Question

What is the Mean Absolute Deviation of the following set?



{2, 10, 7, 12, 8}

7.8

2.64

5

13.2

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Answer 1

To calculate the Mean Absolute Deviation (MAD), we first find the absolute deviation for each number by subtracting the mean of the set from each number and taking the absolute value:

\[\text{Absolute Deviation} = \left|2 - \frac{2+10+7+12+8}{5}\right| = 4\]
\[\text{Absolute Deviation} = \left|10 - \frac{2+10+7+12+8}{5}\right| = 2\]
\[\text{Absolute Deviation} = \left|7 - \frac{2+10+7+12+8}{5}\right| = 1\]
\[\text{Absolute Deviation} = \left|12 - \frac{2+10+7+12+8}{5}\right| = 4\]
\[\text{Absolute Deviation} = \left|8 - \frac{2+10+7+12+8}{5}\right| = 1\]

Next, we find the average of the absolute deviations:

\[\text{MAD} = \frac{4 + 2 + 1 + 4 + 1}{5} = \frac{12}{5} = 2.4\]

Therefore, the Mean Absolute Deviation of the set {2, 10, 7, 12, 8} is 2.4.