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=\frac{21+10+6+7+11}5=11`

The variance of the sample is then computed with the formula


`s^2=\displaystyle\frac1{5-1}\sum_(i=1)^5(\bar x-x_i)^2=\frac{(21-11)^2+\cdots+(11-11)^2}4=\frac{71}2=35.5`

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


`s=√(35.5)\approx5.958`