Correct Answer - Option 2 : 46.36
Formula used
\(\rm Mode =L + \left [ \frac{f1 - f0}{2f1 - f0 - f2} \right ]\times i\)
i = class interval or class size
f1 = frequency of modal class
fo = frequency of pre modal class
f2 = frequency of success modal class
L = lower limit of modal class
Calculation:
Here maximum frequency is 28 ,the class corresponding to this 40-50
So modal class is 40-50
Now lower limit of modal class (l) = 40
Frequency (f1) of modal class = 28
frequency (f0) of preceding the modal class = 14
frequency (f2) of the class succeeding the modal class = 20
Class size = 10
\(\rm Mode = 40 + \left [ \frac{28 - 14}{2 \times 28 - 14 - 20} \right ]\times 10\)
= 40 + 6.36
∴ Mode = 46.36
Another formula to calculate mode = 3 Median - 2 Mean