Chapter 11.2, Problem 11E

a.

To determine

To make a box-and-whisker plot.

Answer to Problem 11E

  

Explanation of Solution

Given information:

The data given is:

  $109,113,119,121,124,125,128,134,134,136,198$

Calculation :

The median of the above data is $125$ .

The upper quartile is $134$ .

The lower quartile is $119$ .

The upper and lower limits are $109\text{ and 198}$ respectively.

The box-and-whisker plot is made below:

  

b.

To determine

To find the outliers in the data set.

Answer to Problem 11E

  $198$ is an outliner.

Explanation of Solution

Given information:

The data given is:

  $109,113,119,121,124,125,128,134,134,136,198$

The median of the above data is $125$ .

The upper quartile is $134$ .

The lower quartile is $119$ .

Formula used:

The formulas used are:

  $\text{Interquartile range=Upper quartile}-\text{Lower quartile}$

  $\begin{array}{l}\text{Outliner=Upper quartile+1}\text{.5IQR}\\ \text{Outliner=Lower Quartile}-\text{1}\text{.5IQR}\end{array}$

Calculation :

The interquartile range is, $\text{IQR}=134-119=15$

  $\begin{array}{l}\text{Outliner}=134+22.5=156.5\\ \text{Outliner}=119-22.5=96.5\end{array}$

So, $198$ is an outliner, because it is greater than $156.5$

c.

To determine

To make a box-and-whisker plot excluding the outliners.

Answer to Problem 11E

  

Explanation of Solution

Given information:

The data given is:

  $109,113,119,121,124,125,128,134,134,136$

Calculation :

The median of the above data is $125$ .

The upper quartile is $134$ .

The lower quartile is $119$ .

The upper and lower limits are $109\text{ and 136}$ respectively.

The box-and-whisker plot is made below:

  

d.

To determine

To explain the difference after moving the outlier from the box-and-whisker plot.

Answer to Problem 11E

Final answer

Explanation of Solution

Given information:

The following box-and-whisker plots are made before and after removing the outliers:

  

  Conclusion :

From the above plots, it can be concluded that after removing the outliers, the mean, upper quartile and lower quartile are much more significantly visible.