Question

7. The human resources manager for a large company commissions a study in which the employment records of 500 company employees are examined for absenteeism during the past year. The business researcher conducting the study organizes the data into a frequency distribution to assist the human resources manager in analyzing the data. The frequency distribution is shown. For each class of the frequency distribution, determine the class midpoint, the relative frequency, and the cumulative frequency. Class Interval Frequency 0-under 2 218 2-under 4 207 4-under 6 56 6-under 8 11 8-under 10 8 ​

Answer 1

To find the class midpoint, we add the lower and upper limits of each class interval and divide by 2.

Class Interval | Frequency | Class Midpoint

0-under 2 | 218 | (0 + 2)/2 = 1

2-under 4 | 207 | (2 + 4)/2 = 3

4-under 6 | 56 | (4 + 6)/2 = 5

6-under 8 | 11 | (6 + 8)/2 = 7

8-under 10 | 8 | (8 + 10)/2 = 9

To find the relative frequency, we divide the frequency of each class by the total number of observations.

Class Interval | Frequency | Class Midpoint | Relative Frequency

0-under 2 | 218 | 1 | 218/500 = 0.436

2-under 4 | 207 | 3 | 207/500 = 0.414

4-under 6 | 56 | 5 | 56/500 = 0.112

6-under 8 | 11 | 7 | 11/500 = 0.022

8-under 10 | 8 | 9 | 8/500 = 0.016

To find the cumulative frequency, we add up the frequencies of all the classes up to and including the current class.

Class Interval | Frequency | Class Midpoint | Relative Frequency | Cumulative Frequency

0-under 2 | 218 | 1 | 0.436 | 218

2-under 4 | 207 | 3 | 0.414 | 425 (= 218 + 207)

4-under 6 | 56 | 5 | 0.112 | 481 (= 425 + 56)

6-under 8 | 11 | 7 | 0.022 | 492 (= 481 + 11)

8-under 10 | 8 | 9 | 0.016 | 500 (= 492 + 8)

Therefore, the class midpoints, relative frequencies, and cumulative frequencies for each class interval are as shown in the table above.