Question

What is the mean absolute deviation (MAD) of the data set?

{2, 5, 6, 12, 15}

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Answer 1

To find the MAD

Step 1 : find the mean of the given data

Data : (xi) : 2, 5, 6, 12, 15

Mean = μ = (2 + 5 + 6 + 12 + 15)/5

Mean = μ = 40/5 = 8

Step 2 : find the difference between each data value and the mean

(xi - μ) = (2-8) , (5-8), (6-8), (12-8) , (15-8)

(xi - μ) = -6, -3, -2, 4,7

Take absolute value of each difference

|(xi - μ) | = 6,3,2,4,7

∑|(xi - μ)| = 6 + 3 + 2 + 4 + 7 = 22

MAD of the data set = 1/5∑|(xi - μ)|

MAD of the data set = 22/5

MAD of the data set = 4.4