Chapter 12.3, Problem 17PPE

To determine

To find: The range and mean of the given data sets.

Answer to Problem 17PPE

  $\begin{array}{l}\text{Set C: Range}=3.8;\text{Mean}=6.7\\ \text{Set D: Range}=28.3;\text{Mean}=9.025\end{array}$

Explanation of Solution

Given information:

Two data sets are given as below −

  $\begin{array}{l}\text{Set C: 4}\text{.5}7.18.36.9\\ \text{Set D: 2}\text{.1}29.51.23.3\end{array}$

Calculation:

Given data sets are −

  $\begin{array}{l}\text{Set C: 4}\text{.5}7.18.36.9\\ \text{Set D: 2}\text{.1}29.51.23.3\end{array}$

For $\text{Set C: 4}\text{.5}7.18.36.9$

Range of a data set is the difference between the greatest and least data value

  $\text{Range}=8.3-4.5=3.8$

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{4.5+7.1+8.3+6.9}{4}\\ \Rightarrow \text{Mean}=6.7\end{array}$

For $\text{Set D: 2}\text{.1}29.51.23.3$

Range of a data set is the difference between the greatest and least data value

  $\text{Range}=29.5-1.2=28.3$

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{2.1+29.5+1.2+3.3}{4}\\ \Rightarrow \text{Mean}=9.025\end{array}$

Hence, for the given two data sets −

  $\begin{array}{l}\text{Set C: Range}=3.8;\text{Mean}=6.7\\ \text{Set D: Range}=28.3;\text{Mean}=9.025\end{array}$