What is the difference between population and sample standard deviation?

Population standard deviation (σ) divides by N (the total count) and is used when your data represents the entire population. Sample standard deviation (s) divides by N-1 (Bessel's correction) and is used when your data is a sample from a larger population. The tool computes both.

How does the calculator handle the median for even-sized data sets?

When the data set has an even number of values, the median is the average of the two middle values after sorting. For example, the median of {1, 3, 5, 7} is (3 + 5) / 2 = 4.

Can the data set have more than one mode?

Yes. If multiple values share the highest frequency, the tool returns all of them. This is called a multimodal distribution. For example, in {1, 2, 2, 3, 3, 4}, both 2 and 3 are modes.

What input formats does the calculator accept?

The calculator accepts numbers separated by commas (1, 2, 3), spaces (1 2 3), or line breaks. You can also paste data directly from a spreadsheet column. Decimal and negative values are fully supported.

How is variance different from standard deviation?

Variance is the average of the squared deviations from the mean, measured in squared units. Standard deviation is the square root of variance, measured in the same units as the original data. Standard deviation is more intuitive because it is on the same scale as your data.

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Statistics Calculator

To calculate descriptive statistics, enter your data set and the calculator computes mean, median, mode, standard deviation (both population and sample), variance, range, and count instantly. Population standard deviation uses N in the denominator; sample standard deviation uses N-1 (Bessel's correction).

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What is Statistics Calculator?

A statistics calculator is an online tool that computes descriptive statistics — including mean, median, mode, standard deviation, variance, range, and quartiles — from a data set of numerical values, providing a complete summary of the data's distribution.

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These tools work great alongside Statistics Calculator:

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Descriptive statistics are the foundation of data analysis, and you should not need a spreadsheet just to find a mean and standard deviation. This free statistics calculator delivers every core measure — mean, median, mode, standard deviation, variance, and range — from a single paste, with both population and sample formulas computed automatically.

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