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
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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