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Calculators/Maths/Statistics

Statistics calculators

Averages, spread, distributions, confidence intervals and correlation for data sets you paste straight in, with the formula shown every time.

Descriptive statisticsMean, median, mode, spread and quartiles for a data set.Weighted averageAverage where each value carries its own weight.Z-score & percentileHow far a value sits from the mean, in standard deviations.Normal distribution probabilityArea under the bell curve between two points.Confidence interval for a meanMargin of error around a sample average.Required sample sizeHow many responses a survey needs.Correlation & linear regressionPearson r and the line of best fit for paired data.Binomial probabilityChance of exactly k successes in n independent trials.Probability of eventsCombines two event probabilities: and, or, neither.Odds ↔ probabilityConverts between fractional odds, decimal odds and percent.GPA / weighted gradeGrade point average across units with credit weights.Grade needed on the finalWhat the last assessment must score to hit a target.Interquartile Range (IQR)Q1, Q3 and the interquartile range for a list of numbers.Roll a D20Rolls one or more dice of a chosen size and gives the probability of the result you asked for.Binomial DistributionFull binomial probability distribution: probability of every outcome, mean, variance, standard deviation and shape.T-testOne or two-sample t-test with the t-statistic converted to a p-value and a significance verdict.Relative frequencyEach category's share of the total, and the running cumulative share, from a list of raw counts.Ascending Order CalculatorSorts a list of numbers into ascending order, with descending order and basic stats shown too.Average Percentage CalculatorSimple and sample-size-weighted average of several percentages, and why they can differ.Letter Grade Average CalculatorAverages several letter grades by converting each to a 4.0 grade-point value, then back to a letter.Relative & Absolute ErrorAbsolute error and relative error, as a decimal ratio, between a measured and true value.Range of a Data SetThe minimum, maximum and range (spread between them) for a list of numbers.Poker Odds CalculatorRough win probability from your number of outs, using the standard rule of 2 and 4 approximation.Conditional probabilityP(A given B), worked from either the joint probability of both events or a joint frequency table.Pie Chart Percentages CalculatorTurns a list of category values into the percentage share and degree angle each slice needs for a pie chart.Simpson's Diversity Index CalculatorSimpson’s Diversity Index (1-D) from a list of species or category counts, plus the underlying Simpson’s Index and its reciprocal.Roulette Odds & Payout CalculatorProbability of winning a chosen roulette bet and its payout ratio, for European (single-zero) or American (double-zero) wheels.Coefficient of variationRelative variability of a data set: standard deviation as a percentage of the mean.SkewnessSample skewness: whether the data leans left or right of the mean.Poisson probabilityChance of a given number of independent events in a fixed interval, given the average rate.Geometric probabilityChance the first success happens on a given trial, for repeated independent trials.Hypergeometric probabilityChance of drawing an exact number of successes from a finite population, without replacement.Chi-square goodness of fitTests whether observed category counts match expected counts.Cohen's d (effect size)Standardised difference between two group means, in pooled standard deviations.Margin of error (proportion)Margin of error for a survey proportion at a chosen confidence level.Relative riskCompares event risk between an exposed and an unexposed (or treated and control) group.T-statistic (one or two sample)How many standard errors a sample mean is from the reference value, or from another mean.Z-test for a proportionTests a sample proportion against a hypothesised population proportion.Expected value of a discrete distributionMean and standard deviation of a discrete random variable from its outcomes and probabilities.Outlier fences (Tukey)The IQR-based cutoffs beyond which a data point counts as an outlier.Residual CalculatorResiduals (observed minus predicted) for a data set against its least-squares regression line.Inverse Normal Distribution CalculatorGiven a target percentile, the value and z-score for a normal distribution with a stated mean and standard deviation.Critical Value CalculatorThe critical t or z value for a given significance level, degrees of freedom and tail direction.P-Hat (Sample Proportion) CalculatorSample proportion p-hat from a count of successes and a sample size, the standard notation used before a margin of error or confidence interval.Normal Approximation CalculatorMean and standard deviation of the normal approximation to a binomial distribution, with the np≥5 rule checked.CovarianceHow two variables move together, in sample or population form.Standard error of the meanHow much a sample mean is expected to vary from the true population mean.F-test for equal variancesCompares the spread of two samples using the ratio of their variances.Negative binomial probabilityChance that the rth success happens on exactly the kth independent trial.Percentile rankWhat percentage of a data set falls at or below a given value.Value at a percentileFinds the data value at any percentile using linear interpolation.Mean absolute deviationThe average distance of each data point from the mean (or median).Bayes’ theoremUpdates the probability of an event given new evidence.Class width for a histogramHow wide each bin should be, from either a target class count or