Statistik

Ermitteln Sie den Perzentilwert jedes Datensatzes mit linearer Interpolation. Kostenloser Online-Perzentilrechner, der Ihre Zahlen ordnet und den Wert am gewählten Perzentil zurückgibt.

Berechnen Sie Populations- und Stichproben-Standardabweichung, Varianz und Mittelwert jedes Datensatzes sofort. Kostenloser Online-Standardabweichungsrechner mit Schritt-für-Schritt-Ergebnissen.

Berechnen Sie den z-Wert (Standardwert) eines Werts aus seinem Mittelwert und seiner Standardabweichung. Kostenloser Online-z-Wert-Rechner, der anzeigt, wie viele Standardabweichungen ein Punkt vom Mittelwert entfernt ist.

Calculate classification accuracy, precision, recall, F1 score, specificity and NPV from a confusion matrix (TP, TN, FP, FN).

Run a one-way ANOVA F-test from group summary statistics (n, mean, SD) and get the F statistic, p-value, and effect size.

Aktualisieren Sie eine A-priori- zu einer A-posteriori-Wahrscheinlichkeit mithilfe von Sensitivität und Falsch-Positiv-Rate über die Bayes-Regel.

Berechnen Sie Binomialwahrscheinlichkeiten P(X=k), höchstens oder mindestens k Erfolge in n Versuchen sowie Mittelwert und Varianz.

Wahrscheinlichkeit, dass mindestens zwei Personen in einer Gruppe denselben Geburtstag haben, für beliebige Gruppengröße und Anzahl der Tage.

Chancen, günstige Karten aus einem Stapel zu ziehen: genau k oder mindestens eine in n Zügen ohne Zurücklegen.

Testen Sie mit einem Chi-Quadrat-Test, ob beobachtete Häufigkeiten den erwarteten Häufigkeiten oder Anteilen entsprechen.

Testen Sie den Zusammenhang zwischen zwei kategorialen Variablen anhand einer Kontingenztafel.

Berechnen Sie den Variationskoeffizienten (VK = SD/Mittelwert) als Prozentsatz aus Daten oder Kennzahlen.

Wahrscheinlichkeit für k Mal Kopf bei n Münzwürfen (fair oder gezinkt), genau, mindestens oder höchstens.

Ermitteln Sie P(A gegeben B) aus der gemeinsamen Wahrscheinlichkeit und P(B) und prüfen Sie, ob zwei Ereignisse unabhängig sind.

Berechnen Sie ein Konfidenzintervall für einen Mittelwert mit der z-Verteilung. Kostenloser Online-Rechner für Konfidenzintervalle für 90%-, 95%- und 99%-Niveaus mit Fehlermarge, unterer und oberer Grenze.

Berechnen Sie den Pearson-Korrelationskoeffizienten (r) zwischen zwei Datensätzen, um die Stärke und Richtung ihres linearen Zusammenhangs zu messen. Kostenloser Online-Korrelationsrechner mit r² und Steigung.

Berechnen Sie die Stichproben- oder Grundgesamtheitskovarianz zwischen zwei gleich langen Variablen x und y.

Calculate all nine deciles (D1–D9) for any data set. Deciles divide data into ten equal parts at the 10th, 20th, … 90th percentiles.

Berechnen Sie Mittelwert, Median, Modus, Spannweite, Varianz und Standardabweichung für jeden Datensatz.

Calculate the expected value, min, max, variance, and standard deviation for any dice expression (NdS + modifier).

Wahrscheinlichkeit, eine Zielsumme mit beliebiger Anzahl und Art von Würfeln zu erreichen, genau, mindestens oder höchstens.

Wenden Sie die 68-95-99,7-Regel auf einen normalverteilten Datensatz an: Erhalten Sie die Ein-, Zwei- und Drei-Sigma-Intervalle und Prozentsätze.

Berechnen Sie Erwartungswert, Varianz und Standardabweichung aus einer diskreten Wahrscheinlichkeitsverteilungstabelle.

Ermitteln Sie Exponentialwahrscheinlichkeiten P(X<x) und P(X>x) für eine gegebene Rate sowie Mittelwert und Varianz.

Erhalten Sie Min, Q1, Median, Q3, Max und IQA aus einem Datensatz für eine Boxplot-Zusammenfassung.

Ermitteln Sie die Wahrscheinlichkeit, dass der erste Erfolg im Versuch k eintritt, sowie kumulative Wahrscheinlichkeit, Mittelwert und Varianz.

