Question

The mean and median of a frequency distribution are 26.1 and 25.8 respectively. The value of mode for the distribution will be:

• A. 24.2
• B. 25.1
• C. 25.2
• D. 26.4

Hint:

Remember the formula: \( \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \). This is useful for estimating the mode when only mean and median are known.

Answer 1

The Correct Option is A

Step 1: Formula connecting mean, median, and mode.
The empirical relation between mean, median, and mode is given by: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 2: Substitute the given values.
\[ \text{Mode} = 3(25.8) - 2(26.1) \] \[ \text{Mode} = 77.4 - 52.2 = 25.2 \] Wait — check again: \( 77.4 - 52.2 = 25.2 \). Hence the correct answer is (C) 25.2, not (A).
Step 3: Final Answer.
\[ \boxed{\text{Mode} = 25.2} \]