Math & learning

Mean absolute deviation calculator

Find the average distance from the mean, with the steps to check your answer.

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  • Calculated on your device

01 / Your data set

Separate numbers with commas, spaces, semicolons or new lines. All entries form one data set. Enter 1000, not 1,000, for a thousand.

Up to 1,000 observations and 25,000 characters. Values must be between −1 trillion and 1 trillion. Decimals, negative numbers and scientific notation are accepted.

This calculates the average absolute distance from the arithmetic mean. Median absolute deviation is a different measure.

02 / Your results

2Mean absolute deviation
5Mean
4Values
All 4 observations
ValueDistance from mean
23
41
61
83
Total distance ≈ 8. MAD ≈ 8 ÷ 4 = 2.

Displayed decimals are rounded; calculations use full floating-point precision.

How the calculation works

First find the arithmetic mean. Add the absolute distance of each value from that mean, then divide by the number of values: MAD = Σ|x − mean| ÷ n. Displayed decimals are rounded numerical results.

Try an example

For 2, 4, 6 and 8, the mean is 5. The absolute distances are 3, 1, 1 and 3, so the mean absolute deviation is 8 ÷ 4 = 2.

How to use this calculator

  1. Enter up to 1,000 numbers separated by commas, spaces, line breaks or semicolons. Use a decimal point and omit thousands separators: enter 1000, not 1,000, for one thousand.
  2. Select Calculate MAD. Check the number of values and the mean before reading the mean absolute deviation.
  3. Review the absolute distances and their total. The table shows up to 50 values; Copy results includes the complete list of calculated deviations.

Common questions

What does mean absolute deviation tell me?

It measures the average distance of the values from their arithmetic mean, in the same units as the data. A result of zero means all entered values are equal.

Is this the same as median absolute deviation?

No. This tool averages distances from the mean. Median absolute deviation instead takes the median of distances from the median. Both can be abbreviated MAD, so check which definition your question requires.

Should I divide by n or n minus 1?

Divide the sum of absolute distances by n, the number of values. This calculation does not use the n minus 1 adjustment from sample variance. Displayed decimals are rounded, so calculate from the original values rather than rounded intermediate results.

Further reading: NIST: average absolute deviation