Question

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

Answer 1

Answer:

a) 5.5

b) None

Step-by-step explanation:

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

First we must find the mean.

$\bar X=\frac{96+89+79+85+87+94+96+98}{8}=\frac{724}{8}=90.5$

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

$MAD=\frac{5.5+1.5+11.5+5.5+3.5+3.5+5.5+7.5}{8} =\frac{44}{8} =5.5$

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.