Sturges’ rule.Spearman’s rank correlationMeasures a monotonic relationship between two variables using their ranks, ties included.Chebyshev’s theoremMinimum share of any data set within k standard deviations of the mean, whatever its shape.Two-proportion z-testTests whether two independent samples have significantly different proportions.Geometric meanThe geometric mean of a set of positive numbers, contrasted with the ordinary arithmetic mean.DPMO CalculatorDefects per million opportunities from a defect count, units produced and opportunities per unit, the standard Six Sigma quality metric.Dice Sum ProbabilityProbability of a target sum when rolling two or more dice together, with the full sum distribution.Drop Rate CalculatorProbability of getting at least one item drop over a number of attempts, from a per-attempt drop chance.Poker Probability CalculatorProbability and odds of being dealt a chosen poker hand from a standard 52-card, 5-card deal.Percent to Letter Grade CalculatorConverts a single percentage score to a letter grade on a common 10-point scale.Implied Probability CalculatorConverts decimal, fractional or American betting odds into the implied win probability.Lottery Odds CalculatorOdds of matching every number in a lottery draw, from the total number pool and how many are drawn.Pooled standard deviationCombines two sample standard deviations into one pooled estimate for equal-variance tests.Z-test for a single meanTests a sample mean against a hypothesised mean when the population standard deviation is known Quartile deviationHalf the interquartile range: a robust spread measure, less sensitive to outliers than the SD.Range rule of thumb for standard deviationA quick estimate of standard deviation from just the minimum and maximum of a data set.Mean & standard deviation from grouped dataEstimates the mean and standard deviation of a frequency table using class midpoints.Empirical rule (68-95-99.7)The share of normal data expected within 1, 2 and 3 standard deviations of the mean.KurtosisSample excess kurtosis: how heavy-tailed a data set is versus a normal distribution.Average Star CalculatorOverall average star rating from a breakdown of how many 1 to 5 star reviews were left.Implied Odds CalculatorWhether a drawing hand is profitable to call once likely future winnings are added to the pot.Continuity Correction CalculatorAdjusts a discrete value by ±0.5 before converting to a z-score, for approximating a discrete distribution with the normal curve.Marks Needed to Pass CalculatorMarks needed on a remaining test to reach an overall passing percentage.Roulette Odds CalculatorWin probability, payout odds and house edge for straight-up and even-money roulette bets, European or American wheel.TRIFR CalculatorTotal Recordable Injury Frequency Rate from recordable injuries and hours worked.Diagnostic test accuracy metricsSensitivity, specificity, predictive values and accuracy from a 2×2 test result table.Birthday paradox probabilityChance that at least two people in a group share the same birthday.Bonferroni correctionAdjusts the significance threshold when running many statistical tests at once.Benford's law leading-digit checkCompares a data set's leading digits against the distribution natural data follows.One-way ANOVA (F-statistic)Tests whether three or more group means differ, from the raw data in each group.Lotto Odds CalculatorOdds of matching every main number in a lottery draw, with or without a separate bonus ball pool.McNemar's testTests whether paired binary outcomes changed, using the two discordant-pair counts.Mann-Whitney U test (Wilcoxon rank-sum)Compares two independent samples for a shift in distribution, using ranks instead of means.MidrangeThe midpoint between the smallest and largest value in a data set, a quick measure of centre.Sum of squaresTotal squared deviation of each data point from the mean, the building block of variance.Confusion matrixTurns the four counts of a binary confusion matrix into accuracy, precision, recall and F1.Youden's indexCombines a test’s sensitivity and specificity into one score of diagnostic performance.Weibull distributionComputes the PDF, CDF, mean and variance of a Weibull distribution from its shape and scale.Rayleigh distributionComputes the PDF, CDF, mean and variance of a Rayleigh distribution from its scale parameter.Fisher's exact testRuns a two-tailed Fisher exact test on a 2×2 contingency table of counts.Process capability indexCalculates Cp and Cpk from specification limits, the process mean and standard deviation.Degrees of freedomWorks out degrees of freedom for a one-sample, two-sample or chi-square test.Index of qualitative variationMeasures diversity among categorical frequencies on a 0 to 1 scale using the IQV formula.Beta distributionPDF, mean and variance of a beta distribution from its two shape parameters.Monty Hall problemWin probability from staying versus switching after the host reveals losing doors.Statistical power analysisAchieved power for a given sample size, and the sample size needed for a target power.Error propagationPropagates the uncertainty of two measurements through a sum, difference, product or quotient.p-value from a test statisticConverts a z, t, chi-square or F test statistic into a p-value, for any tail direction.Test grade / score percentageScore percentage and standard letter grade from correct answers out of total questions.Coin flip probabilityFlips a virtual coin and works out the probability of a given number of heads.Grade CalculatorOverall course grade and letter grade from a list of assignment scores and their weights.Median CalculatorThe middle value of a data set, sorted, with the position(s) used shown.

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