📊 统计学工具📊 Statistics Tools

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📊 统计学工具📊 Statistics Tools

共 51个免费在线工具

t 统计量计算器T Score由样本均值、假设均值与标准差求 t 值Enter the sample mean, hypothesised mean, standard deviation and sample size to compute the t statistic for a mean hypo… 合并方差计算器Merge Variance Calculator由两组样本量方差求合并方差Enter two sample sizes and standard deviations to compute the pooled variance as a weighted average, used for the equal… 泊松分布概率计算器Poisson Pmf输入单位时间（或空间）内事件的平均发生率 λ 和目标发生次数 k，计算泊松分布的概率质量函数 P(X=k)，即恰好发生 k 次事件的概率，常用于客服来电、故障次数等稀有事件的建模。Enter the average event rate lambda per unit time or space and the target count k to compute the Poisson probability ma… 样本标准差计算器Sample Standard Deviation Calculator输入以逗号或空格分隔的一组数值，计算样本标准差 s，反映数据相对均值的平均离散程度，按 n−1 作分母的无偏估计，适合评估一组观测值的波动大小。Enter a comma- or space-separated list of numbers to compute the sample standard deviation s with n - 1 denominator, as… 二项分布概率计算器Binomial Pmf输入试验次数 n 与成功次数 k、成功概率 p，计算 n 次独立伯努利试验恰好 k 次成功的概率，用于离散分布与风险建模。Enter trials n, success count k and success probability p to compute the probability of exactly k successes in n indepe… 卡方检验计算器Chi Square Test卡方检验计算器：输入观测值与期望值频数，计算 χ² 统计量并判断分布偏离显著性，用于拟合优度与独立性检验。Enter observed and expected frequencies to compute the chi-square statistic and judge whether the deviation is signific… 比例样本量计算器Ratio Sample Size Calculator比例样本量计算器：给定置信水平、误差界与预期比例，估计总体比例所需样本量，用于抽样调查设计。Given a confidence level, margin of error and expected proportion, estimate the minimum sample size needed to estimate… 单样本 t 检验计算器One Sample T Test输入样本数据（或样本均值、标准差与样本量），在总体标准差未知时，用样本 t 分布检验样本均值与假设总体均值是否存在显著差异，输出 t 统计量、自由度和 p 值，适用于小样本均值假设检验。Enter sample data (or mean, standard deviation and size) to test a sample mean against a hypothesised population mean w… 单因素 ANOVA 计算器One Way Anova单因素方差分析（One-way ANOVA）在线计算器，输入多组样本自动计算组间/组内平方和、F 值与 p 值，判断均值差异显著性，纯前端运行。Enter two or more group means, standard deviations and sizes to compute between-group and within-group sums of squares… 单样本 Z 检验计算器One Sample Z Test输入样本均值、样本量与已知的总体标准差，检验样本均值是否偏离给定的假设值，输出 Z 统计量及双侧与单侧 p 值，适用于总体标准差已知时的均值显著性检验。Enter the sample mean, sample size and known population standard deviation to test the sample mean against a hypothesis… 皮尔逊相关系数计算器Correlation Coefficient皮尔逊相关系数计算器：输入两变量成对数据，计算 Pearson 相关系数 r 衡量线性相关强度与方向，并给出显著性判断，用于相关分析。Enter paired X and Y data to compute the Pearson correlation coefficient r, measuring the strength and direction of a l… 变异系数计算器Coefficient of Variation输入均值 μ 与标准差 σ，按 CV = σ/μ × 100% 计算变异系数，用于比较不同量纲数据的离散程度与相对波动水平。Enter the mean and standard deviation to compute CV = sigma/mu x 100%, comparing dispersion across data sets measured i… 均值标准误计算器Standard Error均值标准误计算器：输入样本标准差与样本量，求样本均值分布的标准误 SE = s/√n，用于置信区间与显著性检验。Enter the sample standard deviation and sample size to compute the standard error of the mean SE = s / sqrt(n), used in… 平均绝对偏差计算器Mean Absolute Deviation输入一组数值，按 MAD = Σ|xᵢ − x̄|/n 计算平均绝对偏差，衡量数据平均离散程度，用于预测误差与稳健性评估。Enter a series of values to compute the mean absolute deviation MAD = sum|x - xbar| / n, measuring average dispersion f… 总体方差计算器Population Variance总体方差在线计算器，输入完整数据集自动求均值与离差平方平均，衡量数据离散程度，支持批量粘贴、结果实时显示，数据本地处理。Enter a complete data set to compute the population variance as the average squared deviation from the mean, measuring… 正态分布 CDF 计算器Normal Cdf正态分布 CDF 计算器：输入均值、标准差与取值 x，计算标准正态分布累积概率 P(X ≤ x)，用于概率与分位评估。Enter the mean, standard deviation and a value x, or a standard score z, to compute the standard normal cumulative prob… 比例标准误计算器Standard Error Proportion由样本比例与样本量求标准误Enter the sample proportion p and sample size n to compute SE = sqrt[p(1-p)/n], the sampling variability of a proportio… 比例置信区间计算器Confidence Proportion比例置信区间计算器：输入样本成功数与样本量（或样本比例），按正态近似求总体比例在给定置信水平下的置信区间，用于调查与医学估计。