The table shows the height of 100 men who were at the health center.

1. Use class midpoints and calculate the estimated mean

Midpoints: $145,155,165,175$

$\text{Estimated mean}=\frac{145(15)+155(31)+165(41)+175(13)}{100}$

$=\frac{2175+4805+6765+2275}{100}$

$=\frac{16020}{100}=160.2$

1. Use the midpoints to calculate $\sum fx^2$

Class midpoints are $145,155,165,175$.

$\sum fx^2=15(145^2)+31(155^2)+41(165^2)+13(175^2)$
$=2\,677\,400$

2. Substitute into the grouped-data standard deviation formula

Using $\bar{x}=160.2$ from part (a) and $\sum f=100$,

$\text{standard deviation}=\sqrt{\frac{2\,677\,400}{100}-(160.2)^2}$
$=\sqrt{26774-25664.04}$
$=\sqrt{1109.96}$
$=33.315\ldots$