Question

If the mode of a distribution is 18 and the mean is 24, then the median is:

• A. 18
• B. 24
• C. 22
• D. 21

Hint:

Remember Karl Pearson's empirical relation: \[ \text{Mode} = 3\text{Median} - 2\text{Mean}. \] It is applicable for moderately skewed distributions.

Answer 1

The Correct Option is C

Step 1: Write the empirical relation. \[ \text{Mode} = 3(\text{Median}) - 2(\text{Mean}). \] Given \[ \text{Mode}=18, \qquad \text{Mean}=24. \] Substituting the values, \[ 18 = 3(\text{Median}) - 2(24). \]

Step 2: Simplify the equation. \[ 18 = 3(\text{Median}) - 48. \] Adding \(48\) to both sides, \[ 66 = 3(\text{Median}). \]

Step 3: Find the median. \[ \text{Median} = \frac{66}{3} = 22. \] Conclusion: \[ {22} \] Hence, the correct answer is Option (C).