Chapter 13.1, Problem 18HP

(a)

To determine

To find: the age of the new player be so that the mean age is 27.

Answer to Problem 18HP

The age of new player should be 35.

Explanation of Solution

Given information:

The ages of the players on an intramural volleyball team are 29, 25, 26, 31, 28, 23, 21, and 25.

Suppose another player joins the team.

Calculation:

Let’s consider the ages of players in the volleyball game.

29, 25, 26, 31, 28, 23, 21, 25

Sort the data in ascending order.

21, 23, 25, 25, 26, 28, 29, 31

Let’s assume the age of the 9^th player is $x$ .

Mean is the sum of data values divided by the a number of observations.

  $\begin{array}{l}\text{Mean}=\frac{21+23+25+25+26+28+29+31+X}{9}\\ 27=\frac{208+X}{9}\\ X=27\times 9-208\\ X=35\end{array}$

So the age of new player should be.

(b)

To determine

To find: the age of the new player be so that the median age is 25.

Answer to Problem 18HP

Age of the new player should be less than or equal to 25.

Explanation of Solution

Calculation:

Consider the age of players in sorted order.

21, 23, 25, 25, 26, 26, 28, 29, 31

Let’s consider the age of a new player is $"Y"$ .

Three scenarios can be drawn hare considering there is an odd number of observations in the data.

• If the age of a player is greater and equal to 26, the median value will be 26.
• If the age of the player is greater than 25 and less than 26, the median value will be exact age of the player.
• If the age of a player is less than or equal 25, the median value will always be 25.

Hence age of the new player should be less than or equal to 25.