Question

The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean and standard deviation for the players height. height (in) 70-71 72-73 74-75 76-77 78-79 80-81 82-83 frequency 1 8 13 8 15 6 3

Answer 1

In the following calculations will be used mean value from every group(70.5, 72.5 etc)

The mean height is: $m={\frac {70.5+8*72.5+13*74.5+8*76.5+15*78.5+6*80.5+3*82.5} {54}} = 76.7$ inches

The standart deviation is:

$s^{2}=$ ${\frac {(70.5-76.7)^{2}+8*(72.5-76.7)^{2}+13*(74.5-76.7)^{2}+8*(76.5-76.7)^{2}+15*(78.5-76.7)^{2}+6*(80.5-76.7)^{2}+3*(82.5-76.7)^{2}} {53}}$

$s^{2} =$ 9

$s=3$

the mean is 76.7 inches, standart deviation is 3 inches