Enter the number of successes and sample size (or the sample proportion) to get the confidence interval for a populatio… 几何平均数计算器Geometric Mean几何平均数计算器：输入数值集合，按乘积的 n 次根计算几何平均数，适合增长率、比率等相乘型数据的集中趋势度量。Enter a set of positive numbers to compute the geometric mean as the n-th root of their product, suited to growth rates… 均值样本量计算器Sample Size Mean均值样本量计算器：给定置信水平、容许误差与总体标准差，估计总体均值所需的最小样本量，用于实验设计。Given a confidence level, margin of error and population standard deviation, estimate the minimum sample size needed to… 样本方差计算器Sample Variance Calculator样本方差计算器：输入数据集，按 n−1 自由度计算样本方差，衡量数据离散程度，用于推断统计与假设检验。Enter a data set to compute the sample variance using n - 1 degrees of freedom, measuring dispersion for inferential st… 百分等级计算器Percentile Rank百分等级计算器：输入数值与数据集，计算该值低于总体中多少比例的数据（百分等级），用于成绩与排名评估。Enter a data set and a target value to compute the percentile rank, i.e. the percentage of the data below that value, f… 调和平均数计算器Harmonic Mean调和平均数计算器：输入数值集合，按倒数的算术平均之倒数计算调和平均数，适合速率、单价等倒数型数据的平均。Enter a set of numbers to compute the harmonic mean as the reciprocal of the arithmetic mean of reciprocals, suited to… Z 分数计算器Z Fraction Calculator输入原始分数、总体均值与总体标准差，将分数标准化为 Z 分数 (x−μ)/σ，并给出对应的百分位排名，Z>0 表示高于均值、Z<0 表示低于均值，便于横向比较不同分布的数据。Enter a raw score, population mean and population standard deviation to standardise the score as z = (x - mu)/sigma and… 配对 t 检验计算器Paired T Test输入同一组对象的配对测量值（如服药前后），计算每对差值及其均值与标准差，用配对 t 检验判断差值是否显著不为零，输出 t 统计量、自由度与 p 值，用于前后对照实验的差异检验。Enter paired measurements of the same subjects (e.g. before and after treatment) to compute the mean and SD of differen… 样本方差计算器Sample Variance Calculator输入以逗号或空格分隔的一组数值，计算样本方差 s²=Σ(xᵢ−x̄)²/(n−1)，作为标准差的平方衡量数据离散程度，常用于统计描述与后续检验的方差分析。Enter a comma- or space-separated list of numbers to compute the sample variance s2 = sum(x - xbar)2 / (n - 1), the squ… 二项累积分布计算器Binomial Cdf由试验数、成功概率与上限求累积概率Enter the number of trials n, success probability p and upper bound x to get the cumulative probability P(X<=x) of a bi… 最小二乘回归计算器Linear Regressiony = a + b·x（最小二乘）Enter paired (x, y) data to fit the best-fit line by least squares and get the slope, intercept and R-squared, for tren… F 方差检验计算器F Variance Inspection CalculatorF 方差检验计算器：输入两组样本方差与自由度，计算 F 统计量与临界值，检验两总体方差是否相等，用于方差齐性判定。Enter two sample variances and their degrees of freedom to compute the F statistic and critical value and test whether… 决定系数 R² 计算器Correlation R Squared决定系数计算器：输入相关系数 r，按 R² = r² 求决定系数，表示回归模型对因变量变异的解释比例，用于回归拟合优度评估。Enter the correlation coefficient r to compute the coefficient of determination R-squared, the share of variance in the… 对立事件概率计算器Probability Complement对立事件概率计算器：输入事件概率 p，按 P(Aᶜ) = 1 − P(A) 求对立（补）事件概率，用于概率基本运算。Enter the probability of an event p to compute the complementary probability P(Ac) = 1 - P(A), a basic probability oper… 比值比计算器Odds Ratio输入 2×2 列联表的四项频数，计算比值比 OR 及其置信区间，衡量暴露与结局的关联强度，用于流行病学与医学统计分析。Enter the four frequencies of a 2x2 contingency table to compute the odds ratio and its confidence interval, measuring… 独立双样本 t 检验计算器Independent T Test独立双样本 t 检验计算器：输入两组独立样本数据，计算 t 值与 p 值，判断两总体均值是否存在显著差异，用于实验与对比研究。Enter two independent samples (means, standard deviations and sizes) to compute the t value and p value and test whethe… 相对风险计算器Relative Risk Calculator相对风险计算器：输入暴露组与非暴露组的结局发生率，计算相对风险 RR 衡量暴露与结局的关联强度，用于流行病学队列研究。Enter the outcome rates of an exposed and an unexposed group to compute the relative risk RR and its confidence interva… 极差计算器Range Calculator极差计算器：输入数值序列，按 R = max − min 求极差，快速衡量数据离散跨度，用于描述统计初筛。