Statistics
Averages, spread, percentiles, probability, the normal distribution, confidence intervals, sample sizes, correlation and regression.
Mean, Median and Mode Calculator
The mean, median and every mode of a data set, with its range and quartiles.
Variance Calculator
The sample or population variance of a data set, with the standard deviation, mean, sum of squares and coefficient of variation.
Percentile Calculator
The value at any percentile of a data set, by nearest rank or linear interpolation, or the percentile rank of a value.
Probability Calculator
The probability of two events together or either, a conditional probability by Bayes’ theorem, or k successes in n independent trials.
Permutation and Combination Calculator
How many ways to arrange or choose r items from n, with or without repetition, exactly for large numbers.
Z-Score Calculator
How many standard deviations a value, or a sample mean, lies from the mean, with the probability below, above and in both tails.
Normal Distribution Calculator
The probability below, above, between or outside values of any normal distribution, or the value at a given probability.
Confidence Interval Calculator
A confidence interval for a mean or a proportion, using Student’s t automatically when the population standard deviation is unknown.
Margin of Error Calculator
How far a poll or survey result could be from the truth, at any confidence level, with the correction for sampling much of a small population.
Sample Size Calculator
How many people to survey, or measurements to take, for a chosen margin of error and confidence level, rounded up.
Correlation Coefficient Calculator
Pearson’s r, r squared, the covariance and Spearman’s rank correlation for paired data.
Linear Regression Calculator
The least-squares line of best fit through paired data, with r squared and predictions.
Poisson Distribution Calculator
The probability of exactly k events, at most k, fewer than k, at least k or more than k, when events happen at an average rate λ per interval.
Expected Value Calculator
The expected value, variance and standard deviation of a set of outcomes and their probabilities, with a check that the probabilities add up to 100%.
Relative Risk Calculator
The relative risk and odds ratio from a 2 × 2 table of exposure and outcome, with confidence intervals, the risk in each group and the risk difference.
Effect Size Calculator
Cohen’s d and Hedges’ g for the difference between two group means, from each group’s mean, standard deviation and size, with the pooled standard deviation.
Shannon Diversity Index Calculator
Shannon H, evenness and effective species from counts.
P-Value Calculator
The p-value for a z, t, chi-square or F test statistic, one-tailed or two-tailed, with the areas on each side and a comparison with your significance level.
t-Test Calculator
One-sample, two-sample (Welch or pooled) and paired t-tests from summary statistics: the t statistic, degrees of freedom, p-value and a confidence interval for the difference.
Chi-Square Calculator
Chi-square goodness of fit: compare observed counts with what you expected, and get χ², its degrees of freedom and the p-value.
ANOVA Calculator
One-way analysis of variance from each group’s size, mean and standard deviation: the F statistic, p-value, sums of squares and the ANOVA table.
Quartile Calculator
The first and third quartiles, median, interquartile range, five-number summary and 1.5 × IQR outlier fences of a data set, by linear interpolation, nearest rank or Tukey’s hinges.
Odds Calculator
Convert fractional, decimal and moneyline odds into each other and into implied probability, and see the margin built into a two-way market.
Every page in this category shows which convention it uses, because statistics is full of choices that give different answers to the same data. A sample variance divides by n − 1 and a population variance by n. The 75th percentile of eight numbers is 5 by one standard method and 5.5 by another, and both are right. A confidence interval built on a small sample needs Student’s t rather than the normal distribution, or it comes out too narrow. A survey of 400 people out of a company of 500 has a much smaller margin of error than 400 out of a country. Where a page makes one of these choices, it says which, and it lets you pick where the choice is yours. Critical values are calculated exactly for any confidence level and any sample size, not read from a printed table, so a 97% interval or a sample of 37 needs no rounding to the nearest row. Probabilities are entered as percentages, and data sets are entered one value per row, with negative numbers and decimals allowed.