A company collected the ages from a random sample of its mid

A company collected the ages from a random sample of its middle managers with the resulting frequency distribution shown below:

Class Interval                          Frequency

20 to 25                                   8

25 to 30                                   12

30 to 35                                   28

35 to 40                                   16

40 to 45                                   10

45 to 50                                   6

What is the cumulative relative frequency (%) of the fourth class interval?
A. 16
B. 80
C.64
D. 20
E. 60

Solution

What is the cumulative relative frequency (%) of the fourth class interval?

B. 80

Class Interval

FREQUENCY

Cumulative relative frequency

Cumulative percentage

20-25

8

8

(8/80)*100=10%

25-30

12

8 + 12 = 20

(20/80)*100=25%

30-35

28

20+28=48

(48/80)*100=60%

35-40(fourth class)

16

48+16=64

(64/80)*100=80%

40-45

10

64 + 10 = 74

(74/80)*100=92.5%

45-50

6

74 + 6 = 80

(80/80)*100=100%

total

80

or

Class Interval

FREQUENCY

Relative frequency

Cumulative relative frequency

20-25

8

8/80 = 0.1

0.1

25-30

12

12/80 = 0.15

0.1 + 0.15 = 0.25

30-35

28

28/80 = 0.35

0.25 + 0.35 = 0.6

35-40 (fourth class)

16

16/80 = 0.2

0.6 + 0.2 = 0.8

40-45

10

10/80 = 0.125

0.8 + 0.125 = 0.925

45-50

6

6/80 = 0.075

0.925 + 0.075 =1

total

80

1

The percentage of cumulative relative frequency is 0.8*100=80%

Class Interval	FREQUENCY	Cumulative relative frequency	Cumulative percentage
20-25	8	8	(8/80)*100=10%
25-30	12	8 + 12 = 20	(20/80)*100=25%
30-35	28	20+28=48	(48/80)*100=60%
35-40(fourth class)	16	48+16=64	(64/80)*100=80%
40-45	10	64 + 10 = 74	(74/80)*100=92.5%
45-50	6	74 + 6 = 80	(80/80)*100=100%
total	80