If in a moderately skewed distribution the values of mode and mean are `6lambda and 9 lambda ` respectively, then the value of the median is

Options

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

Answer

To find the value of the median in a moderately skewed distribution where the mode is \(6\lambda\) and the mean is \(9\lambda\), we can use the relationship between mode, median, and mean. The formula we will use is:

\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

### Step-by-step Solution:

1. **Write down the known values:**
- Mode = \(6\lambda\)
- Mean = \(9\lambda\)

2. **Substitute the known values into the formula:**
\[ 6\lambda = 3 \times \text{Median} - 2 \times 9\lambda \]

3. **Simplify the equation:**
\[ 6\lambda = 3 \times \text{Median} - 18\lambda \]

4. **Rearrange the equation to isolate the median:**
\[ 6\lambda + 18\lambda = 3 \times \text{Median} \]
\[ 24\lambda = 3 \times \text{Median} \]

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

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