Empiricla relationship between the three measures of central tendency is

Options

A. 2 Mean = 3 Median - Mode
Median - Mean
B. 2 Mode = 3
C. Mode = 2 Mean- 3Median
Mode + Mean
D. 3 Median = 2

Explanation

To solve the question about the empirical relationship between the three measures of central tendency, we will derive the relationships step by step.

### Step-by-Step Solution:

1. **Understanding the Measures of Central Tendency**:
- The three main measures of central tendency are Mean, Median, and Mode.
- The empirical relationship connects these three measures.

2. **Using the Empirical Relationship Formula**:
- The empirical relationship can be expressed as:
\[ 3 \times \text{Median} = \text{Mode} + 2 \times \text{Mean} \]

3. **Rearranging the Formula**:
- To express the relationship in terms of Mean and Median, we can rearrange the formula:
\[ 2 \times \text{Mean} = 3 \times \text{Median} - \text{Mode} \]

4. **Identifying the Correct Option**:
- We need to compare this rearranged formula with the options provided in the question to identify the correct one.

5. **Conclusion**:
- Based on the rearranged formula, we conclude that the empirical relationship between the Mean, Median, and Mode is:
\[ 2 \times \text{Mean} = 3 \times \text{Median} - \text{Mode} \]