Wahrscheinlichkeit, k Erfolge in n Zügen ohne Zurücklegen aus einer endlichen Grundgesamtheit der Größe N zu ziehen.

Berechnen Sie den Interquartilsabstand, die Tukey-Zäune und markieren Sie Ausreißer in einem Datensatz.

Find the interquartile range, quartiles, and five-number summary for any data set — with a normal-distribution visualization of the IQR.

Passen Sie eine Kleinste-Quadrate-Gerade an: Steigung, Achsenabschnitt, R-Quadrat, Gleichung und Vorhersage bei einem Wert.

Calculate lottery jackpot odds and prize-tier probabilities for any pool size and draw count using combinations.

Berechnen Sie die Fehlermarge für einen Mittelwert oder einen Anteil bei einem gewählten Konfidenzniveau.

Calculate the mean absolute deviation, mean, median, range, and standard deviation of any data set.

Find the median, Q1, Q3, interquartile range, mode and range of any dataset — enter numbers separated by commas.

Calculate the midrange of a data set — the average of the minimum and maximum values — instantly from any list of numbers.

Find the mode (most frequently occurring value) of any dataset, with frequency breakdown and support for bimodal and multimodal data.

Calculate Mean Squared Error (MSE), Root MSE (RMSE), Mean Absolute Error (MAE), and R² from actual and predicted values.

Wahrscheinlichkeit für k Misserfolge vor dem r-ten Erfolg, mit kumulativen Optionen, Mittelwert und Varianz.

Wandeln Sie z-Werte in Flächen und Flächen in z um und ermitteln Sie P(X<x), P(X>x) oder dazwischen für jede Normalkurve.

Convert between probability, decimal odds, fractional odds, and American/moneyline odds in one step.

Wandeln Sie Quoten in Wahrscheinlichkeiten und Wahrscheinlichkeiten in Quoten (für und gegen) mit einer übersichtlichen visuellen Aufschlüsselung um.

Testen Sie, ob sich ein Stichprobenanteil mit einem z-Test von einem hypothetischen Anteil unterscheidet.

Testen Sie mit einem Ein-Stichproben-t-Test, ob sich ein Stichprobenmittelwert von einem hypothetischen Wert unterscheidet.

Vergleichen Sie drei oder mehr Gruppenmittelwerte mit einem einfaktoriellen ANOVA-F-Test aus Datenlisten.

Detect outliers in a data set using the Z-score method — flag any value more than k standard deviations from the mean.

Wandeln Sie eine z-, t-, Chi-Quadrat- oder F-Teststatistik in einen p-Wert für jeden Schwanz um.

Testen Sie die mittlere Differenz zwischen gepaarten/Vorher-Nachher-Messungen mit einem gepaarten t-Test.

Berechnen Sie Permutationen (nPr) und Kombinationen (nCr) für beliebige n und r. Kostenloser Online-Rechner für Permutationen und Kombinationen mit Fakultäten und sofortigen Ergebnissen.

Berechnen Sie Poisson-Wahrscheinlichkeiten P(X=k), höchstens oder mindestens k Ereignisse bei einer gegebenen durchschnittlichen Rate Lambda.

Berechnen Sie die Wahrscheinlichkeit zweier unabhängiger Ereignisse: P(A und B), P(A oder B) und das Gegenereignis P(nicht A). Kostenloser Online-Wahrscheinlichkeitsrechner für einzelne und kombinierte Ereignisse.

Find Q1, Q2 (median), Q3, IQR and Tukey outlier fences for any data set — with a normal-distribution visualization and five-number summary.

Calculate the statistical range of a data set — the difference between the maximum and minimum values — plus mid-range and mean.

Calculate residuals (observed − predicted) for a set of data points. Get RSS, MSE, RMSE and a residual plot to diagnose model fit.

Calculate Relative Risk (RR), Odds Ratio (OR), Absolute Risk Difference and Number Needed to Treat/Harm from a 2×2 contingency table.

Calculate Relative Standard Error (RSE = SE / Mean × 100%) to assess the reliability of a survey or sample estimate.

Ermitteln Sie die nötige Stichprobengröße, um einen Mittelwert der Grundgesamtheit innerhalb einer Zielfehlermarge zu schätzen.

Berechnen Sie die nötige Stichprobengröße, um einen Anteil innerhalb einer gewählten Fehlermarge zu schätzen.

Calculate Simpson's Diversity Index (D) plus Shannon entropy and Pielou's evenness from species or category counts.

Ermitteln Sie den Standardfehler des Mittelwerts (SEM) aus einer Datenliste oder aus Stichproben-SD und -größe.

