Chapter 13.4, Problem 21SR

(a)

To determine

To Find:Range, median, upper quartile, lower quartile, interquartile range, and any outlier for each set of data

Answer to Problem 21SR

For rose bowl:

Range: $39$

Median: $27$

Upper quartile = $38$

Lower quartile = $18$

Interquartile range = $20$

For Cotton bowl:

Range: $48$

Median: $28$

Upper quartile = $35$

Lower quartile = $17$

Interquartile range = $18$

Explanation of Solution

Given:Use the data in the stem-and-leaf plot.

  

Finding range for Rose bowl

Highest age = $49$

Lowest age = $10$

Then

Range = highest age − lowest age

  $\begin{array}{l}=49-10\\ =39\end{array}$

The range is $39$ .

Finding range of Cotton bowl

Highest age = $55$

Lowest age = $7$

Then

Range = highest age − lowest age

  $\begin{array}{l}=55-7\\ =48\end{array}$

The range is $48$ .

Finding Upper quartile and lower quartile of rose bowl

From the stem-and-leaf plot

The median of the data is $27$

Upper quartile = $38$

Lower quartile = $18$

For finding interquartile range

Interquartile range = Upper quartile − lower quartile

  $\begin{array}{l}=38-18\\ =20\end{array}$

Now,

Multiply the interquartile range by $1.5$

We get

  $\begin{array}{l}=20\times 1.5\\ =30\end{array}$

Now subtract $30$ from the lower quartile and add $30$ to the upper quartile

I.e.

  $\begin{array}{l}18-30=-12\\ 38+30=68\end{array}$

Since all the data is in the range of $-12\text{ and 68}$

Thus

There is no outlier in the data

Finding Upper quartile and lower quartile of Cotton bowl

From the stem-and-leaf plot

The median of the data is $28$

Upper quartile = $35$

Lower quartile = $17$

For finding interquartile range

Interquartile range = Upper quartile − lower quartile

  $\begin{array}{l}=35-17\\ =18\end{array}$

Now,

Multiply the interquartile range by $1.5$

We get

  $\begin{array}{l}=18\times 1.5\\ =27\end{array}$

Now subtract $27$ from the lower quartile and add $27$ to the upper quartile

I.e.

  $\begin{array}{l}17-27=-10\\ 35+17=62\end{array}$

Since all the data is in the range of $-10\text{ and 62}$

Thus

There is no outlier in the data

(b)

To determine

To Compare:The given data.

Answer to Problem 21SR

The range of cotton bowl is greater than Rose bowl.

The median of rose bowl is greater than cotton bowl.

The Upper quartile and the lower quartile of rose bowl is greater than cotton bowl.

The interquartile range of the rose bowl is also greater than the cotton bowl.

Explanation of Solution

Given:Use the data in the stem-and-leaf plot.

  

From the data given

It is seen that there is one outlier in the data.

The range of cotton bowl is greater than Rose bowl.

The median of rose bowl is greater than cotton bowl.

The Upper quartile and the lower quartile of rose bowl is greater than cotton bowl.

The interquartile range of the rose bowl is also greater than the cotton bowl.