Question

He Alstons ran a family relay race. Below are the distances that each of the six family members ran (in kilometers).

0.3, 0.6, 0.5, 1, 0.4, 0.8

Find the mean absolute deviation (MAD) of the data set.

Answer 1

Just add all of the numbers up and then divide 6 because they're 6 families.

Answer 2

The mean absolute deviation of the data set is 0.2.

Explanation:

Given : The Alstons ran a family relay race. Below are the distances that each of the six family members ran (in kilometers).

0.3, 0.6, 0.5, 1, 0.4, 0.8

To find : The mean absolute deviation (MAD) of the data set ?

Solution :

Step 1 - Calculate the mean,

`m=(0.3+0.6+0.5+1+0.4+0.8)/(6)`

`m=(3.6)/(6)`

`m=0.6`

Step 2 - Calculate the distance between each data point and the mean.

Data points Distance from mean

0.3 |0.3-0.6|=0.3

0.6 |0.6-0.6|=0

0.5 |0.5-0.6|=0.1

1 |1-0.6|=0.4

0.4 |0.4-0.6|=0.2

0.8 |0.8-0.6|=0.2

Step 3 - Add distance together,

`0.3+0+0.1+0.4+0.2+0.2=1.2`

Step 4 - Divide the sum by number of data points,

`MAD=(1.2)/(6)=0.2`

Therefore, The mean absolute deviation of the data set is 0.2.