Statistics & Data Analysis Calculators
Select a calculator below to perform fast, accurate calculations.
Statistics Calculator
Calculate comprehensive summary statistics, dataset mean, median, sample standard deviation, variance, SEM, and range.
Statistics & Data AnalysisMean Calculator
Calculate arithmetic mean (average), total dataset sum, number of observations (N), minimum, maximum, and standard error.
Statistics & Data AnalysisMedian Calculator
Calculate dataset median (middle 50th percentile value), lower quartile Q1, upper quartile Q3, and Interquartile Range (IQR).
Statistics & Data AnalysisMode Calculator
Calculate most frequent modal values, unimodal, bimodal, and multimodal dataset frequencies, occurrence counts, and distributions.
Statistics & Data AnalysisMean, Median & Mode Calculator
Calculate central tendency measures, dataset mean, median, mode, range, sample variance, and standard deviation.
Statistics & Data AnalysisRange Calculator
Calculate total dataset range (Max - Min), minimum value, maximum value, midrange, and observation count (N).
Statistics & Data AnalysisMidrange Calculator
Calculate dataset midrange value (Max + Min) / 2, minimum value, maximum value, and total range spread.
Statistics & Data AnalysisWeighted Mean Calculator
Calculate weighted average for course grades, academic GPA, portfolio stock returns, and weighted datasets.
Statistics & Data AnalysisWeighted Average Calculator
Calculate weighted average scores for school grades, inventory unit costs, financial investments, and weighted survey responses.
Statistics & Data AnalysisGeometric Mean Calculator
Calculate geometric mean, CAGR compounding growth rates, and log-transformed averages for positive numbers.
Statistics & Data AnalysisHarmonic Mean Calculator
Calculate harmonic mean, average speed across equal distances, unit rate averages, and price-to-earnings (P/E) ratios.
Statistics & Data AnalysisRoot Mean Square Calculator
Calculate Root Mean Square (RMS), quadratic mean, AC electrical effective voltage, crest factor, and mean absolute value.
Statistics & Data AnalysisVariance Calculator
Calculate sample variance (s2), population variance (sigma2), sum of squared deviations (SS), mean, and standard deviation.
Statistics & Data AnalysisStandard Deviation Calculator
Calculate sample standard deviation (s), population standard deviation (sigma), variance, coefficient of variation (CV %), and SEM.
Statistics & Data AnalysisPopulation Standard Deviation Calculator
Calculate population standard deviation (sigma), population variance (sigma2), sum of squares (SS), and population mean.
Statistics & Data AnalysisSample Standard Deviation Calculator
Calculate sample standard deviation (s), sample variance (s2), degrees of freedom (df = n-1), and SEM.
Statistics & Data AnalysisPopulation Variance Calculator
Calculate population variance (sigma2), population standard deviation (sigma), sum of squares (SS), and population mean.
Statistics & Data AnalysisSample Variance Calculator
Calculate sample variance (s2), sample standard deviation (s), degrees of freedom (df = n-1), and sample mean.
Statistics & Data AnalysisCoefficient of Variation Calculator
Calculate Coefficient of Variation (CV %), Relative Standard Deviation (RSD), mean, and variability risk levels.
Statistics & Data AnalysisQuartile Calculator
Calculate First Quartile (Q1), Second Quartile (Q2 Median), Third Quartile (Q3), and Interquartile Range (IQR).
Statistics & Data AnalysisPercentile Calculator
Calculate any k-th percentile value (Pk), median (P50), quartiles (Q1, Q3), and linear interpolation ranks.
Statistics & Data AnalysisPercentile Rank Calculator
Calculate percentile rank percentage for test scores, academic rankings, and Z-score equivalents.
Statistics & Data AnalysisQuartile Deviation Calculator
Calculate Quartile Deviation (QD), Semi-Interquartile Range, Coefficient of Quartile Deviation, and IQR.
Statistics & Data AnalysisInterquartile Range Calculator
Calculate Interquartile Range (IQR = Q3 - Q1), Tukey outlier fences (1.5 x IQR), quartiles, and detect statistical outliers.
Statistics & Data AnalysisFive Number Summary Calculator
Calculate five-number summary [Min, Q1, Median Q2, Q3, Max], Interquartile Range (IQR), and boxplot parameters.
Statistics & Data AnalysisZ-Score Calculator
Calculate standardized Z-scores, cumulative normal distribution probabilities, percentiles, and two-tailed p-values.
Statistics & Data AnalysisZ Score from Mean Calculator
Calculate Z-score = (X - mean) / SD, distance from mean, percentile rank %, and normal distribution probabilities.
