统计

使用线性插值求任意数据集的百分位数值。免费的在线百分位数计算器，对你的数字进行排序并返回任意所选百分位数处的值。

即时计算任意数据集的总体和样本标准差、方差和均值。免费的在线标准差计算器，提供分步结果。

根据均值和标准差计算一个值的 z 分数（标准分）。免费的在线 z 分数计算器，显示一个点距离均值有多少个标准差。

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.

利用灵敏度和假阳性率，通过贝叶斯法则将先验概率更新为后验概率。

计算 n 次试验中恰好 k 次、至多或至少 k 次成功的二项概率，以及均值和方差。

任意群体规模和天数下，至少两人同天生日的概率。

不放回从牌堆中抽取 n 张时，恰好 k 张或至少一张有利牌的概率。

使用卡方检验测试观测计数是否与期望计数或比例匹配。

从列联表检验两个分类变量之间的关联性。

从数据或汇总统计量计算变异系数（CV = SD/mean），以百分比表示。

n 次抛硬币中（公平或有偏）恰好、至少或至多 k 次正面朝上的概率。

从联合概率和 P(B) 求 P(A 在 B 条件下)，并检验两事件是否独立。

使用 z 分布计算均值的置信区间。免费的在线置信区间计算器，适用于 90%、95% 和 99% 水平，显示误差幅度、下界和上界。

计算两个数据集之间的皮尔逊相关系数 (r)，以衡量它们线性关系的强度和方向。免费的在线相关性计算器，带有 r² 和斜率。

计算两个等长变量 x 和 y 的样本或总体协方差。

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

为任意数据集计算均值、中位数、众数、极差、方差和标准差。

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

掷任意数量和类型骰子得到目标总点数（恰好、至少或至多）的概率。

将 68-95-99.7 规则应用于正态数据集：获得一、二、三个标准差区间和百分比。

从离散概率分布表计算期望值、方差和标准差。

对给定速率求指数概率 P(X<x) 和 P(X>x)，以及均值和方差。

从数据集获取最小值、Q1、中位数、Q3、最大值和四分位距，用于箱形图摘要。

计算首次成功发生在第 k 次试验的概率，以及累积概率、均值和方差。

从规模为 N 的有限总体中不放回地抽取 n 个，恰好抽到 k 个成功的概率。

计算数据集的四分位距、Tukey 围栏，并标记异常值。

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

拟合最小二乘直线：斜率、截距、R²、方程及指定值处的预测。

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

在选定置信水平下计算均值或比例的误差幅度。

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.

计算第 r 次成功前恰好失败 k 次的概率，支持累积选项，并给出均值和方差。

将 z 分数转换为面积或反向转换，并求任意正态曲线的 P(X<x)、P(X>x) 或区间概率。

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

将赔率转换为概率，或将概率转换为正反赔率，并提供清晰的可视化分布。

使用 z 检验判断样本比例是否与假设比例存在显著差异。

使用单样本 t 检验判断样本均值是否与假设值存在显著差异。

使用单因素方差分析 F 检验比较三个或更多组的均值。

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

将 z、t、卡方或 F 检验统计量转换为任意尾部的 p 值。

使用配对 t 检验检验配对/前后测量之间的均值差异。

为任意 n 和 r 计算排列数 (nPr) 和组合数 (nCr)。免费的在线排列组合计算器，使用阶乘，即时给出结果。

在给定平均速率 lambda 下，计算恰好、至多或至少发生 k 次事件的泊松概率。

计算两个独立事件的概率：P(A and B)、P(A or B) 以及补事件 P(not A)。免费的在线概率计算器，适用于单一和组合事件。

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.

求在目标误差幅度内估计总体均值所需的样本量。

计算在目标误差幅度内估计比例所需的样本量。

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

从数据列表或样本标准差与样本量计算均值标准误差（SEM）。

使用合并双比例 z 检验比较两个独立样本的比例。

使用 Welch 或合并双样本 t 检验比较两个独立组的均值。

计算 [a,b] 上的连续均匀概率：即时求出 P(c<X<d)、均值和方差。

为两个事件计算补集、并集和交集概率，可选独立或提供联合概率。

根据数值和权重对计算加权平均值（加权均值）。免费的在线加权平均值计算器，适用于成绩、GPA、价格和调查数据。

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.