Maths Statistics

Average calculator

Your numbers
Mean 5
sum 40 ÷ count 8 = 5
Everything else about the list
Median 4.5
Mode 4
How many 8
Sum 40
Smallest 2
Largest 9
Range 7
Standard deviation (sample) 2.1381
Standard deviation (population) 2
Live · sample and population deviation both shown

The set above averages 5, and its median is 4.5, and its mode is 4. All three are correct answers to "the average". The mean is pulled by extreme values, the median is not, and the mode is the only one that works on things you cannot add up.

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The mean is the sum of the values divided by how many there are. The median is the middle value once they are sorted, or the midpoint of the two middle values in an even-length list. The mode is the value that appears most often, and a list where every value appears equally has no mode at all.

How to use it

1 Paste or type your numbers. Spaces, commas, semicolons, tabs and newlines all count as separators.
2 The mean appears immediately; the rest of the figures are listed underneath.
3 A pasted spreadsheet column works as it is — there is no need to clean it up first.

Two standard deviations are reported because they answer different questions. The sample deviation divides by one less than the count and is what you want when your numbers are a sample of something larger. The population deviation divides by the count itself and is right only when you have measured everything there is. For eight numbers the two differ by about seven per cent, which is enough to matter in a report.

Questions

One large value drags the mean up and leaves the median where it was. Incomes are the classic case, which is why median income is the figure normally quoted.

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