Statistics & Data AnalysisZ Table Calculator
Standard Normal Distribution Z-Table lookup for P(Z < z), right tail P(Z > z), central area, and two-tailed p-values.
Statistics & Data AnalysisT Score Calculator
Calculate Student t-statistic, psychometric T-score (50 + 10Z), degrees of freedom df, and SEM.
Statistics & Data AnalysisT Distribution Calculator
Calculate Student t-distribution probabilities, one-tailed and two-tailed p-values, and degrees of freedom df.
Statistics & Data AnalysisNormal Distribution Calculator
Calculate normal bell curve probabilities P(X < x), density f(x), Z-score, and percentiles for N(mean, sigma2).
Statistics & Data AnalysisNormal Distribution Probability Calculator
Calculate normal distribution interval probability P(a < X < b), lower and upper Z-scores, and population area percentages.
Statistics & Data AnalysisStandard Normal Distribution Calculator
Calculate Standard Normal Distribution N(0,1) bell curve probabilities Phi(z), probability density phi(z), and upper tails.
Statistics & Data AnalysisBinomial Distribution Calculator
Calculate binomial probability P(X = k) = nCr * p^k * (1-p)^(n-k), cumulative P(X <= k), mean np, and variance.
Statistics & Data AnalysisPoisson Distribution Calculator
Calculate Poisson event probability P(X = k) = (lambda^k * e^-lambda) / k!, cumulative P(X <= k), mean lambda, and variance.
Statistics & Data AnalysisGeometric Distribution Calculator
Calculate geometric probability P(X = k) = (1-p)^(k-1) * p for first success on trial k, expected trials 1/p, and variance.
Statistics & Data AnalysisHypergeometric Distribution Calculator
Calculate sampling without replacement probability P(X = k), expected mean, and finite population variance.
Statistics & Data AnalysisExponential Distribution Calculator
Calculate continuous waiting time CDF P(X <= x) = 1 - e^(-lambda*x), survival P(X > x), mean 1/lambda, and median.
Statistics & Data AnalysisUniform Distribution Calculator
Calculate continuous uniform probabilities P(X <= x) = (x-a)/(b-a), density f(x) = 1/(b-a), mean, and variance.
Statistics & Data AnalysisProbability Calculator
Calculate event probability P(A) = n(A) / n(S), complement P(A-complement), percentage %, and odds ratios.
Statistics & Data AnalysisConditional Probability Calculator
Calculate P(A|B) = P(A and B) / P(B), joint probability, and test event independence.
Statistics & Data AnalysisBayes Theorem Calculator
Calculate posterior probability P(A|B) = [P(B|A)*P(A)] / P(B), total evidence, and Bayesian probability updating.
Statistics & Data AnalysisProbability of Independent Events Calculator
Calculate P(A and B) = P(A)*P(B), union P(A or B), neither event, and exactly one event probabilities.
Statistics & Data AnalysisProbability of Dependent Events Calculator
Calculate P(A and B) = P(A) * P(B|A), sampling without replacement, and dependent event chains.
Statistics & Data AnalysisOdds Calculator
Calculate odds for ratio P/(1-P), odds against (1-P)/P, decimal odds, and fractional betting odds.
Statistics & Data AnalysisOdds to Probability Calculator
Convert betting odds ratio a:b to implied win probability P = a / (a + b), percentage %, and decimal odds.
Statistics & Data AnalysisProbability to Odds Calculator
Convert win probability P to odds for ratio P/(1-P), odds against, decimal, and American odds.
Statistics & Data AnalysisPermutation Calculator
Calculate permutations P(n, r) = n! / (n - r)!, permutations with repetition n^r, circular permutations (n-1)!, and combinations.
Statistics & Data AnalysisCombination Calculator
Calculate combinations C(n, r) = n! / [r!(n-r)!], combinations with repetition C(n+r-1, r), and Pascal triangle coefficients.
Statistics & Data AnalysisFactorial Calculator
Calculate integer factorial n!, double factorial n!!, Stirling approximation, and digit counts for 0 <= n <= 170.
Statistics & Data AnalysisOne Sample t Test Calculator
Calculate one-sample t-statistic t = (x-bar - mu0)/(s/sqrt(n)), degrees of freedom df, p-value, and 95% confidence intervals.
Statistics & Data AnalysisTwo Sample t Test Calculator
Calculate Welch t-statistic for independent samples, mean difference (x-bar1 - x-bar2), df, p-value, and 95% CI.
Statistics & Data AnalysisPaired t Test Calculator
Calculate dependent paired t-statistic t = d-bar/(s_d/sqrt(n)), before-after mean differences, df, p-value, and 95% CI.
Statistics & Data AnalysisOne-Way ANOVA Calculator
Calculate F-statistic F = MSB / MSW, degrees of freedom df1, df2, p-value, and eta squared effect size.
