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:

For moderately skewed distributions, always use the formula $\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}$ to quickly estimate the mode.

Answer 1

The Correct Option is A

Step 1: Recall the empirical relationship between mean, median, and mode
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

Step 2: Substitute values
\[ \text{Mode} = 3(25.8) - 2(26.1) \] \[ = 77.4 - 52.2 \] \[ = 25.2 \]

Step 3: Verify with options
Correct mode $= 25.2$. So the correct option is (C).
\[ \boxed{\text{Mode} = 25.2} \]