Clarity71 FREE TOOLS
Statistics, made clearer.
Summarize datasets, compare distributions and explore probability with stated statistical conventions.
Tools in this category
Geometric Mean Calculator
Find the multiplicative average of strictly positive observations.
Harmonic Mean Calculator
Calculate the harmonic mean of positive numbers, see the reciprocal calculation, and compare it with the arithmetic mean.
Root Mean Square Calculator
Find the square root of the average squared observation.
Population Variance Calculator
Find mean squared distance from the mean using denominator n.
Sample Variance Calculator
Estimate variance using Bessel’s correction for a sample.
Standard Error of the Mean Calculator
Estimate standard error from a sample standard deviation and sample size.
Coefficient of Variation Calculator
Find sample standard deviation relative to a positive mean.
Mean Absolute Deviation Calculator
Find average absolute distance from the arithmetic mean.
Median Absolute Deviation Calculator
Find the median absolute distance from the sample median.
Interquartile Range Calculator
Find the spread of the middle half of your data.
Percentile Calculator
Estimate a requested percentile of a numeric sample.
Percentile Rank Calculator
Find the percentage of observations at or below a selected value.
IQR Outlier Fences Calculator
Calculate Tukey’s lower and upper fences from the sample quartiles.
Trimmed Mean Calculator
Average data after removing equal counts from each sorted tail.
Mode Calculator
Find the most frequent exact numeric values in a dataset.
Normal Distribution Density Calculator
Evaluate the height of a normal probability density curve.
Normal Mean Confidence Interval Calculator
Find a mean interval using a supplied critical z value.
Proportion Margin of Error Calculator
Estimate normal-approximation margin of error for a proportion.
Proportion Sample Size Calculator
Estimate a sample size for a specified absolute proportion margin.
Finite Population Sample Adjustment Calculator
Adjust an initial sample size for a finite population.
Binomial Probability Calculator
Find the probability of exactly k successes in independent trials.
Binomial Mean and Variance Calculator
Find expected successes and variance for a binomial model.
Poisson Probability Calculator
Find the probability of exactly k events for a constant-rate Poisson model.
Geometric Probability Calculator
Find the probability that the first success occurs on a specified trial.
Exponential Survival Probability Calculator
Find probability that a waiting time exceeds a given duration.
Independent Events Intersection Calculator
Calculate the chance that two independent events both occur.
Probability of Either Event Calculator
Find the probability of A or B, including their overlap.
Conditional Probability Calculator
Find probability of A given B from joint and conditioning probabilities.
Bayes’ Theorem Calculator
Update a prior probability using two conditional likelihoods.
Discrete Expected Value Calculator
Find a weighted expected outcome from values and probabilities.
Pearson Correlation Calculator
Measure linear association between paired numeric observations.
Simple Linear Regression Calculator
Fit an ordinary least-squares line to paired numeric data.
P-Value Calculator
Convert a z or t statistic into a one-sided or two-sided p-value with an explicit alternative hypothesis.
One Sample T-Test Calculator
Calculate a one-sample t-test from raw observations. Get the p-value, t statistic and degrees of freedom for a two-sided or one-sided hypothesis.
Two Sample T-Test Calculator
Compare independent sample means using Welch’s test or an explicitly chosen pooled-variance t-test.
Paired T-Test Calculator
Compare matched before-and-after measurements by testing the mean of paired differences.
One-Way ANOVA Calculator
Compare the means of three independent groups and see the between-group and within-group variation.
Chi-Square Goodness of Fit Calculator
Compare observed category counts against fully specified expected counts with a Pearson chi-square test.
Chi-Square Test of Independence
Test association in a 2 × 2 count table and inspect the smallest expected cell count.
Cohen’s d Calculator
Measure the standardized difference between two independent sample means, with an approximate Hedges correction.
T Confidence Interval Calculator
Estimate a population mean interval from sample data when the population standard deviation is unknown.
Normal Distribution Probability Calculator
Find the probability between two bounds for a normal distribution, plus the probabilities in both outside tails.
Spearman Rank Correlation Calculator
Measure monotonic association between paired observations, including tied values assigned average ranks.
Two Proportion Z-Test Calculator
Compare success rates in two independent groups using a pooled two-proportion z-test.
Confusion Matrix Calculator
Evaluate a binary classifier with accuracy, precision, recall, specificity and F1 from four outcome counts.
Multiple Testing Correction Calculator
Adjust a family of p-values using Bonferroni, Holm or Benjamini–Hochberg while preserving your input order.
Uniform Distribution Calculator
Find the cumulative probability and density for a continuous uniform distribution.
Triangular Distribution Calculator
Calculate cumulative probability for a bounded triangular model with a specified mode.
Hypergeometric Probability Calculator
Find the chance of exactly k marked items when sampling without replacement.
Negative Binomial Probability Calculator
Find the probability of k failures before the rth success in independent trials.
Beta Distribution Calculator
Evaluate cumulative probability for a beta distribution on the unit interval.
Gamma Distribution Calculator
Evaluate a gamma cumulative probability using shape and scale parameters.
Weibull Distribution Calculator
Find failure and survival probabilities for a two-parameter Weibull model.
Lognormal Distribution Calculator
Evaluate cumulative probability when the natural logarithm is normally distributed.
Logistic Distribution Calculator
Evaluate cumulative probability for a logistic location-scale distribution.
Cauchy Distribution Calculator
Find cumulative probability for a Cauchy distribution from location and scale.
Pareto Distribution Calculator
Evaluate cumulative and tail probabilities for a Type I Pareto distribution.
Rayleigh Distribution Calculator
Find cumulative probability for a nonnegative Rayleigh-distributed magnitude.
Gumbel Distribution Calculator
Evaluate the maximum-form Gumbel cumulative distribution.
Laplace Distribution Calculator
Evaluate a symmetric Laplace cumulative probability.
Discrete Uniform Distribution Calculator
Calculate cumulative probability across equally likely integers in an inclusive range.
Shannon Entropy Calculator
Measure uncertainty in a discrete distribution using nonnegative category counts.
Gini Coefficient Calculator
Measure inequality in a nonnegative list of values using the population Gini convention.
KL Divergence Calculator
Compare two aligned discrete distributions using Kullback–Leibler divergence.
Cosine Similarity Calculator
Compare the direction of two numeric vectors of equal length.
Sample Covariance Calculator
Measure joint variation of paired numeric observations using the n−1 divisor.
Adjusted Sample Skewness Calculator
Calculate adjusted Fisher–Pearson skewness for a numeric sample.
Sample Excess Kurtosis Calculator
Compute bias-corrected Fisher excess kurtosis from sample observations.
Numeric Frequency Table Generator
Count distinct numeric observations and their relative frequencies.
Forecast Accuracy Calculator
Compare aligned actual and predicted values using MAE, RMSE, bias, MAPE and WAPE.
Process Capability Cp Cpk Calculator
Estimate capability indices from specification limits, process mean and within-process standard deviation.
Choosing a tool for statistics
Start with the type of data and the question. Check sample versus population definitions, independence assumptions and the chosen percentile convention.