Chapter 12.4, Problem 1MP

a.

To determine

To find: The box-and-whisker plot of given data set.

Explanation of Solution

Given information:

Climate data sets for Oakville and Fairview cities are given as below −

  

Calculation:

Climate data sets for Oakville and Fairview cities are given as below −

  

For Oakville,

  $\begin{array}{l}\text{Arranging temperature data in ascending order,}\\ 72\text{ 74 76 77 78 78 82 84 87 89}\\ \text{Median}\left(Q_2\right)=\frac{78+78}{2}=78\\ \text{Mode}=78\\ \text{First quartile}\left(Q_1\right)=76\\ \text{Third quartile}\left(Q_3\right)=84\end{array}$

Plotting box-and-whisker plot as below-

  

For Fairview,

  $\begin{array}{l}\text{Arranging temperature data in ascending order,}\\ \text{77 80 82 82 83 83 86 86 87}\\ \text{Median}\left(Q_2\right)=83\\ \text{First quartile}\left(Q_1\right)=\frac{80+82}{2}=81\\ \text{Third quartile}\left(Q_3\right)=\frac{86+86}{2}=86\end{array}$

Plotting box-and-whisker plot as below-

  

b.

To determine

To find: The interpretation from box-and-whisker plot of the temperature of two cities.

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

For Oakville,box-and-whisker plot is given as below-

  

For Fairview,box-and-whisker plot is given as below

From above two plots, it can be observed that Oakville has relatively less temperature in August.

c.

To determine

To find: The interpretation from box-and-whisker plot of the temperature of two cities.

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Also average temperature for Fairview in $2004$ was ${73}^0$ .

Calculation:

For Oakville, box-and-whisker plot is given as below-

  

For Fairview,average temperature in $2004$ was ${73}^0$ .

  $\begin{array}{l}\text{Arranging temperature data in ascending order,}\\ \text{73}\text{77 80 82 82 83 83 86 86 87}\\ \text{Median}\left(Q_2\right)=\frac{82+83}{2}=82.5\\ \text{First quartile}\left(Q_1\right)=80\\ \text{Third quartile}\left(Q_3\right)=86\end{array}$

Plotting box-and-whisker plot as below

From above two plots, it can be observed that Oakville has relatively less temperature in August.

After including new temperature data box-and-whisker plot changed and minimum value and first quartile distance increased. Although it does not affect the conclusion made in part $b$ of this exercise. Average temperature of Fairview city is still high than Oakville city. In other words, Fairview is more warmer city is August.