Chapter B.2, Problem 15E

(a)

To determine

To find: The mean for each team member.

Answer to Problem 15E

The mean for each team member is given below.

Explanation of Solution

Given:

The table shows the bowling scores of a three-member team for a three-game series.

Team member	Game 1	Game 2	Game 3
Jay	181	222	196
Hank	199	195	205
Buck	202	251	235

The mean is given as:

  $\overline{x}=\frac{{\displaystyle \sum x_i}}{N}\left[\begin{array}{l}\text{where are }{x}_i\text{ number of elements of data and }\\ N\text{are the total number of elements ofdata}\end{array}\right]$

The mean for Jay is calculated as:

  $\begin{array}{c}\overline{x}=\frac{181+222+196}{3}\\ \approx 199.66\end{array}$

The mean for Hank is calculated as:

  $\begin{array}{c}\overline{x}=\frac{199+195+205}{3}\\ \approx 199.66\end{array}$

The mean for Buck is calculated as:

  $\begin{array}{c}\overline{x}=\frac{202+251+235}{3}\\ \approx 229.33\end{array}$

Therefore, the mean for each team member is given above.

(b)

To determine

To find: The mean of the nine scores.

Answer to Problem 15E

The mean of the nine scores is $209.55$ .

Explanation of Solution

The mean of the nine scores is calculated as:

  $\begin{array}{c}\overline{x}=\frac{181+222+196+199+195+205+202+251+235}{9}\\ \approx 209.55\end{array}$

Therefore, the mean of the nine scores is $209.55$ .

(c)

To determine

To find: The median of the nine scores.

Answer to Problem 15E

The median of the nine scores is $\text{202}$ .

Explanation of Solution

The median is given as:

  $\text{Median}=\left(\frac{N+1}{2}\right)\text{th term}\left[N\text{are the odd number of elements of data}\right]$

Arrange the given data in ascending order.

  $\text{181,195,196,199,202,205,222,235,251}$ .

The median of the nine scores is calculated as:

  $\begin{array}{c}\text{Median}=\left(\frac{9+1}{2}\right)\text{th term}\\ =5\text{th term}\\ =\text{202}\end{array}$

Therefore, the median of the nine scores is $\text{202}$ .

(d)

To determine

To find: The measure of central tendency that is best describes the nine scores.

Answer to Problem 15E

The median is the best measure of central tendency.

Explanation of Solution

The median is the measure of central tendency which best describes the nine scores.

As the mean of three different players is not that much useful. Yet median of scores of data can tell us about which player score most the scores more than median.

Therefore, the median is the best measure of central tendency.