Average Calculator

Paste or type your numbers. Every figure is exact, and the working is shown.

Result
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    How it works

    The method

    Mean = sum ÷ count. Median = the middle value after sorting (the mean of the two middle values when the count is even). Mode = the value that appears most often. The sample standard deviation divides by n − 1, the population one by n.

    Worked example

    2, 4, 4, 4, 5, 5, 7, 9: sum 40, mean 5, median (4 + 5) ÷ 2 = 4.5, mode 4, population standard deviation 2.

    Common mistakes

    One very large or very small value moves the mean a lot but the median very little. Use the sample formula when your numbers are a sample from a bigger group.

    Questions & answers

    How do I enter my numbers?

    Type them with a space between each, put one on each line, or paste a column from a spreadsheet. If your language writes decimals with a comma (2,5), separate numbers with spaces or new lines, not commas.

    It says something “is not a number”. What is wrong?

    A letter, a unit or a symbol is in the list (like 5kg or

    0). Remove it so only numbers are left. Thousands separators also break numbers apart: type 12500, not 12,500.

    What is the difference between mean, median and mode?

    Mean is the sum divided by how many numbers. Median is the middle number when they are sorted, so one very big or small number moves it little. Mode is the number that appears most often; a list can have none, one or several.

    Should I use the sample or the population standard deviation?

    Use sample when your numbers are a part of a bigger group (a survey, some test scores). Use population when you have every member of the group. Sample divides by (n − 1), population by n.

    Why does the standard deviation end with …?

    It is a square root that usually never ends. The digits shown are found exactly and every one is correct; … means more digits follow. Nothing is rounded. The variance above it is exact.

    How are the quartiles worked out?

    The sorted list is split into a lower and an upper half (the middle number is left out when the count is odd), and Q1 and Q3 are the medians of those halves. Some programs use other methods, so their quartiles can differ slightly.

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