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Question : Find the mode for the given distribution (rounded off to two decimal places).

Class Interval 5-10 10-15 15-20 20-25 25-30 30-35
Frequency 8 7 6 9 11 10

Option 1: 35.25

Option 2: 40.25

Option 3: 30.33

Option 4: 28.33


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 8th Jan, 2024

Correct Answer: 28.33


Solution : Here, the maximum frequency is 11, and the corresponding class is 25–30.
So the modal class is 25–30.
Now lower limit of the modal class ($l$) = 25,
Frequency of the modal class ($f_1$) = 11
Frequency of the preceding modal class ($f_0$) = 9
Frequency of the succeeding modal class ($f_2$) = 10
class size ($h$) = 5
We know, mode = $l + (\frac{f_1-f_0}{2f_1-f_0-f_2})×h$
= $25 + (\frac{11-9}{2(11)-9-10})×5$
= $25 + (\frac{2}{3})×5$
= $25 + 3.33$
= $28.33$
Hence, the correct answer is 28.33.

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