How to Calculate Absolute Deviation (and Average Absolute Deviation)

By Contributor; Updated April 24, 2017
Determine sample differences by knowing the absolute deviation.

In statistics, the absolute deviation is a measure of how much a particular sample deviates from the average sample. In simple terms, this means how much one number in a sample of numbers varies from the average of the numbers in the sample. Absolute deviation helps analyze data sets and can be a very useful statistic.

Find the average sample using one of three methods. The first method is by finding the mean. To find the mean, add together all of the samples and divide by the number of samples.
For example if your samples are 2, 2, 4, 5, 5, 5, 9, 10, 12, add them to get a total of 54. Then divide by the number of samples, 9, to calculate a mean of 6.

The second method of calculating the average is by using median. Arrange the samples in order from lowest to highest, and find the middle number. From the example, the median is 5.

The third method of calculating the average sample is by finding the mode. The mode is which ever sample occurs most. In the example, the sample 5 occurs three times, making it the mode.

Calculate the absolute deviation from the mean by taking the mean average, 6, and finding the difference between the mean average and the sample. This number is always stated as a positive number. For example, the first sample, 2, has an absolute deviation of 4, which is its difference from the mean average of 6. For the last sample, 12, the absolute deviation is 6.

Calculate the average absolute deviation by finding the absolute deviation of each sample and averaging them. From the example, calculate the absolute deviation from the mean for each sample. The mean is 6. In the same order, the absolute deviations of the samples is 4,4,2,1,1,1,3,4,6. Take the average of these numbers and calculate the average absolute deviation as 2.888 . This means the average sample is 2.888 from the mean.

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