Question

In a moderately asymmetrical distribution, the mode and mean are 32.1 and 35.4 respectively. Calculate the median.

• A. 35
• B. 35.3
• C. 34.3
• D. 34

Hint:

To estimate the median in an asymmetrical distribution, use the empirical formula: Mode = 3 × Median − 2 × Mean.

Answer 1

The Correct Option is C

For a moderately skewed distribution, we use the empirical relation:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Substituting the given values:
\[ 32.1 = 3 \times \text{Median} - 2 \times 35.4
32.1 = 3 \times \text{Median} - 70.8
3 \times \text{Median} = 32.1 + 70.8 = 102.9
\text{Median} = \frac{102.9}{3} = \boxed{34.3} \]