < k), P(X ≥ k), P(X > k) — plus mean, variance and standard deviation, with a full probability bar chart across 0..n and show/hide step-by-step working.

Exact Poisson probabilities from an average rate λ — P(X = k), P(X ≤ k), P(X < k), P(X ≥ k), P(X > k) — with mean, variance, standard deviation, a probability bar chart over the meaningful range of k and show/hide step-by-step working.

68-95-99.7 rule for any normal distribution — enter the mean and standard deviation to get the μ±1σ, μ±2σ and μ±3σ ranges with a shaded bell-curve diagram, optional value-in-band check and show/hide step-by-step working.

Exponential-distribution probabilities from either the rate λ or the mean 1/λ — P(X ≤ x), P(X > x) and P(a < X ≤ b) — with mean, variance, standard deviation, a shaded PDF curve, a full explanation of the memoryless property and show/hide step-by-step working.

Probability of rolling any sum with 1–6 dice of 4, 6, 8, 10, 12 or 20 sides — exact, at-least and at-most probabilities as fraction, decimal and percent, with a full distribution bar chart and show/hide step-by-step working.

Odds ratio (OR) and relative risk (RR) from a 2×2 contingency table with 95% confidence intervals via the log-transform method — color-coded a/b/c/d cells, Haldane–Anscombe correction for zero cells, and a clear explanation of when to use OR vs RR.

Find the percentile of any test score — from a full class score list (linear-interpolation method matching NumPy percentile / Excel PERCENTILE.INC) or from the class mean and standard deviation using the standard-normal CDF. Shaded bell-curve diagram, highlighted sorted-list view, show/hide step-by-step working and a clear explanation of percentile vs percentage score.

Interactive Central Limit Theorem demo — pick a Uniform, Skewed or Bimodal population, draw thousands of samples of any size n, and watch the sampling distribution of the mean turn into a bell curve regardless of the population's shape. Side-by-side histograms, empirical vs theoretical mean and SE (σ/√n) and show/hide step-by-step working.

Build a full frequency distribution — frequency, relative frequency (decimal + %), cumulative frequency and cumulative relative frequency — from raw categorical data, raw numeric data grouped into class intervals (Sturges or manual width), or a pre-tallied table. Bar chart / histogram, an ogive (the cumulative chart most calculators skip) and show/hide step-by-step working.

Exact probability of getting a given number of heads in n coin flips — exactly, at least, at most — for a fair or biased coin, plus the probability of a streak of k consecutive heads (or tails) somewhere in n flips. Full binomial distribution bar chart and show/hide step-by-step working.

Odds of winning any lottery — pick-N-from-M games plus Powerball, Mega Millions and EuroMillions style formats with a separate bonus ball. Shown as 1-in-N, probability and percent, with a partial-match tier option, a perspective bar chart against real-world rare events (lightning, hole-in-one, plane crash) on a log scale and show/hide step-by-step working using C(n, r).

Probability the first success happens on trial k — P(X = k), P(X ≤ k) and P(X > k) — using (1 − p)^(k−1)·p, with mean 1/p, variance (1 − p)/p², a full probability bar chart with your k highlighted and show/hide step-by-step working.

Sampling without replacement — P(X = k), P(X ≤ k) and P(X ≥ k) for drawing n items from a finite population of N with K successes. Uses exact BigInt combinations, includes mean nK/N with the finite-population variance correction, a side-by-side binomial comparison, full probability bar chart and show/hide step-by-step working. Works for card hands, lottery matches, quality control and MTG deck-building.

Discrete or continuous uniform on [a, b] in one tool. Discrete gives P(X = x) = 1/n with mean (a+b)/2 and variance (n²−1)/12; continuous gives P(c ≤ X ≤ d) = (d−c)/(b−a) with density 1/(b−a) and variance (b−a)²/12. Auto-clips sub-intervals to the support, ships a shaded PDF/PMF diagram and show/hide step-by-step working.

Non-parametric two-sample test (aka Wilcoxon rank-sum). Ranks both groups together with average ranks for ties, reports U₁, U₂ and U, normal-approximation z with continuity + tie correction, one- or two-sided p-value, plain-language verdict at your chosen α, dot-plot diagram showing overlap and show/hide step-by-step working.

Paired non-parametric test. Enter Before/After values, drops zero differences with a note, ranks |d| with average ranks for ties, reports W⁺, W⁻ and W, normal-approximation z with continuity + tie correction, one- or two-sided p-value, plain-language verdict, lollipop diagram of signed changes and show/hide step-by-step working.

Survey / test internal-consistency reliability. Editable respondents × items grid pre-filled with a Likert example, per-item variances and total-score variance, α with the (k/(k−1))·(1 − Σσᵢ²/σ²ₜ) substitution shown, plain-language verdict with a warning at α ≥ 0.95 for redundant items, variance-contribution diagram and show/hide step-by-step working.

Smooth any time series with a Simple Moving Average (SMA) or Exponential Moving Average (EMA). Enter your data and a window size, get the full smoothed series in a table, an overlaid raw-vs-smoothed line chart, auto or custom α = 2/(n+1) for EMA and show/hide step-by-step working.

Non-parametric one-way ANOVA on 3+ independent groups — ranks with average-rank tie handling, H statistic with tie correction, df = k−1 and an exact chi-square p-value with reject/fail-to-reject verdict at your chosen α.

Standardized effect size between two groups from raw data or summary stats — Cohen's d, Hedges' g (small-sample corrected), Glass's Δ and an approximate 95% CI for d, with plain-language interpretation and step-by-step working.