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Statistics Calculator

Mean, median, mode, range, variance and standard deviation

Your numbers

Mean

Count

Sum

Median

Mode

Std Dev (sample)

Range

Statistics Calculator — Complete Guide

A column of numbers says very little until it is summarised. The five numbers this calculator returns — mean, median, mode, range and standard deviation — are the vocabulary in which nearly every report, study and dashboard describes a dataset, and computing them by hand is exactly the kind of arithmetic that produces silent mistakes.

What this calculator does

Paste any list of numbers — from a spreadsheet column, a quiz, a sensor log — in any order with any separators. You get the count and sum, the three centres (mean, median, mode), the range, and the sample standard deviation with the variance behind it.

The definitions

mean = Σx ÷ n median = middle value of the sorted list mode = the most frequent value (or values) range = maximum − minimum s² = Σ(x − x̄)² ÷ (n − 1) s = √s²

The variance divides by n − 1 (Bessel's correction) because a sample underestimates the spread of the population it came from. The mode column shows "none" when every value occurs exactly once.

A worked example

Quiz scores: 4, 8, 15, 16, 23, 42. Count 6, sum 108, mean 18. Sorted: 4, 8, 15, 16, 23, 42 — the median is (15 + 16) ÷ 2 = 15.5. Every value is unique, so the mode is "none". The range is 42 − 4 = 38, and the sample standard deviation works out to ≈ 13.5 — typical scores sit roughly 13–14 points from the mean.

Dataset	Mean	Median	Takeaway
3, 4, 50	19	4	outlier drags the mean up
2, 4, 4, 10	5	4	mode = 4
10, 10, 10	10	10	SD = 0, no spread

Which centre should you quote?

Mean — best for well-behaved data without extreme values.
Median — best when the data is skewed: incomes, house prices, response times.
Mode — best for categorical or discrete data: best-selling size, most common score.

A useful habit: report the mean together with the standard deviation, or the median together with the range — a centre without a spread always tells half the story.

统计计算器完整使用指南

一列数字在被概括之前说明不了什么。均值、中位数、众数、极差、标准差——这五个数字几乎是所有报告、研究和仪表盘描述数据的通用词汇，而手工计算它们恰恰是最容易悄悄出错的那类算术。

这个计算器能做什么

粘贴任意一列数字——来自表格列、测验成绩或传感器日志——顺序不限、分隔符不限。你会得到数据个数与总和、三个「中心」（均值、中位数、众数）、极差，以及样本标准差及其背后的方差。

定义

均值 = Σx ÷ n 中位数 = 排序后位于中间的值众数 = 出现次数最多的值（可多个）极差 = 最大值 − 最小值 s² = Σ(x − x̄)² ÷ (n − 1) s = √s²

方差除以 n − 1（贝塞尔校正），因为样本总会低估其来源总体的波动。当每个值都只出现一次时，众数一栏显示「无」。

算例演示

测验成绩：4, 8, 15, 16, 23, 42。个数 6、总和 108、均值 18。排序后为 4, 8, 15, 16, 23, 42——中位数 = (15 + 16) ÷ 2 = 15.5。每个值都唯一，众数为「无」。极差 = 42 − 4 = 38，样本标准差约 13.5——典型成绩在均值上下 13–14 分内波动。

数据	均值	中位数	要点
3, 4, 50	19	4	离群值拉高均值
2, 4, 4, 10	5	4	众数 = 4
10, 10, 10	10	10	标准差 = 0，无波动

该引用哪个「中心」？

均值——适合没有极端值的规整数据。
中位数——适合偏态数据：收入、房价、响应时间。
众数——适合类别或离散数据：最畅销尺码、最常见的分数。

一个好用的小习惯：报均值就带上标准差，报中位数就带上极差——只有中心没有波动，永远只讲了一半的故事。

Frequently Asked Questions

What is the difference between mean, median and mode?

The mean is the arithmetic average (sum ÷ count), the median is the middle value when sorted, and the mode is the most frequent value. Medians resist outliers — for salaries of 3, 4 and 50 (thousand), the mean 19 is misleading while the median 4 is not.

Which standard deviation formula is used?

The sample formula: the square root of the sum of squared deviations divided by n − 1. Use it when your data is a sample of a larger population. For a complete population, divide by n instead — the result is slightly smaller.

How should I separate the numbers?

Any separator works: spaces, commas, semicolons or new lines — you can paste straight from a spreadsheet column or a sentence. Values with percent signs or other symbols are read by their numeric part, so "45%" counts as 45.

Last reviewed: October 5, 2026 · How we calculate · Sources: Standard statistical formulas (sample statistics)