If in a moderately asymmetrical distribution the mode and the mean of the data are `6 lamda " and" 9 lamda`, respectively, then the median is

Options

A. `8 lamda`
B. `7 lamda`
C. `6 lamda`
D. `5 lamda`

Explanation

To find the median of a moderately asymmetrical distribution when the mode and mean are given, we can use the relationship between these three measures of central tendency.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mode (Mo) = \(6\lambda\)
- Mean (M) = \(9\lambda\)

2. **Use the relationship between mode, median, and mean:**
In a moderately asymmetrical distribution, the relationship can be expressed as:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Substituting the known values into this equation:
\[ 6\lambda = 3 \times \text{Median} - 2 \times 9\lambda \]

3. **Simplify the equation:**
First, calculate \(2 \times 9\lambda\):
\[ 2 \times 9\lambda = 18\lambda \]
Now substitute this back into the equation:
\[ 6\lambda = 3 \times \text{Median} - 18\lambda \]

4. **Rearranging the equation:**
Add \(18\lambda\) to both sides:
\[ 6\lambda + 18\lambda = 3 \times \text{Median} \]
This simplifies to:
\[ 24\lambda = 3 \times \text{Median} \]

5. **Solve for the median:**
Divide both sides by 3:
\[ \text{Median} = \frac{24\lambda}{3} = 8\lambda \]

### Final Answer:
The median of the distribution is \(8\lambda\).