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?

The mean absolute deviation is 3.75

Step-by-step 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