Question

Find the mode of the following data:

Hint:

To calculate the mode of grouped data, use the formula for the mode and identify the modal class based on the highest frequency.

Answer 1

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.