Chapter 11.5, Problem 38S

To determine

To find: The standard deviation for the population of the data.

Answer to Problem 38S

The standard deviation of the population is $5.2846$ .

Explanation of Solution

Given:

The given graph is shown in Table 1

Table 1

13	18	17	21	16	9	11	28	8	10
7	19	16	16	12	19	21	11	8	13

Calculation:

Consider the mean of the given data se is,

  $\begin{array}{c}\mu =\frac{13+18+17+21+16+9+11+28+8+10+7+19+16+16+12+21+11+8+13}{20}\\ =14.65\end{array}$

Consider the standard deviation of the population is,

  $\begin{array}{c}\sigma =\sqrt{\frac{1}{n}{{\displaystyle \sum _{i=1}^n\left(x_i-\mu \right)}}^2}\\ =\sqrt{\frac{1}{20}{{\displaystyle \sum _{i=1}^{20}\left(x_i-14.65\right)}}^2}\end{array}$

Then, the value of ${{\displaystyle \sum _{i=1}^{20}\left(x_i-14.65\right)}}^2$ for all the value of $x_i$ that is the given data set is $558.55$ .

  $\begin{array}{c}\sigma =\sqrt{\frac{1}{20}\left(558.55\right)}\\ =5.2846\end{array}$

Thus, the standard deviation of the population is $5.2846$ .