Statistics & Data AnalysisTwo-Way ANOVA Calculator
Calculate main effects FA, FB, interaction effect FAB, MSE, degrees of freedom, and two-factor factorial ANOVA.
Statistics & Data AnalysisChi-Square Calculator
Calculate chi-square statistic, degrees of freedom df, p-value, and critical significance thresholds.
Statistics & Data AnalysisChi-Square Goodness of Fit Calculator
Calculate goodness-of-fit chi2 = sum((Oi - Ei)^2 / Ei), degrees of freedom df = k-1, p-value, and Cramer V effect size.
Statistics & Data AnalysisChi-Square Test of Independence Calculator
Calculate 2x2 contingency table chi-square, Yates correction, odds ratio OR = ad/bc, phi coefficient, and p-value.
Statistics & Data AnalysisZ Test Calculator
Calculate Z-statistic Z = (x-bar - mu0)/(sigma/sqrt(n)), known population SD sigma, p-value, and 95% confidence intervals.
Statistics & Data AnalysisOne Sample Z Test Calculator
Calculate one-sample Z = (x-bar - mu0)/(sigma/sqrt(n)), margin of error, p-value, and 95% confidence interval.
Statistics & Data AnalysisTwo Sample Z Test Calculator
Calculate two-sample Z-statistic, mean difference (x-bar1 - x-bar2), standard error, p-value, and 95% CI.
Statistics & Data AnalysisZ Test for Single Proportion Calculator
Calculate one-proportion Z-statistic Z = (pHat - p0)/sqrt(p0(1-p0)/n), sample proportion pHat, p-value, and 95% CI.
Statistics & Data AnalysisZ Test for Two Proportions Calculator
Calculate two-proportion Z-statistic, proportion difference (pHat1 - pHat2), pooled proportion, p-value, and 95% CI.
Statistics & Data AnalysisPearson Correlation Calculator
Calculate Pearson correlation coefficient r, R-squared coefficient of determination, t-statistic, p-value, and covariance.
Statistics & Data AnalysisSpearman Rank Correlation Calculator
Calculate Spearman rank correlation coefficient rho = 1 - (6sum(d2)/(n(n2-1))), rank differences, t-statistic, and p-value.
Statistics & Data AnalysisCovariance Calculator
Calculate sample covariance Cov(X,Y) = sum((x-xBar)(y-yBar))/(n-1), population covariance sigma_XY, and Pearson correlation.
Statistics & Data AnalysisSimple Linear Regression Calculator
Calculate least squares slope beta1, intercept beta0, linear regression equation yHat = beta0 + beta1*x, R2, and Y predictions.
Statistics & Data AnalysisMultiple Linear Regression Calculator
Calculate multiple regression R-squared, adjusted R-squared, overall model F-statistic, and residual degrees of freedom.
Statistics & Data AnalysisR-Squared Calculator
Calculate coefficient of determination R2 = SSR / SST, explained variance %, unexplained error %, and sum of squares.
Statistics & Data AnalysisAdjusted R-Squared Calculator
Calculate adjusted R2 = 1 - [(1-R2)(N-1)/(N-k-1)], predictor penalty, and multiple regression model comparison.
Statistics & Data AnalysisConfidence Interval for Mean Calculator
Calculate 90%, 95%, 99% confidence interval [xBar +- z*(s/sqrt(n))], margin of error, and SEM.
Statistics & Data AnalysisConfidence Interval for Proportion Calculator
Calculate 90%, 95%, 99% proportion confidence interval [pHat +- z*sqrt(pHat(1-pHat)/n)], margin of error %, and sample size.
Statistics & Data AnalysisConfidence Interval for Difference Between Means Calculator
Calculate 90%, 95%, 99% CI [(xBar1-xBar2) +- z*SE], mean difference, and margin of error.
Statistics & Data AnalysisConfidence Interval for Difference Between Proportions Calculator
Calculate 90%, 95%, 99% CI [(pHat1-pHat2) +- z*SE], proportion difference %, and A/B test margin of error.
Statistics & Data AnalysisMargin of Error Calculator
Calculate margin of error ME = z*(s/sqrt(n)), confidence level z*, standard error, and sample size requirements.
Statistics & Data AnalysisCohens d Calculator
Calculate standardized effect size d = (xBar1 - xBar2)/s_pooled, Hedges g, Glass delta, and Cohen effect magnitude rating.
Statistics & Data AnalysisRelative Risk Calculator
Calculate relative risk RR = [a/(a+b)] / [c/(c+d)], 95% CI, absolute risk reduction ARR, and relative risk reduction RRR.
