Question

Find the mean absolute deviation for each set of data:

1. {3, 5, 6, 3, 2, 2, 1, 0, 0, 4, 7, 4, 5, 5, 6}

2. {-3, -2, -1, 0, 1, 2, 3}

Answer 1

1) 1.8

2) 1.7

Explanation:

(for part A)

Mean: 3 + 5 + 6 + 3 + 2 + 2 + 1 + 0 + 0 + 4 + 7 + 4 + 5 + 5 + 6 = 53/15 = 3.5

3.5 - 3 = 0.5

3.5 - 5 = 1.5

3.5 - 6 = 2.5

3.5 - 3 = 0.5

3.5 - 2 = 1.5

3.5 - 2 = 1.5

3.5 - 1 = 2.5

3.5 - 0 = 3.5

3.5 - 0 = 3.5

3.5 - 4 = 0.5

3.5 - 7 = 3.5

3.5 - 4 = 0.5

3.5 - 5 = 1.5

3.5 - 5 = 1.5

3.5 - 6 = 2.5

mean absolute deviation: 0.5 + 1.5 + 2.5 + 0.5 + 1.5 + 1.5 + 2.5 + 3.5 + 3.5 + 0.5 + 3.5 + 0.5 + 1.5 + 1.5 + 2.5 = 27.5/15 = 1.8

(part B)

Mean: -3 + -2 + -1 + 0 + 1 + 2 + 3 = 0/7 = 0

0 - (-3) = 3

0 - (-2) = 2

0 - (-1) = 1

0 - 0 = 0

0 - 1 = 1

0 - 2 = 2

0 - 3 = 3

mean absolute deviation: 3 + 2 + 1 + 0 + 1 + 2 + 3 = 12/7 = 1.7