Question

Empirical relation between Mean, Median and Mode is

• A. Mode + Median =4 Median - 3 Mean
• B. Mode - Median = 2 (Median - Mean)
• C. Mode - Median = 2 (Median + Mean)
• D. Mode + Median 4 Median + 3' Mean

Answer 1

The Correct Option is B

To solve the problem, we need to recall the empirical relationship that connects the mode, median, and mean of a moderately skewed distribution.

1. Understanding the Empirical Relation:
In statistics, for a moderately skewed distribution, the following empirical relationship holds true:

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

2. Rearranging the Equation:
We can rearrange the above formula to express the relation in a different form:

\( \text{Mode} - \text{Median} = 2 \times (\text{Median} - \text{Mean}) \)

3. Identifying the Correct Option:
This matches option (2) exactly:

\( \text{Mode} - \text{Median} = 2 \times (\text{Median} - \text{Mean}) \)

Final Answer:
The correct empirical relation is (B): \({\text{Mode} - \text{Median} = 2 (\text{Median} - \text{Mean})} \).