Chapter 10.1, Problem 18HP

(a).

To determine

To calculate: the age of new player for required mean age of team.

Answer to Problem 18HP

New player is of age $\underset{\_}{35}$ , so that the mean of team is 27.

Explanation of Solution

Given information:

1. The ages of the players of the team are as follows$29,25,26,31,28,23,21,25$ .
2. Mean of the ages is $27$when new player join the team.

Formula used:

  $\text{mean=}\frac{\text{Sum}\text{of}\text{the}\text{data}}{\text{number}\text{of}\text{items}\text{in}\text{data}\text{set}}$

Calculation:

Data set of the ages of the players on of the team is as follows.

  $29,25,26,31,28,23,21,25$ .

Assume age of new player be represented by variable $x.$

Using $\text{mean=}\frac{\text{Sum}\text{of}\text{the}\text{data}}{\text{number}\text{of}\text{items}\text{in}\text{data}\text{set}}$

Mean of ages after new player joins = $\frac{29+25+26+31+28+23+21+25+x}{9}$

  $27=\frac{208+x}{9}$

  $243=208+x$

  $x=243-208$

  $x=35$

Hence new player is of age $\underset{\_}{35}$ , so that the mean of team is 27.

(b).

To determine

To calculate: the age of new player for required median of age dataset.

.

Answer to Problem 18HP

Age of the new player must be less than or equal to 25 to get the median age of 25.

Explanation of Solution

Given information:

1. The age of the players on an intramural volleyball team is $29,25,26,31,28,23,21,25$ .
2. Median is $25$when new player join the team.

Formula used:

median= middle number of data arranged from least to greatest.

Calculation:

Data set of the ages of the players on of the team is as follows.

  $29,25,26,31,28,23,21,25$ .

Arrange the age of the players in ascending order.

  $21,23,25,25,26,28,29,31$

When the new player joins the team total number of ages becomes 9 .So for 9 ages , median age that is middle term will be fifth term. For median to be 25 , 25 must be fifth age in ascending order. So age of new player must be less than or equal to 25 to make the median age of data set as 25.

Hence any age less than or equal to 25 will given the median 25.