The given frequency distribution is in inclusive form.
The table is converted into exclusive class boundaries:
| Class Boundaries |
Frequency |
| 49.5–59.5 |
5 |
| 59.5–69.5 |
20 |
| 69.5–79.5 |
40 |
| 79.5–89.5 |
50 |
| 89.5–99.5 |
30 |
| 99.5–109.5 |
6 |
The modal class from the above distribution is \(79.5–89.5\)
∴ Mode is calculated using the formula:
\[
\text{Mode} = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h
\]
Where:
- \(l = 79.5\) = lower boundary of modal class
- \(f_1 = 50\) = frequency of modal class
- \(f_0 = 40\) = frequency of preceding class
- \(f_2 = 30\) = frequency of succeeding class
- \(h = 10\) = class width
\[
= 79.5 + \frac{50 - 40}{2 \times 50 - 40 - 30} \times 10
= 79.5 + \frac{10}{30} \times 10
= 79.5 + \frac{100}{30}
= 79.5 + 3.33
= 82.83 \text{ (approx.)}
\]
