Chapter 2, Problem 1UTA

The following tables show the first-round winning scores of the NCAA men's and women's basketball teams.

TABLE 2-17 Men's Winning First-Round NCAA Tournament Scores

95	70	79	99	83	72	79	101
69	82	86	70	79	69	69	70
95	70	77	61	69	68	69	72
89	66	84	77	50	83	63	58

TABLE 2-18 Women's Winning First-Round NCAA Tournament Scores

80	68	51	80	83	75	77	100
96	68	89	80	67	84	76	70
98	81	79	89	98	83	72	100
101	83	66	76	77	84	71	77

Use the software or method of your choice to construct separate histograms for the men's and women's winning scores Try 5, 7, and 10 classes for each. Which number of classes seems to be the best choice? Why?

To determine

To graph: The histogram for men’s and women’s winning score data..

Explanation of Solution

Calculation: For Men’s winning score data:

The largest value of the data set is 101 and the smallest value is 50 in the men’s winning score data.

$\begin{array}{l}\text{Class width}\text{=}\frac{\text{Largest data value - smallest data value}}{\text{Desired number of classes}}\\ \end{array}$.

Using five classes, the class width is calculated in the following way:

$\begin{array}{c}\text{Class width}=\frac{101-50}{5}\\ =10.2\\ \approx 11\end{array}$

The frequency table is as follows:

Class-limits	Class boundaries	Frequency
50–60	49.5–60.5	2
61–71	60.5–71.5	13
72–82	71.5–82.5	8
83–93	82.5–93.5	5
94–104	93.5–104.5	4

To construct the histogram by using the MINITAB, the steps are as follows:

Step 1: Enter the class boundaries in C1 and frequency in C2.

Step 2: Go to Graph > Histogram > Simple.

Step 3: Enter C1 in Graph variable, then go to Data options > Frequency > C2.

Step 4: Click on OK.

The obtained histogram is

Using seven classes, the class width is calculated in the following way:

$\begin{array}{c}\text{Class width}=\frac{101-50}{7}\\ =7.3\\ \approx 8\end{array}$

Class-limits	Class boundaries	Frequency
50–57	49.5–57.5	1
58–65	57.5–65.5	3
66–73	65.5–73.5	13
74–81	73.5–81.5	5
82–89	81.5–89.5	6
90–97	89.5–97.5	2
98–105	97.5–10.5	2

To construct the histogram by using the MINITAB, the steps are as follows:

Step 1: Enter the class boundaries in C3 and frequency in C4.

Step 2: Go to Graph > Histogram > Simple.

Step 3: Enter C3 in Graph variable, then go to Data options > Frequency > C4.

Step 4: Click on OK.

The obtained histogram is

Using 10 classes, the class width is calculated in the following way:

$\begin{array}{c}\text{Class width}=\frac{101-50}{10}\\ =5.1\\ \approx 6\end{array}$

Class-limits	Class boundaries	Frequency
50–55	49.5–55.5	1
56–61	55.5–61.5	2
62–67	61.5–67.5	2
68–73	67.5–73.5	12
74–79	73.5–79.5	5
80–85	79.5–85.5	4
86–91	85.5–91.5	2
92–97	91.5–97.5	2
98–103	97.5–103.5	2
104–109	103.5–109.5	0

To construct the histogram by using the MINITAB, the steps are as follows:

Step 1: Enter the class boundaries in C5 and frequency in C6.

Step 2: Go to Graph > Histogram > Simple.

Step 3: Enter C5 in Graph variable, then go to Data options > Frequency > C6.

Step 4: Click on OK.

The obtained histogram is

For Women’s winning score data:

The largest value of the data set is 101 and the smallest value is 51 in the women’s winning score data.

$\begin{array}{l}\text{Class width}\text{=}\frac{\text{Largest data value - smallest data value}}{\text{Desired number of classes}}\\ \end{array}$

Using five classes, the class width calculated in the following way:

$\begin{array}{c}\text{Class width}=\frac{101-51}{5}\\ =10\\ \approx 11\end{array}$

The frequency table is as follows:

Class-limits	Class boundaries	Frequency
51–61	50.5–61.5	1
62–72	61.5–72.5	7
73–83	72.5–83.5	14
84–94	83.5–94.5	4
95–105	94.5–105.5	6

To construct the histogram by using the MINITAB, the steps are as follows:

Step 1: Enter the class boundaries in C7 and frequency in C8.

Step 2: Go to Graph > Histogram > Simple.

Step 3: Enter C8 in Graph variable, then go to Data options > Frequency > C8.

Step 4: Click on OK.

The obtained histogram is

Using seven classes, the class width is calculated in the following way:

$\begin{array}{c}\text{Class width}=\frac{101-51}{7}\\ =7.1\\ \approx 8\end{array}$

The frequency table is as follows:

Class-limits	Class boundaries	Frequency
51–58	51.5–58.5	1
59–66	58.5–66.5	1
67–74	66.5–74.5	6
75–82	74.5–82.5	11
83–90	82.5–90.5	7
91–98	90.5–98.5	3
99–106	98.5–106.5	3

To construct the histogram by using the MINITAB, the steps are as follows:

Step 1: Enter the class boundaries in C9 and frequency in C10.

Step 2: Go to Graph > Histogram > Simple.

Step 3: Enter C9 in Graph variable, then go to Data options > Frequency > C10.

Step 4: Click on OK.

The obtained histogram is:

Using 10 classes, the class width calculated in the following way:

$\begin{array}{c}\text{Class width}=\frac{101-51}{10}\\ =5\end{array}$

The frequency table is as follows:

Class-limits	Class boundaries	Frequency
51–55	50.5–55.5	1
56–60	55.5–60.5	0
61–65	60.5–65.5	0
66–70	65.5–70.5	5
71–75	70.5–75.5	3
76–80	75.5–80.5	9
81–85	80.5–85.5	6
86–90	85.5–90.5	2
91–95	90.5–95.5	0
96 and more	95.5 and more	6

To construct the histogram by using the MINITAB, the steps are as follows:

Step 1: Enter the class boundaries in C11 and frequency in C12.

Step 2: Go to Graph > Histogram > Simple.

Step 3: Enter C11 in Graph variable, then go to Data options > Frequency > C12.

Step 4: Click on OK.

The obtained histogram is

Using number classes five and seven in both data sets of men’s and women’s seem to be the best because histograms for that classes shows reliable distribution but using classes ten show gap between the bars. Since, using five classes seems best than using classes seven.