Question

The modal class for the following frequency distribution is

x	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60
f	3	12	27	57	75	80

• A. 30 - 40
• B. 20 - 30
• C. 10 - 20
• D. 50 - 60

Answer 1

The Correct Option is A

Step 1: Identify the Class Intervals and Frequencies 

Given a cumulative frequency distribution, we determine the class intervals:

Class Interval	Frequency
0 - 10	3
10 - 20	12 - 3 = 9
20 - 30	27 - 12 = 15
30 - 40	57 - 27 = 30
40 - 50	75 - 57 = 18
50 - 60	80 - 75 = 5

Step 2: Identify the Modal Class

The modal class is the class with the highest frequency. From the table above, the highest frequency is 30, which corresponds to the class interval 30 - 40.

Final Answer: 30 - 40

Answer 2

To determine the modal class for the given frequency distribution, we must first compute the frequencies within each class interval. The tabulated data represents cumulative frequencies, indicating how many data points fall below each upper class boundary.

The frequencies for each class are derived by subtracting the cumulative frequency of the previous class from the current cumulative frequency:

Class Interval	Cumulative Frequency	Frequency
0 - 10	3	3
10 - 20	12	12 - 3 = 9
20 - 30	27	27 - 12 = 15
30 - 40	57	57 - 27 = 30
40 - 50	75	75 - 57 = 18
50 - 60	80	80 - 75 = 5

From these calculations, the class interval 30 - 40 has the highest frequency of 30. Thus, the modal class is 30 - 40.