Question

Question 1

A set of values is shown below.

12.7, 22, 23.5, 24, 11, 22

What is the mean absolute deviation of the set of values?

Answer 1

`M.A.D= 4.9`

Explanation:

Given

12.7, 22, 23.5, 24, 11, 22

Required

Determine the M.A.D

Start by calculating the Mean

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

In this case, n = 6

So:

`Mean = (12.7 + 22 + 23.5 + 24 + 11 + 22)/(6)`

`Mean = (115.2)/(6)`

`Mean = 19.2`

Subtract the mean from each element

`12.7 - 19.2 = -6.5`

`22 - 19.2 = 2.8`

`23.5 - 19.2 = 4.3`

`24 - 19.2 = 4.8`

`11 - 19.2 = -8.2`

`22 - 19.2 = 2.8`

Take absolute value of the results above

`|-6.5| = 6.5`

`|2.8| = 2.8`

`|4.3| = 4.3`

`|4.8| = 4.8`

`|-8.2| = 8.2`

`|2.8| = 2.8`

The mean of the above gives the MAD

`M.A.D= (\sum |x - u|)/(n)`

`M.A.D= (6.5 + 2.8 + 4.3 + 4.8 + 8.2 + 2.8)/(6)`

`M.A.D= (29.4)/(6)`

`M.A.D= 4.9`