Mean, Median & Standard Deviation Calculator

What each measure tells you

• Mean — the arithmetic average (sum ÷ count)
• Median — the middle value once sorted (average of the two middle values if the count is even)
• Mode — the most frequently occurring value(s)
• Standard deviation — how spread out the values are from the mean

Population vs sample standard deviation

Population standard deviation divides by the total count (n) and is used when your numbers represent an entire population. Sample standard deviation divides by (n − 1) instead — a small correction that gives a better estimate when your numbers are only a sample drawn from a larger population.

Worked example

For the set 4, 8, 6, 5, 3, 7: the mean is 5.5, the median is 5.5, there's no repeated value (no mode), the range is 5, and the population standard deviation is about 1.708.

When one value skews the mean

For 12, 14, 15, 15, 18, 95 the mean is 28.167 but the median is 15, the mode is 15 and the range is 83. The single value of 95 drags the mean above every other number, while the median stays near the typical value. When a list has an outlier, compare the mean with the median before deciding which describes it better.

Population versus sample, with numbers

For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2.000. Treating the same eight numbers as a sample gives 2.138, because the squared deviations are divided by 7 instead of 8. The gap shrinks as the list grows, and with only a few values it is noticeable.

A list with two equally common values, such as 2, 2, 5, 5, 9, shows both as modes (2, 5), with a mean of 4.600 and a median of 5.

How to enter data

• Separate numbers with commas, spaces or line breaks, so a column pasted from a spreadsheet works.
• Use a decimal point. A decimal comma is read as a separator, so 3,5 becomes the two numbers 3 and 5, and 3,5 4,2 is analyzed as four values.
• Semicolons and other symbols are not accepted and give an error message.
• At least two numbers are needed. The mean is shown to three decimals; the median and range are shown as calculated.
• Variance is not shown, but you can square either standard deviation to get it.

What this does not cover

There are no quartiles, percentiles, confidence intervals or weighted averages, and the numbers are treated as plain values with no units or labels. For a set of measurements from a larger group, use the sample standard deviation; use the population figure only when the list is the whole group.