Mean Absolute Deviation CalculatorFree online math calculator — instant results, no sign-up
Calculate the mean absolute deviation from the arithmetic mean.
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About the Mean Absolute Deviation Calculator
The Mean Absolute Deviation Calculator measures how far your values lie from their arithmetic mean, on average, using absolute distances. For the default values 2, 4, 6, 8, 10, it calculates a mean of 6 and a mean absolute deviation of 2.4. This tool measures deviation from the mean, not the median.
- Values
- Enter the numerical observations to analyze, such as 2, 4, 6, 8, 10, all expressed in the same units or all unitless.
Formula and method
x̄ = (Σᵢ₌₁ⁿ xᵢ) / n; MAD = (Σᵢ₌₁ⁿ |xᵢ − x̄|) / n. For the default values: x̄ = (2 + 4 + 6 + 8 + 10) / 5 = 6; MAD = (|2 − 6| + |4 − 6| + |6 − 6| + |8 − 6| + |10 − 6|) / 5 = 12 / 5 = 2.4.
- xᵢThe value of observation i.
- iThe observation index, running from 1 through n.
- nThe number of observations.
- x̄The arithmetic mean of the entered values.
- ΣSummation over all observations.
- |xᵢ − x̄|The absolute distance of an observation from the arithmetic mean.
- MADThe mean absolute deviation from the arithmetic mean.
Add the values and divide by their count to obtain the arithmetic mean. Subtract that mean from each value, take the absolute value of each difference, and average those absolute differences. For 2, 4, 6, 8, 10, the mean is 6, the absolute differences are 4, 2, 0, 2, 4, and their average is 2.4.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Values2, 4, 6, 8, 10
Results
- Mean absolute deviation2.4
How to use the Mean Absolute Deviation Calculator
- 1Enter your observations in Values, or keep the default list 2, 4, 6, 8, 10.
- 2Check that every entry is numeric and that all observations use the same units.
- 3Run the calculation to find the arithmetic mean; the default list has a mean of 6.
- 4Review the mean absolute deviation result; the default list gives 2.4.
- 5Interpret the result in the original units as the average absolute distance from the mean.
Reading your result
The Mean absolute deviation output reports the average absolute distance between the entered values and their arithmetic mean. For the default inputs, 2.4 means that the observations are, on average, 2.4 units away from 6. A result of zero means all entered values are identical; larger results indicate greater spread in the original units, so comparisons should use the same measurement scale.
Limitations
The calculation requires at least one finite numeric value and gives every observation equal weight, including repeated values. It describes only the entered data and does not provide an uncertainty interval or a population estimate correction. Extreme values can affect both the arithmetic mean and the mean absolute deviation, although absolute differences amplify large deviations less than squared differences do. This measure is not median absolute deviation or standard deviation, and there is no universal threshold for a high or low result.
Common questions
Why is the mean absolute deviation 2.4 for 2, 4, 6, 8, 10?+
The arithmetic mean is 6. The absolute distances from 6 are 4, 2, 0, 2, 4, which sum to 12; dividing by the five observations gives 2.4.
Why take absolute values instead of averaging the signed deviations?+
Signed deviations from the arithmetic mean sum to zero. Taking absolute values prevents distances below and above the mean from canceling, allowing the result to measure spread.
Is this the same as median absolute deviation?+
No. This calculator averages absolute distances from the arithmetic mean. Median absolute deviation instead takes the median of absolute distances from the median, so the two measures can produce different results.
Does this calculator divide by n or n − 1?+
It divides the sum of absolute deviations by n, the number of entered observations. The n − 1 adjustment used in sample variance is not part of this mean absolute deviation formula.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.