Medium Practice — Set 1

Quick Recap — Statistics Computations

• $\sigma^2=\dfrac{\sum x^2}{n}-\bar x^2$ (shortcut formula).
• Effect of change: adding $k$ to every value shifts the mean by $k$ but leaves the variance unchanged; multiplying by $k$ multiplies the mean by $k$ and the variance by $k^2$.
• Variance of the first $n$ naturals $=\dfrac{n^2-1}{12}$.
• Coefficient of variation $=\dfrac{\sigma}{\bar x}\times100\%$; mean deviation $=\dfrac{\sum|x-\bar x|}{n}$.