Statistics & Probability calculators (14)

Descriptive statistics, z-scores, normal and binomial probability, confidence intervals, sample size, regression.

Markdown version: /statistics.md · JSON: /api/v1/calculators?category=statistics

• Descriptive Statistics Calculator — Computes summary statistics for a list of numbers: count, sum, mean, median, mode, range, sample and population variance and standard deviation, standard error, coefficient of variation, quartiles (linear interpolation) and skewness. (md · api)
• Z-Score Calculator — Standardises a value against a mean and standard deviation (z = (x − μ) / σ) and reports the corresponding percentile and tail probabilities under the normal distribution. (md · api)
• Normal Distribution Calculator — Computes cumulative probabilities P(X < x), P(X > x) and P(x < X < x2) and the density for a normal (Gaussian) distribution with a given mean and standard deviation. (md · api)
• Confidence Interval Calculator — Computes a confidence interval for a population mean from the sample mean, standard deviation and sample size using the normal (z) critical value: mean ± z · s / √n. (md · api)
• Sample Size Calculator — Computes the number of respondents needed to estimate a population proportion within a given margin of error at a given confidence level (Cochran's formula), with an optional finite population correction. (md · api)
• Margin of Error Calculator — Computes the margin of error (half-width of the confidence interval) of a sample proportion from the sample size, confidence level and observed percentage, with an optional finite population correction. (md · api)
• Binomial Distribution Calculator — Computes the probability of exactly, at most, at least, fewer than or more than k successes in n independent trials with success probability p, plus the mean, variance and standard deviation of the distribution. (md · api)
• Poisson Distribution Calculator — Computes the probability of exactly, at most, at least, fewer than or more than k events when events occur independently at a constant average rate λ per interval, plus the mean, variance and standard deviation. (md · api)
• Probability of Two Events Calculator — Combines the probabilities of two events A and B that are either independent or mutually exclusive into the probabilities of both, at least one, exactly one, one but not the other, and neither occurring. (md · api)
• Correlation Coefficient Calculator — Computes the Pearson product-moment correlation coefficient r, the coefficient of determination r², and the sample covariance for two paired lists of numbers, with a strength/direction interpretation. (md · api)
• Linear Regression Calculator — Fits an ordinary least-squares line to paired (x, y) data and returns the slope, intercept, equation, Pearson r, R², the standard error of the estimate and an optional prediction for a new x. (md · api)
• Weighted Average Calculator — Computes the weighted arithmetic mean Σ(w·x) / Σw of a list of values and a matching list of weights, along with the total weight and the unweighted mean for comparison. (md · api)
• Percentile Calculator — For a list of numbers, computes the value at a given percentile (linear interpolation, as in Excel PERCENTILE.INC) and/or the percentile rank of a given value (percentage of values below it, counting ties as half). (md · api)
• Expected Value Calculator — Computes the expected value E[X] = Σ x·p(x), the variance and the standard deviation of a discrete random variable from its list of outcomes and their probabilities. (md · api)