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?

Answer 1

The mean absolute deviation (MAD) of this data set is 2.4

Explanation:

step 1

Find the mean

To find out the mean sum all values and divide by the number of values in the data set

we have the set of data

`[2, 4, 7, 2, 3, 7, 9, 3, 1, 7]`

The number of values is 10

so

The mean is equal to

`[2+4+7+2+3+7+9+3+1+7]/10=45/10=4.5`

step 2

Find out the absolute value of the difference of each value from that mean

`\left|2-4.5\right|=2.5`

`\left|4-4.5\right|=0.5`

`\left|7-4.5\right|=2.5`

`\left|2-4.5\right|=2.5`

`\left|3-4.5\right|=1.5`

`\left|7-4.5\right|=2.5`

`\left|9-4.5\right|=4.5`

`\left|3-4.5\right|=1.5`

`\left|1-4.5\right|=3.5`

`\left|7-4.5\right|=2.5`

so

we have

`[2.5, 0.5, 2.5, 2.5, 1.5, 2.5, 4.5, 1.5, 3.5, 2.5]`

step 3

we know that

The Mean Absolute Deviation (MAD) is the mean of those distances

`[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`

therefore

The mean absolute deviation (MAD) of this data set is 2.4