Vergleichen Sie zwei unabhängige Stichprobenanteile mit einem gepoolten Zwei-Anteile-z-Test.

Vergleichen Sie zwei unabhängige Gruppenmittelwerte mit dem t-Test nach Welch oder dem gepoolten Zwei-Stichproben-t-Test.

Stetige gleichmäßige Wahrscheinlichkeit über [a,b]: Ermitteln Sie P(c<X<d), Mittelwert und Varianz sofort.

Berechnen Sie Komplement-, Vereinigungs- und Schnittwahrscheinlichkeiten für zwei Ereignisse, unabhängig oder mit gegebener gemeinsamer Wahrscheinlichkeit.

Berechnen Sie einen gewichteten Durchschnitt (gewichteten Mittelwert) aus Wert-Gewicht-Paaren. Kostenloser Online-Rechner für gewichtete Durchschnitte für Noten, GPAs, Preise und Umfragedaten.

Calculate the mean x̄ = Σ m·p(x), variance, and standard deviation from a grouped frequency distribution using class midpoints.

Calculate the 5-number summary (min, Q1, median, Q3, max), IQR, range, and Tukey outlier fences from any data set.

Calculate A/B test statistical significance: enter visitor and conversion counts for control and variant to get the p-value, z-statistic, and relative lift.

Propagate absolute uncertainties through addition, subtraction, multiplication, and division using in-quadrature rules.

Sort any list of numbers in ascending or descending order instantly — also shows min, max, range and median.

Check whether a dataset conforms to Benford's Law using a chi-square test and MAD — useful for fraud detection and data validation.

Explore the Bertrand box paradox: set box counts (GG, GS, SS) and calculate the conditional probability that the second coin is gold given the first was gold.

Explore the Bertrand paradox: three valid definitions of a random chord in a circle yield three different probabilities.

Compute the PDF, CDF, mean, variance and mode of the Beta distribution for any shape parameters α and β.

Find the minimum group size for a target probability of two people sharing a birthday — the counterintuitive birthday paradox solved with interactive math.

Calculate the Bonferroni-corrected p-value threshold for multiple hypothesis tests to control the family-wise error rate (FWER).

Calculate min, Q1, median, Q3, max, IQR and outlier fences from a dataset, with a box-plot number line.

Explore the boy-or-girl probability paradox: how knowing a child is a boy changes the probability that both children are boys.

Calculate the standard error of the mean and sampling distribution using the Central Limit Theorem. Shows 68%, 95%, and 99.7% intervals.

Apply Chebyshev's inequality to find the minimum proportion of data within k standard deviations of the mean — valid for any probability distribution.

Calculate the class width for a grouped frequency distribution: (maximum − minimum) ÷ number of classes, with rounding guidance.

Calculate R² from actual and predicted values. Shows SS_res, SS_tot, residual stats and an actual-vs-predicted plot.

Calculate Cohen's d, Hedges' g and Glass's Δ from two group means, SDs and sample sizes.

Find the probability of getting at least one streak of k consecutive heads in n coin flips (fair or biased).

Simulate flipping a fair or biased coin up to 200 times and see the heads/tails breakdown, longest streaks and distribution.

Calculate Matthews Correlation Coefficient (MCC), Cohen's Kappa and a full confusion matrix from TP, TN, FP and FN counts.

Find k in the direct proportion y = kx from any (x, y) pair and predict y for any new x value.

Apply continuity correction to approximate a binomial probability using the normal distribution. Enter n, p and k to get the corrected z-scores and probability.

Compute Pearson r, r², regression slope, and t-statistic between two data sets with a live scatter plot and regression line.

Find the critical value for z, t, chi-square, or F distributions given a significance level and tail type.

Fit a cubic polynomial y = dx³ + cx² + bx + a to your data using least-squares regression. Shows R², all 4 coefficients and a prediction.

Convert decimal (European) odds to payout, profit and implied win probability for any stake.

Calculate degrees of freedom for one-sample t-test, two-sample t-test, Welch's t-test, one-way ANOVA and chi-square tests.

Find the expected average, standard deviation, min and max for rolling any number of dice — d4 through d100 or custom sides.

Calculate all key measures of statistical dispersion — range, variance, standard deviation, IQR and MAD — from a list of numbers.

Enter a data set to compute mean, median, mode, range and standard deviation, with a distribution curve showing data spread and key markers.

Convert between effect size measures: Cohen's d, Pearson r, eta-squared, Cohen's f, odds ratio and probability of superiority.