Enter a series of values to compute the range R = max - min, a quick measure of the spread of a data set 标准分 Z 值计算器Z Score Calc标准分 Z 值计算器：输入原始值、均值与标准差，求标准分 Z = (x−μ)/σ，用于数据标准化与离群判断。Enter a raw value, mean and standard deviation to compute the z score (x - mu)/sigma, for standardisation and outlier d… 样本偏度计算器Skewness Sample样本偏度计算器：输入数值序列，按三阶中心矩公式求样本偏度 g₁，判断分布左偏/右偏及对称程度。Enter a series of values to compute the sample skewness g1 from the third standardised central moment, judging left/rig… Cohen's d 效应量计算器Cohens DCohen&#x27;s d 效应量计算器Enter two group means and pooled standard deviation (or group SDs and sizes) to compute Cohen's d and measure effect si… Cramér's V 计算器Cram é r ' s V CalculatorCramér&#x27;s V 计算器From the chi-square value, sample size and degrees of freedom of a contingency table, compute Cramer's V to measure the… t 检验统计量T输入样本均值、假设总体均值、样本标准差与样本量，计算单样本 t 统计量 t=(x̄−μ)/(s/√n)，并给出自由度，|t| 越大表示样本均值偏离假设值的证据越强，用于均值假设检验的第一步。Enter the sample mean, hypothesised population mean, sample standard deviation and sample size to compute the one-sampl… 变异系数比较Enter the mean and standard deviation o…变异系数比较工具：输入两组数据的均值与标准差，计算变异系数 CV 消除量纲后比较离散程度，用于不同单位数据的波动性对比。Enter the mean and standard deviation of two data sets to compare their coefficients of variation CV, removing the effe… 标准差与方差Standard Deviation and Variance输入一组数值并选择类型（1 为样本、2 为总体），计算样本或总体标准差、方差以及变异系数 CV，用于衡量数据的离散程度与相对波动水平，便于不同量纲数据的比较。Enter a set of values and choose sample or population to compute standard deviation, variance and the coefficient of va… 均值中位数众数Enter up to seven values to quickly com…输入最多 7 个数值，快速计算这组数据的算术均值、中位数、众数与极差，并给出数据总和，适合在课堂上或日常中快速描述一组数据的集中趋势与离散程度。Enter up to seven values to quickly compute the arithmetic mean, median, mode and range and the total, a fast way to de… 线性回归拟合Enter paired (x, y) sample data to fit…输入成对(x,y)样本数据，用最小二乘法拟合直线y=ax+b，输出斜率a、截距b、相关系数及拟合优度，并可代入任意x预测y值，用于趋势分析与数据建模。Enter paired (x, y) sample data to fit the line y = ax + b by least squares, output the slope a, intercept b, correlati… 加权平均数Enter values together with their weight…加权平均数计算器：输入数值与对应权重，按权重自动归一化计算加权平均数，用于成绩、指标等加权汇总。Enter values together with their weights to compute a weighted mean with automatic weight normalisation, for weighted s… 假设检验 p 值近似P输入 Z 统计量，用正态分布近似快速估算双尾 Z 检验的 p 值，并提示 p<0.05 时通常在 5% 水平下拒绝原假设，适用于大样本假设检验时快速判断显著性。Enter a z statistic to approximate the two-sided p value using the normal distribution, with a note that p below 0.05 u… 置信区间估算Enter the sample mean, standard deviati…输入样本均值、总体或样本标准差与样本量，并指定置信水平（如 95%），用 Z 分布估算总体均值的置信区间，给出上下限，适用于大样本或已知总体标准差时的区间估计。Enter the sample mean, standard deviation, sample size and a confidence level (e.g. 95%) to estimate the confidence int… 偏度与峰度Enter a data set to compute skewness an…输入一组数据，计算偏度Skewness与峰度Kurtosis，判断分布是否左偏或右偏、是否比正态分布更尖或平缓，辅助识别数据分布形态与异常尾部特征。Enter a data set to compute skewness and kurtosis and judge whether the distribution is left- or right-skewed and more… 样本量估算Sample Size Estimate输入可接受的误差幅度、置信水平与总体标准差，估算估计总体均值所需的最小样本量 n，帮助在调查或实验中以足够精度规划抽样数量，避免样本不足导致误差过大。Enter the acceptable margin of error, confidence level and population standard deviation to estimate the minimum sample… 正态分布概率Statistics输入均值、标准差以及区间上下界，计算正态分布下该区间的概率（即曲线下面积），下界可填很大的负数近似负无穷，用于求某取值范围内的累积概率或分位数区间。Enter the mean, standard deviation and lower/upper bounds to compute the probability (area under the normal curve) for… 四分位距 IQRIqr输入数据集，计算 Q1、Q2、Q3 与四分位距 IQR，并据 1.5×IQR 规则标出异常值边界，用于箱线图与离群点检测。Enter a data set (or count, minimum, Q1, median, Q3 and maximum) to compute Q1, Q2, Q3 and the interquartile range, and…
📖关于「统计学工具」About Statistics Tools▼

