The given data is:
Step 1:
Identify the modal class. The class with the highest frequency is \( 60-80 \), with a frequency of 12. So, the modal class is \( 60-80 \).
Step 2:
Let:
- \( l = 60 \) (lower boundary of the modal class),
- \( f_1 = 12 \) (frequency of the modal class),
- \( f_0 = 10 \) (frequency of the class preceding the modal class, i.e., \( 40-60 \)),
- \( f_2 = 6 \) (frequency of the class succeeding the modal class, i.e., \( 80-100 \)),
- \( h = 20 \) (class width).
Step 3:
Now, apply the formula for the mode:
\[
\text{Mode} = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h
\]
Substitute the values into the formula:
\[
\text{Mode} = 60 + \frac{12 - 10}{2 \times 12 - 10 - 6} \times 20
\]
Simplify:
\[
\text{Mode} = 60 + \frac{2}{24 - 16} \times 20 = 60 + \frac{2}{8} \times 20 = 60 + 5 = 65.
\]
Conclusion:
The mode of the given data is 65.
