Question

Relation between mean, median, and mode will be:

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

Hint:

In a skewed distribution, the relation between mean, median, and mode can be expressed using the formula \( Mo = 3M - 2Md \).

Answer 1

The Correct Option is D

Step 1: Standard relation between mean, median, and mode.
The relationship between mean (\( M \)), median (\( Md \)), and mode (\( Mo \)) for a skewed distribution is given by the empirical formula: \[ M = \frac{Mo + 2Md}{3} \]
Step 2: Manipulating the formula.
Rearranging the formula to express the mean in terms of median and mode: \[ M = \frac{Mo + 2Md}{3} \] Multiplying through by 3: \[ 3M = Mo + 2Md \] Now, subtract \( 2Md \) from both sides: \[ 3M - 2Md = Mo \] This simplifies to: \[ Mo = 3M - 2Md \]
Step 3: Conclusion.
Therefore, the correct relation is \( Mo = 3M - 2Md \), which corresponds to option (D).