Question

Help me find Sample variance and standard deviation

Answer 1

First, find the mean. You'll need it to compute the variance.

$\bar x=\displaystyle\frac15\sum_{i=1}^5x_i=\dfrac{21+10+6+7+11}5=11$

The variance of the sample is then computed with the formula

$s^2=\displaystyle\dfrac1{5-1}\sum_{i=1}^5(\bar x-x_i)^2=\dfrac{(21-11)^2+\cdots+(11-11)^2}4=\dfrac{71}2=35.5$

The standard deviation is the square root of the variance, so

$s=\sqrt{35.5}\approx5.958$