Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Question
Chapter 2, Problem 6RE
a.
To determine
Find the number of classes.
a.
Expert Solution
Answer to Problem 6RE
The number of classes is 8.
Explanation of Solution
The given information is a frequency distribution corresponding to the number of freshmen elected in each of the elections.
From the frequency distribution, it can be observed that there are 8 classes.
Thus, the number of classes is 8.
b.
To determine
Find the class width of the given frequency distribution.
b.
Expert Solution
Answer to Problem 6RE
The class width of the data is 20.
Explanation of Solution
Calculation:
The class width is determined by the formula as follows:
Substitute 40 as “Lower limit for the second class” and 20 as “Lower limit for the first class”.
For each class “Class width” is same.
Thus, the class width is 20.
c.
To determine
List the class limits.
c.
Expert Solution
Answer to Problem 6RE
The lower class limits are 20, 40, 60, 80, 100, 120, 140, 160 and the upper class limits are 39, 59, 79, 99, 119, 139, 159, 179.
Explanation of Solution
Lower class limits:
The smallest value that is appear in a class interval is called lower class limits for that class.
Upper class limits:
The largest value that is appear in a class interval is called upper class limits for that class.
From the frequency distribution, it can be observed that there are 8 classes. The smallest and largest values in the class 20-39 are 20 and 39. Thus, the lower class limit for the class 20-39 is 20 and upper class limit is 39.
Similarly the remaining lower class limits are 20, 40, 60, 80, 100, 120, 140, 160 and the upper class limits are 39, 59, 79, 99, 119, 139, 159, 179.
Thus, the lower and upper class limits are 20, 40, 60, 80, 100, 120, 140, 160 and 339, 59, 79, 99, 119, 139, 159, 179 respectively.
d.
To determine
Construct a frequency histogram.
d.
Expert Solution
Answer to Problem 6RE
Output obtained from MINITAB software for number of freshmen elected is:
Explanation of Solution
Calculation:
Software procedure:
- Step by step procedure to draw the frequency histogram for number of freshmen elected using MINITAB software.
- Choose Graph > Bar Chart.
- From Bars represent, choose unique values from table.
- Choose Simple.
- Click OK.
- In Graph variables, enter the column of Frequency.
- In Categorical variables, enter the column of Number of Freshmen elected.
- Click OK
- Select Edit Scale, Enter 0 in Gap between clusters.
Observation:
From the bar graph, it can be seen that the maximum number of freshmen elected is in the class interval 80-99.
e.
To determine
Construct a relative frequency distribution for the data.
e.
Expert Solution
Answer to Problem 6RE
The relative frequency distribution for the data is:
| Number of Freshmen elected | Relative Frequency |
| 20-39 | 0.039 |
| 40-59 | 0.255 |
| 60-79 | 0.196 |
| 80-99 | 0.275 |
| 100-119 | 0.137 |
| 120-139 | 0.059 |
| 140-159 | 0.020 |
| 160-179 | 0.020 |
Explanation of Solution
Calculation:
Relative frequency:
The general formula for the relative frequency is,
Therefore,
Similarly, the relative frequencies for number of freshmen elected are obtained below:
| Number of Freshmen elected | Frequency | Relative Frequency |
| 20-39 | 2 |  |
| 40-59 | 13 | |
| 60-79 | 10 | |
| 80-99 | 14 | |
| 100-119 | 7 | |
| 120-139 | 3 | |
| 140-159 | 1 | |
| 160-179 | 1 |
f.
To determine
Construct a relative frequency histogram for these data.
f.
Expert Solution
Answer to Problem 6RE
Output obtained from MINITAB software for number of freshmen elected is:
Explanation of Solution
Calculation:
Relative Frequency Histogram:
Software procedure:
- Step by step procedure to draw the relative frequency histogram for number of freshmen elected using MINITAB software.
- Choose Graph > Bar Chart.
- From Bars represent, choose unique values from table.
- Choose Simple.
- Click OK.
- In Graph variables, enter the column of Relative Frequency.
- In Categorical variables, enter the column of Number of Freshmen elected.
- Click OK
- Select Edit Scale, Enter 0 in Gap between clusters.
Observation:
From the bar graph, it can be seen that the maximum number of freshmen elected is in the class interval 80-99.
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Chapter 2 Solutions
Essential Statistics
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