Chapter 14.2, Problem 9CFU

(a)

To determine

To find: Thestem and the leaf plot for the wining scores.

Answer to Problem 9CFU

The required stem plot is shown in Figure 1

Explanation of Solution

Given:

The winning scores of the first 40 liberty bowl is given.

The given data set is,

  $\begin{array}{l}7,1,15,6,16,32,13,14,14,34,47,17,7,31,31,7,20,36,21,20\\ 9,28,31,21,19,21,21,21,20,34,42,23,38,13,18,30,19,41,41,23\end{array}$

Calculation:

Consider the given data set is,

  $\begin{array}{l}7,1,15,6,16,32,13,14,14,34,47,17,7,31,31,7,20,36,21,20\\ 9,28,31,21,19,21,21,21,20,34,42,23,38,13,18,30,19,41,41,23\end{array}$

As the data ranges from 7 to 47 use the tens place from the stems. This is obtained by the drawing the vertical line to the right of the stems. The second step is to list the leaves in this case the leaves is the ones digit.

The Figure for the stem plot is shown in Figure 1

  

Figure 1

(b)

To determine

To find: The mean of the data.

Answer to Problem 9CFU

The mean of the data is $23.55$ .

Explanation of Solution

Consider the sum of the number that is contribute by the stem 0 and having the leaves is,

  $0+\left(6+7+7+7+9\right)=36$

Consider the sum of the three number is contributed by the step 1 that have 10 leaves is,

  $\begin{array}{c}10\left(10\right)+\left(3+3+4+4+5+6+7+8+9+9\right)=100+58\\ =158\end{array}$

The sum of the number that is contributed by the stem 2 that have 11 leaves is,

  $\begin{array}{c}11\left(20\right)+\left(1+1+1+1+1+3+3+8\right)=220+19\\ =239\end{array}$

The sum of the number that is contributed by the stem 3 that have 9 leaves is,

  $\begin{array}{c}9\left(30\right)+\left(1+1+1+2+4+4+6+8\right)=270+27\\ =297\end{array}$

The sum of the number that is contributed by the stem, 4 and have 5 leaves is,

  $\begin{array}{c}5\left(40\right)+\left(1+1+1+2+7\right)=200+12\\ =212\end{array}$

Consider the mean of the data is,

  $\begin{array}{c}\overline{X}=\frac{{\displaystyle \sum _{i=1}^8{f}_i{x}_i}}{{\displaystyle \sum _{i=1}^8{f}_i}}\\ =\frac{36+158+239+297+212}{40}\\ =23.55\end{array}$

(c)

To determine

To find: The median class of the data.

Answer to Problem 9CFU

Thus, the median is $21$ .

Explanation of Solution

Consider the median of the data from the stem and the leaf plot is the middle number of the plot it can be two.

The number of measurements is 40 and by the definition the middle term is 20 and 21 measurement are leaves 1 and 1 with the stem. Then, the mean of the number is 21.

(d)

To determine

To find: The median of the data.

Answer to Problem 9CFU

The value of the mode is $21$ .

Explanation of Solution

Consider the mode of the data set is the number that appears more frequently.

Then, by the observations the stem and the leaf plot shows that there is a leaf 1 in the stem and there are 21 repeated 5 times. Therefore the mode is 21.

(e)

To determine

To find: The most representative measure of the central tendency for the measure of the points that is scored by the winning team at the liberty bowl.

Answer to Problem 9CFU

The mean, median and the mode any of them can be used as the central tendency.

Explanation of Solution

From the calculations of the mean, median and the mode any of them can be used as the central tendency.