Chapter 7.1, Problem 19E

(a)

To determine

The range of the data set.

Answer to Problem 19E

  $25$

Explanation of Solution

Given:

The given data set is:

  $40,35,45,55,60$

Calculation:

The range of data set will be:

  $\begin{array}{l}=\text{Highest value - Lowest value}\\ =60-35\\ =25\end{array}$

(b)

To determine

The standard deviation of the data set.

Answer to Problem 19E

  $\sigma =9.27$

Explanation of Solution

Given:

The given data set is:

  $40,35,45,55,60$

Calculation:

The mean of the data set is:

  $\begin{array}{l}\overline{x}=\frac{40+35+45+55+60}{5}\\ \overline{x}=\frac{235}{5}\\ \overline{x}=47\end{array}$

The standard deviation of data set will be:

  $\begin{array}{l}\sigma =\sqrt{\frac{{\left(x_1-\overline{x}\right)}^2+{\left(x_1-\overline{x}\right)}^2+\mathrm{..............}+{\left(x_n-\overline{x}\right)}^2}{n}}\\ \sigma =\sqrt{\frac{{\left(40-47\right)}^2+{\left(35-47\right)}^2+{\left(45-47\right)}^2+{\left(55-47\right)}^2+{\left(60-47\right)}^2}{5}}\\ \sigma =\sqrt{\frac{{\left(-7\right)}^2+{\left(-12\right)}^2+{\left(-2\right)}^2+{\left(8\right)}^2+{\left(13\right)}^2}{5}}\\ \sigma =\sqrt{\frac{144+49+4+64+69}{5}}\\ \sigma =\sqrt{\frac{430}{5}}\\ \sigma =\sqrt{86}\\ \sigma =9.27\end{array}$