Chapter 12.3, Problem 4P

a.

To determine

To find: The mean, median, and range of the given data set.

Answer to Problem 4P

  $\text{Mean}=20.8;\text{ Median}=21;\text{ Range}=5$

Explanation of Solution

Given information:

A data set is given as below −

  

Calculation:

Given data set is -

  

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

  $\text{Range}=24-19=5$

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{\left(19\times 4\right)+\left(20\times 5\right)+\left(21\times 6\right)+\left(22\times 2\right)+\left(23\times 2\right)+\left(24\times 1\right)}{20}\\ \Rightarrow \text{Mean}=20.8\end{array}$

  $\text{Median}=\frac{21+21}{2}=21$

Hence, for the given data set −

  $\text{Mean}=20.8;\text{ Median}=21;\text{ Range}=5$

b.

To determine

To find: Whether mean is equal to the median.

Answer to Problem 4P

Mean is not equal to the median.

Explanation of Solution

Given information:

Same as part

  $a$ of this exercise.

Calculation:

Given data set is -

  

Since line plot is not symmetrical, mean is not equal to the median.