Question

Find the mode of the following distribution:
\[ \begin{array}{c|c|c|c|c|c|c} \text{Class-Interval} & 80-85 & 85-90 & 90-95 & 95-100 & 100-105 & 105-110 & 110-115 \\ \hline \text{Frequency} & 33 & 27 & 85 & 155 & 110 & 45 & 15 \end{array} \]

Hint:

The mode is estimated using the modal class and interpolation formula.

Answer 1

The mode is the class with the highest frequency.
Here, the modal class is \( 95-100 \) with frequency 155.
Using the mode formula:
\[ \text{Mode} = L + \frac{(f_1 - f_0)}{2f_1 - f_0 - f_2} \times h. \] \[ = 95 + \frac{(155 - 85)}{(2 \times 155 - 85 - 110)} \times 5. \] \[ = 95 + \frac{70}{115} \times 5. \] \[ = 95 + 3.04 \approx 98.04. \]