Question

Using the following data, calculate the mean absolute deviation:

10 7 1 6 7 9 8 10 2 5


What is the mean absolute deviation for these data?
2
2.4
6.5
7

Answer 1

First set of data:
Mean - 6.5
Absolute deviation - 2.4

Second set of data:
Mean - 4.475
Absolute deviation - 2.275

Answer 2

The mean absolute deviation of first data is
`2.54`

and for second data is
`2.115`

Explanation:

Mean of data
`x_1,x_2,x_3,x_4,...x_(n)` is calculated as:

`mean=(x_1+x_2+x_3+x_4+...+x_n)/(n)`

and mean absolute deviation is calculated as
`√(mean)`

The given first data : 10 7 1 6 7 9 8 10 2 5

`mean=(x_1+x_2+x_3+x_4+...+x_n)/(n)`

`mean=(10+7+1+6+7+9+8+10+2+5)/(10)`

`mean=6.5`

mean absolute deviation
`√(6.5)=2.54`

The given first data : 2 2.4 6.5 7

`mean=(x_1+x_2+x_3+x_4+...+x_n)/(n)`

`mean=(2+2.4+6.5+7)/(4)`

`mean=(17.9)/(4)`

`mean=4.475`

mean absolute deviation
`√(4.475)=2.115`

Therefore, the mean absolute deviation of first data is
`2.54`

and for second data is
`2.115`