Question : Find the mode for the given distribution (rounded off to two decimal places).
Option 1: 35.25
Option 2: 40.25
Option 3: 30.33
Option 4: 28.33
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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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