Statistics Calculators
Probability, distributions, hypothesis testing, regression, Bayesian, and time series calculators.
Mean Calculator
Compute the arithmetic mean of a set of values by summing them and dividing by the count.
Weighted Mean Calculator
Calculate a weighted average where each value contributes according to its assigned weight.
Geometric Mean Calculator
Compute the geometric mean of positive values, useful for growth rates and multiplicative processes.
Harmonic Mean Calculator
Find the harmonic mean of positive values, ideal for averaging rates and ratios.
Trimmed Mean Calculator
Compute a trimmed mean by removing extreme values before averaging to reduce outlier influence.
Median Calculator
Find the median of a dataset by identifying the middle value when observations are sorted.
Mode Calculator
Determine the mode by identifying the most frequently occurring value in a dataset.
Range Calculator
Calculate the range of a dataset as the difference between the maximum and minimum values.
Interquartile Range Calculator
Compute the interquartile range (IQR) as the difference between the third and first quartiles.
Variance Calculator
Calculate the sample and population variance to measure how spread out values are from the mean.
Standard Deviation Calculator
Calculate the sample and population standard deviation to quantify how spread out values are.
Coefficient of Variation Calculator
Compute the coefficient of variation to express standard deviation as a percentage of the mean.
Skewness Calculator
Estimate the skewness of a distribution using Pearson's approximation based on the mean, median, and standard deviation.
Kurtosis Calculator
Estimate kurtosis to measure whether data tails are heavier or lighter than a normal distribution.
Percentile Calculator
Estimate the value at a given percentile rank using linear interpolation between data bounds.
Quartile Calculator
Compute the three quartiles (Q1, Q2, Q3) from five pre-sorted data values.
Five-Number Summary Calculator
Produce the five-number summary (min, Q1, median, Q3, max) from sorted data values.
Sum of Squares Calculator
Calculate the total sum of squared deviations from the mean, a building block for variance and regression.
Mean Absolute Deviation Calculator
Calculate the mean absolute deviation (MAD) to measure average distance of data points from the mean.
Root Mean Square Calculator
Calculate the root mean square (RMS) of a set of values, used in physics and signal processing.
Probability Calculator
Calculate the probability of an event as the ratio of favorable outcomes to total possible outcomes.
Conditional Probability Calculator
Calculate the probability of event A given that event B has occurred using the conditional probability formula.
Bayes Theorem Calculator
Apply Bayes' theorem to compute posterior probability from prior probability, likelihood, and evidence.
Union Probability Calculator
Calculate the probability that at least one of two events occurs using the addition rule.
Complement Probability Calculator
Calculate the probability that an event does NOT occur, which is 1 minus the probability of the event.
Independent Events Calculator
Calculate the joint probability of two independent events occurring together by multiplying their individual probabilities.
Permutation Calculator
Calculate the number of permutations (ordered arrangements) when choosing r items from n items.
Combination Calculator
Calculate the number of combinations (unordered selections) when choosing r items from n items.
Binomial Probability Calculator
Calculate the probability of exactly k successes in n independent Bernoulli trials with success probability p.
Expected Value Calculator
Calculate the expected value (weighted average of outcomes) of a discrete probability distribution.
Poisson Probability Calculator
Calculate the probability of observing exactly k events in a fixed interval when events occur at a known average rate lambda.
Normal Distribution Calculator
Calculate the probability density function (PDF) value and key properties of the normal distribution for a given x, mean, and standard deviation.
Z-Score Calculator
Calculate the z-score (standard score) that indicates how many standard deviations a value is from the mean.
Standard Normal Calculator
Calculate the probability density function value for the standard normal distribution (mean=0, SD=1) at a given z-value.
Exponential Distribution Calculator
Calculate the probability density and cumulative probability for the exponential distribution, which models time between independent events.
Geometric Distribution Calculator
Calculate the probability that the first success occurs on the k-th trial in a sequence of independent Bernoulli trials.
Hypergeometric Calculator
Calculate the probability of drawing exactly k successes in n draws from a finite population without replacement.
Negative Binomial Calculator
Calculate the probability that the r-th success occurs on the k-th trial in a sequence of independent Bernoulli trials.
Uniform Distribution Calculator
Calculate probability density, cumulative probability, and properties of the continuous uniform distribution on [a, b].
Chi-Square Statistic Calculator
Calculate the chi-square statistic by summing squared differences between observed and expected frequencies divided by expected frequencies.
Confidence Interval Calculator
Calculate the confidence interval for a population mean using the sample mean, standard deviation, sample size, and z-value.
Sample Size Calculator
Determine the minimum sample size needed to achieve a desired margin of error at a given confidence level.
Margin of Error Calculator
Calculate the margin of error for a confidence interval given the z-value, standard deviation, and sample size.
Standard Error Calculator
Calculate the standard error of the mean, which measures how much the sample mean varies from sample to sample.
T-Statistic Calculator
Calculate the t-statistic for a one-sample t-test comparing a sample mean to a hypothesized population mean.
Chi-Square Test Calculator
Calculate the chi-square test statistic and degrees of freedom for a goodness-of-fit or independence test.
F-Statistic Calculator
Calculate the F-statistic as the ratio of two sample variances to test whether population variances are equal.
P-Value Calculator
Estimate the two-tailed p-value for a z-test using the standard normal distribution PDF-based approximation.
Effect Size Calculator
Calculate Cohen's d effect size, which measures the standardized difference between two group means.
Power Analysis Calculator
Estimate the required sample size per group to achieve a desired statistical power for a two-sample z-test.
ANOVA F-Ratio Calculator
Calculate the ANOVA F-ratio from between-group and within-group mean squares to test whether group means differ significantly.
