Question

The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15

Answer 1

2.57

Explanation:

The mean absolute deviation is the mean of the absolute values of the differences from the mean.

Application

The mean of the dataset is the sum of values, divided by their number:

mean = (20 +16 +21 +16 +22 +16 +15)/7 = 126/7 = 18

The absolute values of the differences from 18 will have an average of ...

mean(|differences|) = (2 +2 +3 +2 +4 +2 +3)/7 = 18/7

mad(data) ≈ 2.57

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Additional comment

Some calculators have the mad( ) function built-in. See the second attachment, for example.