Calculate standard deviation of given data

Question

I want to find the standard deviation of the following data:

18: 200 times

19: 200 times

20 : 120 times

21: 340 times.

Is this the correct formula:

$\sqrt{\frac{18^2 \times 200+19^2 \times 200 + 20^2 \times 120 + 21^2 \times 340}{200+200+120+340}- (\frac{18 \times 200+19 \times 200 + 20\times 120 + 21 \times 340}{200+200+120+340})^2}$ ?

Thanks!

Answer 1

This is correct as long as you are not using Bessel's correction to calculate sample variance (which is dividing by $n-1$ instead of $n$ to obtain an unbiased estimator). If you are using Bessel's correction, you'll need to multiply your final answer by $\sqrt{\frac{200+200+120+340}{200+200+120+340-1}}$.