Correlation Coefficient Calculator
Calculate the Pearson correlation coefficient (r) between two variables from summary statistics.
Coefficient of Determination Calculator
Calculate R-squared from the correlation coefficient to determine what proportion of variance in Y is explained by X.
Linear Regression Slope Calculator
Calculate the slope (b1) of the least-squares regression line from summary statistics.
Linear Regression Intercept Calculator
Calculate the y-intercept (b0) of the least-squares regression line from the means of x and y and the slope.
Residual Calculator
Calculate the residual (prediction error) as the difference between the observed and predicted values in regression.
Type I Error Calculator
Calculate the probability of Type I error (false positive) across multiple independent tests, and the Bonferroni-corrected significance level.
Type II Error Calculator
Estimate the probability of a Type II error (beta) and statistical power for a one-sample z-test.
Odds Ratio Calculator
Calculate the odds ratio from a 2x2 contingency table to compare the odds of an outcome between two groups.
Relative Risk Calculator
Calculate the relative risk (risk ratio) from a 2x2 contingency table to compare event rates between two groups.
Moving Average Calculator
Calculate the simple moving average (SMA) of the most recent data points to smooth time-series data.
Exponential Smoothing Calculator
Apply single exponential smoothing to forecast the next value in a time series by weighting recent observations more heavily.
Growth Rate Calculator
Calculate the growth rate between two values, expressed as a percentage change over a single period.
Compound Growth Calculator
Calculate the Compound Annual Growth Rate (CAGR) that represents the steady growth rate over multiple periods.
Percentage Change Calculator
Calculate the percentage change between an old value and a new value to quantify the relative magnitude of change.
Ratio Calculator
Calculate the ratio between two quantities, simplify it to lowest terms, and convert to other representations.
Proportion Calculator
Solve a proportion (a/b = c/d) for the missing value using cross-multiplication.
Index Number Calculator
Calculate a simple price or quantity index number relative to a base period value.
Weighted Index Calculator
Calculate a weighted composite index number from multiple items with different relative importance weights.
Time Series Trend Calculator
Estimate a linear trend from time-series data using the slope of the regression line over time periods.
Seasonal Adjustment Calculator
Remove seasonal effects from time-series data by dividing the observed value by its seasonal index.
Outlier Detection Calculator
Detect potential outliers using the IQR method by checking if a value falls outside the inner fences (Q1 - 1.5*IQR, Q3 + 1.5*IQR).
Data Normalization Calculator
Normalize a value to the [0, 1] range using min-max normalization, given the minimum and maximum of the dataset.
Standardization Calculator
Standardize a value by subtracting the mean and dividing by the standard deviation (z-score standardization).
Entropy Calculator
Calculate Shannon entropy, which measures the uncertainty or information content of a probability distribution.
Gini Coefficient Calculator
Calculate the Gini coefficient to measure inequality in a distribution, ranging from 0 (perfect equality) to 1 (maximum inequality).
Lorenz Curve Calculator
Calculate Lorenz curve coordinates showing cumulative income share versus cumulative population share.
Herfindahl Index Calculator
Calculate the Herfindahl-Hirschman Index (HHI) to measure market concentration by summing squared market shares.
Sampling Error Calculator
Calculate the maximum sampling error for a proportion at a given confidence level and sample size.
Finite Population Correction Calculator
Apply the finite population correction factor to adjust the standard error when sampling a significant fraction of the population.
Linear Regression Slope Calculator
Calculate the slope of a simple linear regression line from summary statistics of x and y data.
Regression Intercept Calculator
Calculate the y-intercept of the least-squares regression line from the slope and mean values of x and y.
R-Squared Calculator
Calculate the coefficient of determination R² from the sum of squares of regression and total sum of squares.
Adjusted R-Squared Calculator
Calculate adjusted R² that accounts for the number of predictors in a multiple regression model.
Standard Error of Regression Calculator
Calculate the standard error of the regression (root mean square error) measuring prediction accuracy.
Residual Calculator
Calculate the residual (prediction error) for an observation from its actual and predicted values.
Prediction Interval Calculator
Calculate a prediction interval for a new observation in simple linear regression from the standard error and sample size.
Correlation P-Value Calculator
Calculate the t-statistic for testing whether a correlation coefficient is significantly different from zero.
Multiple Regression F-Test Calculator
Calculate the F-statistic for testing overall significance of a multiple regression model.
ANOVA F-Statistic Calculator
Calculate the F-statistic for one-way ANOVA from between-group and within-group mean squares.
Mann-Whitney U Test Calculator
Calculate the Mann-Whitney U statistic for comparing two independent samples.
Kruskal-Wallis H Test Calculator
Calculate the Kruskal-Wallis H statistic for comparing three or more groups.
Spearman Rank Correlation Calculator
Calculate Spearman rank correlation coefficient.
Kendall Tau Calculator
Calculate Kendall tau from concordant and discordant pairs.
Chi-Square Goodness of Fit Calculator
Test if observed frequencies match expected frequencies.
Runs Test for Randomness Calculator
Test whether a binary sequence is random using the Wald-Wolfowitz runs test.
Durbin-Watson Statistic Calculator
Detect autocorrelation in regression residuals.
Levene Test Calculator
Test homogeneity of variances across groups.
Wilcoxon Signed-Rank Test Calculator
Non-parametric paired comparison test.
Fisher Exact Test Calculator
Calculate Fisher exact test for 2x2 contingency tables.
McNemar Test Calculator
Test for paired nominal data in a 2x2 table.
Cochran Q Test Calculator
Test equality of proportions across related groups.