Question

Jordan had the following scores on her math tests last quarter: 96, 89, 79, 85, 87, 94,

96, and 98. Find the mean absolute deviation for the set of data. Round to the nearest
tenth. How many data values are closer than one mean absolute deviation away from
the mean?

Answer 1

a) 5.5

b) None

Explanation:

The given data set is {96,89,79,85,87,94,96,98}

First we must find the mean.

`\bar X=(96+89+79+85+87+94+96+98)/(8)=(724)/(8)=90.5`

We now find the absolute value of the distance of each value from the mean.

This is called the absolute deviation

{
`|96-90.5|,|89-90.5|,|79-90.5|,|85-90.5|,|87-90.5|,|94-90.5|,|96-90.5|,|98-90.5|`}

{
`5.5,1.5,11.5,5.5,3.5,3.5,5.5,7.5`}

We now find the mean of the absolute deviations

`MAD=(5.5+1.5+11.5+5.5+3.5+3.5+5.5+7.5)/(8) =(44)/(8) =5.5`

The least absolute deviation is 1.5. This is not within one absolute deviation.

Therefore none of the data set is closer than one mean absolute deviation away from the mean.