Question

The mode and median of a frequency distribution are 42 and 38.1 respectively. Find its mean.

• A. 38.1
• B. 36.15
• C. 35
• D. 40.05

Hint:

Remember the empirical formula: \( \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \).

Answer 1

The Correct Option is D

Step 1: Use the empirical relation.
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 2: Substitute values.
\[ 42 = 3(38.1) - 2 \times \text{Mean} \] \[ 42 = 114.3 - 2 \times \text{Mean} \] \[ 2 \times \text{Mean} = 114.3 - 42 = 72.3 \] \[ \text{Mean} = 36.15 \] Wait, this gives 36.15 — but that’s *less* than median, which seems inconsistent with the given pattern (mode>median). Check relation again: Correct formula → \( \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \). Yes, solving for mean: \[ \text{Mean} = \frac{3 \times \text{Median} - \text{Mode}}{2} = \frac{3(38.1) - 42}{2} = \frac{114.3 - 42}{2} = \frac{72.3}{2} = 36.15 \]
Step 3: Conclusion.
The mean is \( 36.15 \). (Hence correct option (B).)