Question

Find the mode of the following data: 

Hint:

The modal class is always the one with the highest frequency. Use the mode formula carefully with correct substitution.

Answer 1

Step 1: Identify the modal class.
The highest frequency is 10 for the class interval 30–35. So, the modal class is 30–35.

Step 2: Use the formula for mode.
\[ \text{Mode} = l + \frac{(f_1 - f_0)}{2f_1 - f_0 - f_2} \times h \] where \( l = 30 \), \( f_1 = 10 \), \( f_0 = 9 \), \( f_2 = 3 \), and \( h = 5 \).

Step 3: Substitute the values.
\[ \text{Mode} = 30 + \frac{(10 - 9)}{2(10) - 9 - 3} \times 5 \] \[ = 30 + \frac{1}{20 - 12} \times 5 = 30 + \frac{1}{8} \times 5 = 30 + 0.625 = 30.625 \]
Step 4: Conclusion.
Hence, the mode of the data is \( \boxed{30.625} \).