📝栏目简介

统计学工具集合收录了 51 个免费在线工具，覆盖统计学场景下的常见计算、换算与查询需求。无论你是相关领域的从业者、学生还是普通用户，都能在这里找到即用即走的实用小工具。所有工具纯前端运行，数据不上传服务器，保护隐私安全。This collection gathers 51 free online Statistics tools for everyday calculations, conversions and lookups. Whether you are a professional, a student or a casual user, you will find handy tools you can use right away. Everything runs client-side — no data is uploaded.

✨核心功能与适用场景

本页收录的统计学工具包括（部分代表工具）：Featured Statistics tools on this page include:

  • t 统计量计算器T Score
  • 样本标准差计算器Poisson Pmf
  • 比例样本量计算器Chi Square Test
  • 单因素 ANOVA 计算器One Way Anova
  • 变异系数计算器Correlation Coefficient
  • 总体方差计算器Standard Error
  • 比例置信区间计算器Normal Cdf
  • 样本方差计算器Geometric Mean
  • Z 分数计算器Sample Variance Calculator
  • 二项累积分布计算器Harmonic Mean
  • F 方差检验计算器Sample Variance Calculator
  • 比值比计算器F Variance Inspection Calculator
  • 极差计算器Probability Complement
  • Cohen's d 效应量计算器Independent T Test
  • 变异系数比较Z Score Calc
  • 均值中位数众数Cram é r ' s V Calculator
  • 假设检验 p 值近似Standard Deviation and Variance
  • 样本量估算Sample Size Estimate

这些工具帮助你快速完成统计学相关的常见任务，无需记忆复杂公式或手动换算，输入即可得结果。These tools help you complete Statistics tasks quickly — no formulas to memorise and no manual conversion, just enter your values and get the result.

❓常见问题

统计学分类下的工具需要下载或注册吗？Do Statistics tools require any download or sign-up?

不需要。本页 51 个统计学工具（如t 统计量计算器、样本标准差计算器、比例样本量计算器、单因素 ANOVA 计算器、变异系数计算器、总体方差计算器）都是纯前端页面，打开网页即可使用，无需安装软件、无需注册账号；输入的数据只在你的浏览器内处理，不会上传服务器。No. The 51 Statistics tools on this page (including T Score, Poisson Pmf, Chi Square Test, One Way Anova, Correlation Coefficient, Standard Error) are pure front-end pages: just open them and start using. No software to install, no account needed, and anything you enter is processed inside your browser — never uploaded.

统计学工具的结果能直接用于医疗、法律或财务决策吗？Can the results be used directly for medical, legal or financial decisions?

不能直接作为决策依据。本页工具多为通用计算、换算与查询，结果仅供日常参考；涉及诊断、诉讼、投资、工程验收等专业场景，请以权威标准、原始仪器读数或持证专业人士的结论为准。所有运算都在本地完成，数据不上传。No — treat them as everyday references only. Most tools here are general-purpose calculators, converters and lookups; for diagnosis, litigation, investment or engineering acceptance, rely on authoritative standards, raw instrument readings or a licensed professional. Everything is computed locally and nothing is uploaded.