Question

The mean and S.D of $100$ observations are $50$ and $4$ respectively. Find the sum of squares of observation.

Answer 1

$\frac{\sum x_i}{100}=50\Rightarrow \sum x_i=5000$
$\frac{\sum {\left(x_i-50\right)}^2}{N}=16$
$\frac{{\sum x_i}^2-100\sum x_i+2500}{100}=16$
$\sum {x_i}^2-100\times 5000+2500=16\times 100$
$\sum {x_i}^2=500000-900$
$\sum {x_i}^2=499100$