Math

Statistics Calculator

Summarize a numerical dataset with its count, total, average, median, modes, range and population standard deviation. These measures describe different aspects of the same values rather than competing versions of one answer.

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Using the Statistics Calculator

Look at the median as well as the mean when unusually large or small observations are present. Compare the standard deviation with the scale of the measurements to judge how tightly values cluster around their average.

Worked example

Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.

Example inputs

Numbers, separated by commas
2, 4, 4, 6, 9

Example result

Count
5
Sum
25
Mean
5
Median
4
Mode
4
Range
7
Population standard deviation
2.3664319

Method and assumptions

The mean is sum/count; the median is the middle sorted value; all equally frequent repeated modes are reported.

Check what the data represents

A statistical result is only meaningful in relation to the observations and assumptions behind it. Keep track of whether values describe a whole population or a sample, whether observations are independent, and which distribution the method uses. More decimal places cannot compensate for a sample that does not represent the question you are trying to answer.

Common question

Are repeated observations counted more than once?

Yes. Repeated values represent repeated observations and affect the mean, median, modes and spread. Remove duplicates only if they are data-entry errors, not merely because the values are identical.