Question

Alan recorded the points he scored on the basketball court in ms2 school yard. What is the mean absolute deviation of his scores

Answer 1

The mean absolute deviation is: 7.44

Explanation:

Given

`Scores: 98, 78, 84, 75, 91`

Required

The mean absolute deviation

First, calculate the mean

`\bar x = (\sum x)/(n)`

`\bar x = (98+78+84+75+91)/(5)`

`\bar x = (426)/(5)`

`\bar x = 85.2`

The mean absolute deviation (M) is:

`M = (1)/(n)\sum|x - \bar x|`

So, we have:

`M = (1)/(5)(|98 - 85.2|+|78 - 85.2|+|84 - 85.2|+|75 - 85.2|+|91 - 85.2|)`

`M = (1)/(5)(|12.8|+|-7.2|+|-1.2|+|-10.2|+|5.8|)`

Remove absolute brackets

`M = (1)/(5)(12.8+7.2+1.2+10.2+5.8)`

`M = (1)/(5)*37.2`

`M = 7.44`