Question

The relation between mean, median and mode for a moderately asymmetrical distribution is:

• A. \(\text{Mode}=3\text{Median}-2\text{Mean}\)
• B. \(\text{Mode}=3\text{Mean}-2\text{Median}\)
• C. \(\text{Median}=3\text{Mode}-2\text{Mean}\)
• D. \(\text{Mean}=3\text{Median}-2\text{Mode}\)

Hint:

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

Answer 1

The Correct Option is A

Step 1: Expand the right-hand side. \[ \text{Mean}-\text{Mode} = 3\text{Mean}-3\text{Median}. \]

Step 2: Rearrange the equation. \[ -\text{Mode} = 2\text{Mean}-3\text{Median}. \] Multiplying by \(-1\), \[ \text{Mode} = 3\text{Median}-2\text{Mean}. \] Conclusion: \[ {\text{Mode}=3\text{Median}-2\text{Mean}} \] Hence, the correct answer is Option (A).