In a moderately asymmetrical distribution, the mode and mean are 31.5…

The correct answer is Option (3) → 33.5

We can use Karl Pearson’s empirical relationship among mean, median, and mode:

$\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}$

Given:

• Mode = 31.5
• Mean = 34.5

Substitute into the formula:

$31.5 = 3 \times \text{Median} - 2(34.5)$

Simplify step by step:

$31.5 = 3 \times \text{Median} – 69$

$3 \times \text{Median} = 31.5 + 69 = 100.5$

$\text{Median} = \frac{100.5}{3} = 33.5$