Statistics & Data AnalysisOdds Ratio Calculator
Calculate odds ratio OR = (ad)/(bc), 95% CI, case-control odds, and logistic regression odds ratios.
Statistics & Data AnalysisMann-Whitney U Test Calculator
Calculate non-parametric Mann-Whitney U, Wilcoxon rank sum R1, R2, Z approximation, and p-value.
Statistics & Data AnalysisWilcoxon Signed-Rank Test Calculator
Calculate non-parametric paired Wilcoxon W, W+ positive ranks sum, W- negative ranks sum, Z approximation, and p-value.
Statistics & Data AnalysisKruskal-Wallis Test Calculator
Calculate Kruskal-Wallis H statistic H = [12/(N(N+1))] * sum(Ri^2/ni) - 3(N+1), degrees of freedom df = k-1, and p-value.
Statistics & Data AnalysisSimple Moving Average Calculator
Calculate Simple Moving Average SMA = (P1 + P2 + ... + Pn) / n over any custom time series window.
Statistics & Data AnalysisWeighted Moving Average Calculator
Calculate Weighted Moving Average WMA = sum(wi * Pi) / sum(wi) assigning higher weights to recent observations.
Statistics & Data AnalysisExponential Smoothing Calculator
Calculate Single Exponential Smoothing forecast S_t = alpha * Y_t + (1-alpha) * S_{t-1} with smoothing constant alpha.
Statistics & Data AnalysisStandard Error Calculator
Calculate Standard Error of the Mean SEM = s / sqrt(n), margin of error, and confidence precision.
Statistics & Data AnalysisSum of Squares Calculator
Calculate Total Sum of Squares SS = sum((x - mean)^2), mean, variance, and sample standard deviation.
Statistics & Data AnalysisRoot Mean Square Error (RMSE) Calculator
Calculate Root Mean Square Error RMSE = sqrt( (1/n) * sum((y_actual - y_pred)^2) ) for predictive model evaluation.
Statistics & Data AnalysisMean Absolute Error (MAE) Calculator
Calculate Mean Absolute Error MAE = (1/n) * sum(|y_actual - y_pred|) for model prediction performance.
Statistics & Data AnalysisMean Absolute Percentage Error (MAPE) Calculator
Calculate Mean Absolute Percentage Error MAPE = (100%/n) * sum(|(actual - pred)/actual|) for forecast accuracy.
Statistics & Data AnalysisPooled Variance Calculator
Calculate Pooled Variance s_p^2 = [(n1-1)s1^2 + (n2-1)s2^2] / (n1 + n2 - 2) for two-sample t-tests.
Statistics & Data AnalysisPooled Standard Deviation Calculator
Calculate Pooled Standard Deviation s_p = sqrt( [ (n1-1)s1^2 + (n2-1)s2^2 ] / (n1+n2-2) ) for effect size scaling.
Statistics & Data AnalysisF-Test for Equality of Variances Calculator
Calculate F-test ratio F = s1^2 / s2^2 (larger variance / smaller variance), df1, df2, and variance ratio significance.
Statistics & Data AnalysisLevenes Test Calculator
Calculate Levenes Test for Homogeneity of Variances across group absolute deviation medians.
Statistics & Data AnalysisNumber Needed to Treat (NNT) Calculator
Calculate Number Needed to Treat NNT = 1 / ARR (Absolute Risk Reduction) for clinical treatment trials.
Statistics & Data AnalysisAbsolute Risk Reduction (ARR) Calculator
Calculate Absolute Risk Reduction ARR = Control Risk - Treatment Risk, percentage point risk difference, and NNT.
Statistics & Data AnalysisRelative Risk Reduction (RRR) Calculator
Calculate Relative Risk Reduction RRR = (Control Risk - Treatment Risk) / Control Risk = 1 - RR.
Statistics & Data AnalysisSensitivity and Specificity Calculator
Calculate Diagnostic Sensitivity = TP/(TP+FN), Specificity = TN/(TN+FP), Accuracy, and Youden J index.
Statistics & Data AnalysisPositive Predictive Value (PPV) Calculator
Calculate Positive Predictive Value PPV = TP / (TP + FP) and post-test disease probability.
Statistics & Data AnalysisNegative Predictive Value (NPV) Calculator
Calculate Negative Predictive Value NPV = TN / (TN + FN) and post-test healthy confidence.
Statistics & Data AnalysisLikelihood Ratio Calculator
Calculate Positive Likelihood Ratio LR+ = Sens/(1-Spec) and Negative Likelihood Ratio LR- = (1-Sens)/Spec.
Statistics & Data AnalysisSample Size Calculator
Determine minimum sample size required for survey research based on confidence level, margin of error, and population size.