Chapter 13.3, Problem 17STP

To determine

To Choose:The statement that is not supported by the data

Answer to Problem 17STP

Option (D)

An outlier of the data is $29$ games

Explanation of Solution

Given:The table shows the total number of wins by the team that won the women’s NCAA basketball tournament for the past $15$ years.

  

Which of the following statement is not supported by the data

(A) Less than half of the teams won more than $34$ games and half won less than $34$ games.

(B) The range of the data is $10$ games.

(C) About one fourth of the team won $32$ fewer games.

(D) An outlier of the data is $29$ games.

Finding range Highest age = $39$

Lowest age = $29$

Then

Range = highest age − lowest age

  $\begin{array}{l}=39-29\\ =10\end{array}$

The range is $10$ .

Finding Upper quartile and lower quartile of rose bowl

Arranging the data in the ascending order

  $29,31,31,32,33,33,34,34,34,34,35,36,37,39,39$

Median

  $\begin{array}{l}29,31,31,32,33,33,34,\underset{\_}{34},34,34,35,36,37,39,39\\ =34\end{array}$

Upper quartile

  $\begin{array}{l}29,31,31,32,33,33,34,34,34,34,35,\underset{\_}{36},37,39,39\\ =36\end{array}$

Lower quartile

  $\begin{array}{l}29,31,31,\underset{\_}{32,}33,33,34,34,34,34,35,36,37,39,39\\ =32\end{array}$

For finding interquartile range

Interquartile range = Upper quartile − lower quartile

  $\begin{array}{l}=36-32\\ =4\end{array}$

Now,

Multiply the interquartile range by $1.5$

We get

  $\begin{array}{l}=4\times 1.5\\ =6\end{array}$

Now subtract $6$ from the lower quartile and add $6$ to the upper quartile

I.e.

  $\begin{array}{l}32-6=26\\ 36+6=42\end{array}$

There is no outlier in the data.

Hence, Option (D) is incorrect

There is no outlier in the data.