Propagate measurement uncertainties through addition, subtraction, multiplication, division, and power operations using standard error-propagation formulas.

Predict a future value using two known data points by fitting a continuous exponential growth model P(t) = P₀·e^(rt).

Fit an exponential curve y = a·e^(bx) to data points using least-squares linearisation and compute R² goodness-of-fit.

Calculate the F-statistic and two-tailed p-value to test whether two sample variances are significantly different.

Calculate false positive rate, false discovery rate, PPV and NPV for any diagnostic test given prevalence, sensitivity and specificity.

See how a rare condition causes most positive test results to be false positives, even with a highly accurate test.

Calculate Q1 (the first quartile / 25th percentile) for any data set using the Tukey hinges method, with the five-number summary and IQR.

Compute the exact p-value for a 2×2 contingency table using Fisher's exact test, plus odds ratio and 95% CI.

Calculate the weighted average star rating, Bayesian average and positive review percentage from a 5-star distribution.

Convert fractional betting odds (e.g. 5/2) to decimal odds, implied probability, and potential payout.

Build a grouped frequency distribution from any data set: class boundaries, frequencies, relative frequencies and cumulative counts.

Plot a frequency polygon and compute the weighted mean and standard deviation from grouped data class midpoints and frequencies.

Arrange any list of numbers from greatest to least (descending order) instantly, with min, max, range, mean and median.

Build a frequency histogram from any dataset: enter comma-separated values, choose the number of bins, and see counts, relative frequencies, mean and standard deviation.

Perform a one-sample z-test: enter sample mean, population mean, std dev and n to get z-statistic, p-value and a reject/fail-to-reject decision.

Convert American, decimal or fractional betting odds to implied probability and strip out the bookmaker vig.

Calculate the Index of Qualitative Variation (IQV) to measure diversity or dispersion across nominal categories — from 0 (no variation) to 1 (maximum variation).

Find the z-score or x value for a given cumulative probability under a normal distribution. Enter p, mean and standard deviation.

Calculate the joint probability P(A∩B), the union P(A∪B), and conditional probabilities P(A|B) and P(B|A) for two events.

Sort a list of numbers from least to greatest (ascending order) and see the min, max, range, median, and mean.

Sort a list of decimal numbers from least to greatest with preserved precision. Also shows min, max, range, median, and mean.

Calculate the mean, median, mode, variance, PDF and CDF of a lognormal distribution from its log-mean μ and log-standard deviation σ.

Calculate the lower fence (Q1 − 1.5 × IQR) and upper fence to identify statistical outliers in a dataset using Tukey's box-plot method.

Compute the Mann-Whitney U statistic, z-score and two-tailed p-value for two independent groups using the normal approximation.

Run McNemar's chi-square test on a paired 2×2 table to compare two proportions from the same subjects.

Calculate mean, median, mode, range and standard deviation for any list of numbers. Paste or type your data set.

Calculate the median absolute deviation (MAD) of a dataset — a robust alternative to standard deviation that resists outliers.

Find the minimum and maximum values in any data set, plus range, mean, and median — with a number line visualization.

Convert moneyline odds to implied probability, decimal odds, fractional odds, and calculate your potential payout on any wager.

Calculate the exact win probability for staying or switching in the Monty Hall problem — generalised to any number of doors and host reveals.

Approximate binomial probabilities P(X ≤ k), P(X ≥ k), or P(X = k) using the normal distribution with continuity correction.

Calculate P(A or B) — the probability that at least one of two events occurs — for independent or mutually exclusive events.

Arrange any list of numbers — including fractions like 1/2 and 3/4 — from least to greatest, and show their positions on a number line.

Sort a list of decimal numbers from smallest to largest and see them aligned by decimal place — useful for comparing prices, measurements or test scores.

Sort any list of numbers in ascending or descending order and assign a rank to each value — tied numbers receive an average rank automatically.

Calculate p-hat (sample proportion), standard error, margin of error, and confidence interval for a proportion.

Explore Parrondo's paradox: calculate the expected gain per step of two individually losing games and their winning alternating combination.

Calculate the total number of possible password combinations, entropy in bits, and estimated brute-force crack time.

Compute the Pearson correlation coefficient r between two variables with step-by-step working, r², t-statistic, and significance test at α = 0.05.

Find the percentile rank of a score in a dataset — what percentage of values fall at or below it. Uses the (L + 0.5E) / N formula.

Find the central angle of a pie chart slice in degrees — enter the slice value and the total, and get the sector angle and percentage share.

