Probability Statistics Calculator

Complete probability and statistics workspace

This single PHP file accepts raw observations, grouped data, weighted values, probability parameters, frequency tables, and paired datasets. It returns readable results with formulas, interpretation aids, charts, detailed tables, input validation, saved session history, copy tools, CSV output, text output, print support, and shareable calculator state.

• Mean, median, mode, range, and midrange
• Geometric, harmonic, weighted, and trimmed means
• Quartiles, percentiles, IQR, and deviations
• Variance, standard deviation, standard error, and CV
• Skewness, kurtosis, RMS, and squared deviations
• Frequency and cumulative-frequency tables
• Union, intersection, complement, and conditional probability
• Independent, dependent, and repeated events
• Bayes theorem and total evidence probability
• Factorials, permutations, combinations, and multinomials
• Binomial, Poisson, geometric, and negative-binomial models
• Hypergeometric and discrete-uniform models
• Normal, uniform, exponential, gamma, and beta models
• Chi-square, Student t, F, Weibull, and lognormal models
• Left, right, between, outside, and inverse probabilities
• Z-scores, percentiles, raw scores, and empirical rule
• Mean and proportion confidence intervals
• Difference-of-means and difference-of-proportions intervals
• Z-tests, t-tests, proportion tests, and Welch tests
• Pearson and Spearman correlation
• Linear regression, residuals, R², and slope tests
• One-way ANOVA
• Chi-square goodness-of-fit and independence tests
• Sample-size planning and finite population correction
• IQR and z-score outlier detection
• Z-score, min-max, log, square-root, and power transforms
• Two-dataset comparisons
• Uniform, normal, exponential, and Bernoulli generation
• Coin, dice, and Monty Hall simulations
• Bootstrap confidence intervals

How to use this calculator

Select a category and calculation. Enter numeric lists with commas, spaces, semicolons, or new lines. Percentages may be entered as decimals or values such as 5%. Press Calculate to view the primary answer, supporting measures, formulas, calculation steps, tables, and charts. Use the output tools to copy, download, print, or share the current calculation.

Statistical interpretation

Statistical validity depends on sampling quality, independence, distribution assumptions, measurement reliability, and suitable expected counts. A small p-value does not measure practical importance. Confidence intervals should be interpreted with their sampling method and model assumptions. Review context before making scientific, medical, financial, or operational decisions.