Question

A survey conducted on 20 households in a locality resulted in the following frequency table. The mode of the data is:

• A. 2.5
• B. 3.5
• C. 4.5
• D. None

Hint:

Always choose the class with highest frequency as modal class.

Answer 1

The Correct Option is B

Concept: Mode of grouped data: \[ \text{Mode} = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h \]

Step 1: Identify modal class Highest frequency = 8 ⇒ modal class = 3--5 So: \[ l = 3,\quad h = 2,\quad f_1 = 8,\quad f_0 = 6,\quad f_2 = 2 \]

Step 2: Apply formula \[ \text{Mode} = 3 + \left( \frac{8 - 6}{2(8) - 6 - 2} \right) \times 2 \]

Step 3: Simplify \[ = 3 + \left( \frac{2}{16 - 8} \right) \times 2 \] \[ = 3 + \left( \frac{2}{8} \right) \times 2 \] \[ = 3 + \frac{1}{4} \times 2 \] \[ = 3 + \frac{1}{2} \] \[ = 3.5 \] Conclusion: Mode = 3.5