Enter comma-separated values and labels to instantly calculate the percentage and degree angle for each slice of a pie chart.

Convert a pie chart sector angle (in degrees) to a percentage share — enter the angle and get the percentage, radians, and remainder.

Calculate the point estimate (sample mean), standard error, margin of error and confidence interval for a population mean.

Fit a polynomial curve of any degree (1–5) to your data using least-squares regression and compute R² and RMSE.

Calculate population variance (σ²), population standard deviation (σ), and sample variance (s²) from a list of numbers.

Calculate the number of possible combinations when choosing r items from n — without replacement (standard nCr) or with replacement (repetition allowed).

Convert pre-test probability to post-test probability using sensitivity, specificity and the likelihood ratio. Works for positive and negative test results.

Convert favorable and total outcomes into a probability fraction, percentage, and odds — with complement and odds-for display.

Calculate Cp and Cpk process capability indices from specification limits, process mean and standard deviation. Includes sigma level and out-of-spec estimate.

Fit a least-squares parabola y = cx² + bx + a to your data. Outputs R², all 3 coefficients, the equation and an optional prediction.

Fit a degree-4 polynomial y = ex⁴ + dx³ + cx² + bx + a to your data using least-squares regression. Shows R², all 5 coefficients and a prediction.

Convert a z-score back to the original raw score using x = μ + z·σ. Enter the z-score, mean and standard deviation to get the raw value and percentile.

Calculate the PDF, CDF, mean, mode, median and variance of the Rayleigh distribution for a given scale parameter σ and value x.

Calculate the relative error and percent error between a measured value and a true (accepted) value, plus accuracy category.

Calculate the relative frequency of an event as a proportion and percentage of total observations, plus the complement.

Calculate Relative Risk (RR), Absolute Risk Difference and a 95% confidence interval from two event-rate percentages.

Calculate roulette payouts, win probability and house edge for any bet type on American (38-pocket) or European (37-pocket) wheels.

Calculate the standard error, margin of error and confidence interval for a sample proportion using the normal approximation.

Calculate the sampling error (margin of error) for a proportion survey and find the sample size needed for ±3% or ±5% precision.

Calculate sensitivity, specificity, PPV, NPV, accuracy, F1, likelihood ratios and Youden's J from a 2×2 confusion matrix.

Calculate diagnostic sensitivity (recall / true positive rate): TP ÷ (TP + FN). Also shows the miss rate (false negative rate).

Calculate Shannon entropy H from a probability distribution — in bits, nats or hartleys — with maximum entropy and efficiency for any number of outcomes.

Compute Simpson's Diversity Index (D), Shannon entropy, Pielou's evenness, and Berger–Parker dominance from species counts.

Compute sample or population skewness of a dataset using the Fisher-Pearson coefficient, plus Pearson median skewness and excess kurtosis.

Compute Spearman's rank correlation coefficient rₛ for paired data — handles ties using average ranks.

Calculate test specificity (true negative rate) and false positive rate from true negatives and false positives.

Calculate required sample size or statistical power for a two-sample test. Uses Cohen's d, significance level α, and the z-approximation.

Build a stem-and-leaf plot from your data set and get the five-number summary instantly.

Compute the sum of squared deviations SS = Σ(xᵢ − x̄)² plus sample and population variance and standard deviation from any list of numbers.

Compute the one-sample t-statistic, degrees of freedom, standard error, and two-tailed p-value from sample mean, standard deviation, and sample size.

Calculate Q3 (the third quartile / 75th percentile) for any data set using the Tukey hinges method, with the five-number summary and IQR.

Explore the two-envelopes paradox: calculate the expected value of switching vs keeping your envelope and find the break-even probability for switching.

Calculate both Tukey fences (upper: Q3 + k × IQR, lower: Q1 − k × IQR) to find outlier thresholds for any data set.

Calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) for a Shewhart control chart using the process mean and sigma.

Calculate the upper Tukey fence (Q3 + k × IQR) from Q1 and Q3 to identify potential high outliers in a data set.

Calculate sample variance, population variance, standard deviation, coefficient of variation, and standard error from any numeric data set.

Calculate union, intersection, A-only, B-only, and conditional probabilities for two overlapping sets with a Venn diagram breakdown.

Calculate Weibull PDF, CDF, survival probability, mean, median, mode, and variance from shape k and scale λ.

Run a non-parametric Wilcoxon rank sum / Mann-Whitney U test to compare two independent groups without assuming normality.

Calculate Youden's J statistic to measure a diagnostic test's overall discriminatory ability from sensitivity and specificity.