Chapter 14.3, Problem 28E

a.

To determine

To calculate: The mean of the data represented by the stem-and-leaf plot.

Answer to Problem 28E

The mean is $77.5142$

Explanation of Solution

Given information:

  

Formula used:

Formula of Mean

  $\overline{X}=\frac{{\displaystyle \sum X}}{n}$ where X represents each of the values in the data set.

Calculation:

According to the stem-and-leaf plot ,

  $\left\{\begin{array}{l}44,44,49,54,55,62,62,64,65,69,71,74,75,76,77,78,79,\\ 80,82,84,85,86,87,88,89,89,89,90,92,93,93,95,96,98,99\end{array}\right\}.$

So, $n=35$ .

The mean of the data is

  $\begin{array}{l}=\frac{\text{Sum of all observation}}{35}\\ =\frac{2713}{35}\\ =77.5142\end{array}$

Hence, the mean is $77.5142$

b.

To determine

To calculate: The median of the data.

Answer to Problem 28E

The median is 80.

Explanation of Solution

Given information:

  

Formula used:

Median represents the middle value.

Median for even terms = $\frac{{\left(\frac{n}{2}\right)}^{th}\text{term}+{\left(\frac{n}{2}+1\right)}^{th}\text{term}}{2}$

Median for odd terms = ${\left(\frac{n+1}{2}\right)}^{th}\text{term}$

Calculation:

According to the stem-and-leaf plot,

The total number in leaves are 35.

  $\begin{array}{l}={\left(\frac{35+1}{2}\right)}^{th}\text{term}\\ \text{=}{\left(18\right)}^{th}\text{term}\end{array}$

This implies the median is the 18^thleaf on the plot.

The median is 80.

Hence, the median is 80.

c.

To determine

To calculate: The mode of the data.

Answer to Problem 28E

The mode is 89.

Explanation of Solution

Given information:

  

Formula used:

The mode of a set of data is the most frequent value. Some sets of the data have multiple modes and others have no mode.

Calculation:

According to the stem-and-leaf plot ,

It shows the modes by repeated digits for a particular stem.

There are three 9s with the stem 8.

The modes is 89.

Hence, the mode is 89.