If the mean and standards deviation of 100 observations are 50 and 4 respectively. Find the sum of all the observations and the sum of their squares.

Explanation

`bar{x}=50, n=100` and `sigma=5`

`Rightarrow 50=frac{sum x_{i}}{100}`

`Rightarrow sum x_{i}=50 times 100=5000`

`s^{2}=frac{sum x_{i}^{2}}{n}-(bar{x})^{2}`

`Rightarrow 25=frac{sum x_{i}^{2}}{100}-(50)^{2}`

`Rightarrow 2525=frac{sum x_{i}^{2}}{100}`

`therefore sum x_{i}^{2}=252500`