Answer to Question #201469 in Statistics and Probability for Homam

Question

The following data represents the students' scores :

(81,35,86,91,69,72,47,66,80,55,90,53,43,56,80,77,59)

Wanted to find:

standard deviation

Answer 1

Standard deviation:

$\sigma=\sqrt{\frac{\sum(x_i-\overline{x})^2}{N}}$

Mean:

$\overline{x}=\frac{\sum x_i}{N}$

$\overline{x}=\frac{1140}{17}=67$

$\sigma=\sqrt{\frac{14^2+32^2+19^2+24^2+2^2+5^2+20^2+1+13^2+12^2+23^2+14^2+24^2+11^2+13^2+10^2+8^2}{17}}=\sqrt{\frac{4655}{17}}=16.55$