(a) Find the mean u and the standard deviation o for the collection of N = 8 stocks. (b) Find the sample mean i and sample standard deviation s of the random sample of stocks.

5.

(a)

The mean for the collection of $N=8$ stocks is,

$\begin{array}{rcl}\mu & =& \frac{{\displaystyle \sum _{i=1}^N{x}_i}}{N}\\ & =& \frac{5+3+6+8+4+7+10+5}{8}\\ & =& \frac{48}{8}\\ & =& 6\end{array}$

Thus, the mean for the collection of $N=8$ stocks is $6.

The standard deviation for the collection of $N=8$ stocks is,

$\begin{array}{rcl}\sigma & =& \sqrt{\frac{{\displaystyle \sum _{i=1}^N\left(x_i-\mu \right)}}{N}}\\ & =& \sqrt{\frac{{\left(5-6\right)}^2+{\left(3-6\right)}^2+{\left(6-6\right)}^2+{\left(8-6\right)}^2+{\left(4-6\right)}^2+{\left(7-6\right)}^2+{\left(10-6\right)}^2+{\left(5-6\right)}^2}{8}}\\ & =& \sqrt{\frac{1+9+0+4+4+1+16+1}{8}}\\ & =& \sqrt{\frac{36}{8}}\\ & =& \sqrt{4.5}\\ & =& 2.1213\end{array}$

Thus, the standard deviation for the collection of $N=8$ stocks is $2.1213.