Chapter 7.1, Problem 31E

(a)

To determine

The winning team.

If the team with more median score wins, the result remains the same or not.

Answer to Problem 31E

The team A with greater mean will win.

The result will not be the same if median is the criteria of winning.

Explanation of Solution

Given:

The given data sets are:

  $\begin{array}{l}\text{Team A: 172,130,173,212}\\ \text{Team B: 136,184,168,192}\end{array}$

Calculation:

The mean and median of team A will be:

  $\begin{array}{l}\text{Mean = }\frac{130+172+173+212}{4}\text{ = }171.75\\ \text{Median = }\frac{172+173}{2}=172.5\end{array}$

The mean and median of team B will be:

  $\begin{array}{l}\text{Mean = }\frac{136+168+184+192}{4}\text{ =}170\\ \text{Median = }\frac{168+184}{2}=176\end{array}$

The team A with greater mean will win.

The result will not be the same if median is the criteria of winning.

(b)

To determine

The more consistent team.

Answer to Problem 31E

Team B is more consistent.

Explanation of Solution

Given:

The given data sets are:

  $\begin{array}{l}\text{Team A: 172,130,173,212}\\ \text{Team B: 136,184,168,192}\end{array}$

Calculation:

Team B is more consistent.

This is so because, the team is having an outlier, whereas, team B is having no outlier.

(c)

To determine

The winning team.

Answer to Problem 31E

The team B with greater mean will win.

Explanation of Solution

Given:

The given data sets are:

  $\begin{array}{l}\text{Team A: 172,130,173,212}\\ \text{Team B: 136,184,168,192}\end{array}$

Calculation:

All the scores of team A are increased by 15.

All the scores of team B are increased by 12.5%.

The new scores will be:

  $\begin{array}{l}\text{Team A: 145,187,188,227}\\ \text{Team B: 153,189+207,216}\end{array}$

The mean of team A will be:

  $\text{Mean = }171.75+15=186.15$

The mean of team B will be:

  $\begin{array}{l}\text{Mean = }\left(\frac{12.5}{100}\times 170\right)+170\\ \text{Mean = }\left(21.25\right)+170\\ \text{Mean =}191.25\end{array}$

The team B with greater mean will win.