Answer
The variance:
$s^2=100$
The standard deviation:
$s=10$
Work Step by Step
At first, let's evaluate the sample mean:
$x̅=\frac{83+65+91+87+84}{5}=82$
Now, the variance:
$s^2=\frac{Σ(x_i-x̅^2)}{n-1}=\frac{(83-82)^2+(65-82)^2+(91-82)^2+(87-82)^2+(84-82)^2}{5-1}=\frac{1+289+81+25+4}{4}=100$
The standard deviation:
$s=\sqrt {400}=10$
