Data, sampling, and estimation
Statistics Calculators
Summarize numeric datasets and plan samples without hiding denominator choices, interpolation rules, or survey-design assumptions. Each calculator identifies the statistical boundary behind its answer and keeps a reproducible example beside the calculation.
200 statistics calculatorsDescriptive dataSampling and estimationConfidence intervalsHypothesis testsDistribution analysisTime seriesRobust and nonparametric methodsRegression and correlation
Explore center, spread, order statistics, robust summaries, and dataset scale. Pages that depend on quartiles or percentiles identify their interpolation convention instead of presenting the result as universal across software.
Plan sample sizes, margins of error, finite-population adjustments, cluster effects, stratum allocations, and survey-weight effective sample size. These tools separate arithmetic precision from representativeness and study design.
Estimate uncertainty for means, proportions, rates, ratios, correlations, regression quantities, predictions, and normal-theory variability. Each page states the interval convention and exposes any critical value supplied by the user.
Evaluate mean, proportion, contingency-table, variance, rank, sequence, and outlier questions. Results include the statistic, reference degrees of freedom where applicable, and a two-sided or upper-tail p-value labeled by method.
Measure paired association, fit simple regression quantities, inspect explained variation and collinearity, and convert between common model scales. Pages distinguish arithmetic identities from claims about causation or model adequacy.
Work with Bernoulli, binomial, Poisson, uniform, exponential, Weibull, lognormal, gamma, beta, F, and normal quantities, then summarize skewness, kurtosis, and count dispersion with their parameter conventions visible.
Use resistant centers, pairwise differences, ranks, empirical probabilities, and robust fences when a mean-and-variance summary is not enough. Each tool names its order-statistic convention and screening limits.
Smooth ordered observations, measure serial dependence, evaluate forecast errors, estimate seasonal factors, and project trends while keeping window placement and forecast conventions explicit.
Plan sample sizes, compare standardized effects, count factorial runs, and make design assumptions visible before collecting data.
Translate two-by-two counts and population denominators into sensitivity, risk, prevalence, likelihood, and agreement measures with their conditioning rules stated.
Choosing a descriptive summary
The arithmetic mean uses every observation, while the median and trimmed or winsorized means respond differently to long tails and extreme values. Spread measures also answer different questions: standard deviation follows deviations from the mean, the interquartile range describes the middle half, and range uses only the two endpoints.
Sample and population denominators
Variance and standard deviation pages distinguish a complete population from a sample used to estimate a larger population. That choice changes the denominator and should be made from the study boundary, not selected because one numerical answer looks preferable.
Percentiles and software conventions
Quantiles can differ across programs because several interpolation rules are legitimate. The dataset percentile and quartile pages in this category state that they use type-7 linear interpolation, making comparison and reproduction possible.
Planning a sample
Sample-size formulas begin with a confidence level, expected variability, and desired precision. Finite populations, nonresponse, clustering, unequal weights, and stratum allocation can then change how many records must be approached or observed.
What a larger sample cannot repair
Increasing the count generally reduces sampling error under the assumed design. It does not repair a biased frame, a poor measurement, systematic nonresponse, dependence ignored by the formula, or a mismatch between the sampled population and the population named in the conclusion.