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.
[tex]\bar X=\frac{96+89+79+85+87+94+96+98}{8}=\frac{724}{8}=90.5[/tex]
We now find the absolute value of the distance of each value from the mean.
This is called the absolute deviation
{[tex]|96-90.5|,|89-90.5|,|79-90.5|,|85-90.5|,|87-90.5|,|94-90.5|,|96-90.5|,|98-90.5|[/tex]}
{[tex]5.5,1.5,11.5,5.5,3.5,3.5,5.5,7.5[/tex]}
We now find the mean of the absolute deviations
[tex]MAD=\frac{5.5+1.5+11.5+5.5+3.5+3.5+5.5+7.5}{8} =\frac{44}{8} =5.5[/tex]
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.
