To create:
The frequency distribution with class boundaries, midpoint, relative frequency and cumulative frequency.
Answer to Problem 2CR
Solution:
The frequency distribution with class boundaries, midpoint, relative frequency and cumulative frequency is shown in Table 5.
Explanation of Solution
Given:
The data for number weights in pounds is given as,
Calculation:
The number of classes with the class width of 25 will be 6. Calculate the number of values that fall within the class interval and complete the frequency table. The values lying between
Similarly, completing all the frequencies as shown in table below,
Number of absent | |
Class | Frequency |
5 4 5 4 4 2 |
Table 1
The formula to calculate the class boundary is,
For the first class,
Substitute
Continuing the same way, the class boundaries of all the five classes are shown in the table given below,
Class | Frequency | Class boundaries |
5 | ||
4 | ||
5 | ||
4 | ||
4 | ||
2 |
Table 2
The formula to calculate the midpoint of any class is,
For the first class,
Substitute
Continuing the same way, the midpoint of all the five classes are shown in the table given below,
Class | Frequency | Class boundaries | Midpoint |
5 | |||
4 | |||
5 | |||
4 | |||
4 | |||
2 |
Table 3
The formula to calculate the relative frequency of any class is,
Here
The sum of the frequencies is,
For the first class,
Substitute 5 for
Continuing the same way, the relative frequency of all the five classes are shown in the table given below,
Class | Frequency | Class boundaries | Midpoint | Relative frequency |
5 | ||||
4 | ||||
5 | ||||
4 | ||||
4 | ||||
2 |
Table 4
The cumulative frequency of any class is calculated by adding the frequency of that class and all the previous classes.
The cumulative frequency of all the five classes are shown in the table given below,
Class | Frequency | Class boundaries | Midpoint | Relative frequency | Cumulative frequency |
5 | 5 | ||||
4 | |||||
5 | |||||
4 | |||||
4 | |||||
2 |
Table 5
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Chapter 2 Solutions
Beginning Statistics, 2nd Edition
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