What is the difference between population and sample standard deviation?

Population standard deviation (σ) is used when you have data for an entire population. It divides by n (the total count). Sample standard deviation (s) is used when your data is a subset of a larger population — it divides by n-1, known as Bessel's correction. This correction removes the bias that occurs when estimating a population standard deviation from a sample. When in doubt, use sample standard deviation.

How is the median calculated for an even number of values?

When the count is even, the median is the average of the two middle values after sorting. For example, in {4, 8, 15, 16}, the median is (8 + 15) / 2 = 11.5. When the count is odd, the median is simply the middle value.

What does IQR (interquartile range) tell you?

The IQR is the difference between Q3 (75th percentile) and Q1 (25th percentile). It measures the spread of the middle 50% of your data, making it a robust measure of variability that is unaffected by extreme outliers. A large IQR indicates high spread; a small IQR indicates the middle data points are clustered close together.

What input formats are supported?

You can enter numbers separated by commas, spaces, semicolons, or new lines — or any combination. For example: '1,2,3', '1 2 3', or one number per line all work. The calculator accepts integers, decimals, and negative numbers.

What happens when there is no mode?

The mode is the value that appears most frequently. If every number appears exactly once (no repeats), there is no mode. If multiple values share the highest frequency, all of them are shown as the mode. For example, in {1,1,2,2,3}, both 1 and 2 are modes.

统计计算器

从任意数字列表计算均值、中位数、众数、标准差、方差、四分位数等统计量。支持逗号、空格或换行分隔的输入。

输入数字

用逗号、空格、分号或换行分隔数字

使用方法

从任意数字列表计算均值、中位数、众数、标准差、方差、四分位数等统计量。支持逗号、空格或换行分隔的输入。

1Type or paste your numbers into the input box. Use any separator you like — commas, spaces, semicolons, or one number per line. Click 'Load Example' to try the calculator with a sample dataset.
2Results appear instantly as you type. The four summary cards at the top show count, sum, minimum, and maximum at a glance.
3The detailed table below shows mean, median, mode, range, population and sample variance, population and sample standard deviation, and the three quartiles (Q1, Q3, IQR).
4For a single value, sample variance and sample standard deviation show N/A because Bessel's correction requires at least two data points.
5Use the IQR value to identify outliers: data points more than 1.5 × IQR below Q1 or above Q3 are typically considered outliers in box plot analysis.

主要功能

13 statistical measures — count, sum, min, max, mean, median, mode, range, quartiles, IQR, and both population and sample variance/standard deviation
Flexible input — commas, spaces, semicolons, or new lines, all accepted simultaneously
Instant results — updates live as you type, no submit button needed
Handles multiple modes — shows all values that share the highest frequency
Handles edge cases — N/A for sample statistics when only one value is entered

常见问题

了解更多

Statistics Calculator Guide — Mean, Median, Mode & Standard Deviation