Question

Use the data set below to answer the following question.

2,4,7,2,3,7,9,3, 1,7
What is the mean absolute deviation (MAD) of this data set?


3.5

2.4

4.5

1.2

Answer 1

2.4

Explanation:

We have to find the mean first

`Mean = (Sum)/(No.\ of\ values)\\ = (2+4+7+2+3+7+9+3+1+7)/(10)\\ = (45)/(10)\\ = 4.5`

Now we have to find deviations.

Note that the deviations are calculated by subtracting the mean from the value. The distance is always positive so the deviations will be positive

Value Deviation

2 2-4.5 = |-2.5| = 2.5

4 4-4.5 = |-0.5| = 0.5

7 7-4.5 = 2.5

2 2-4.5 = |-2.5| = 2.5

3 3-4.5 = |-1.5| = 1.5

7 7-4.5 = 2.5

9 9-4.5 = 4.5

3 3-4.5 = |-1.5| = 1.5

1 1-4.5 = |-3.5| = 3.5

7 7-4.5 = 2.5

The last step is to find the mean of deviations.

`Mean\ of\ deviations = ((2.5+0.5+2.5+2.5+1.5+2.5+4.5+1.5+3.5+2.5)/(10)\\ = (24)/(10) \\=2.4`

The mean absolute deviation of given data set is 2.4 ..