Question

The data below show the numbers of miles driven to work each day by the employees of a small company 15, 25, 13, 15, 18, 20, 22, 24 The mean of the data is 19 miles. What is the mean absolute deviation of the data?

Answer 1

The mean absolute deviation is 3.75

Explanation:

Given:

Miles travel: 15, 25, 13, 15, 18, 20, 22, 24

Mean: 19 miles

Required:

Mean absolute deviation.

Given that the mean of the data is known, we start by subtracting the mean from each dataset

15 - 19 = -4

25 - 19 = 6

13 - 19 = -6

15 - 19 = -4

18 - 19 = -1

20 - 19 = 1

22 - 19 = 3

24 - 19 = 5

Then we calculate the absolute value of each

|-4| = 4

|6| = 6

|-6| = 6

|-4| = 4

|-1| = 1

|1| = 1

|3| = 3

|5| = 5

Add up these result;

4 + 6 + 6 + 4 + 1 + 1 + 3 + 5

= 30

Divide by number of data, to give mean absolute deviation (MAD)

MAD = 30/8

MAD = 3.75

Hence, the mean absolute deviation is 3.75