For a slightly asymmetric distribution, mean and medain are 5 and 6, respectively. What is its mode ?

Options

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

Explanation

To find the mode of a slightly asymmetric distribution given the mean and median, we can use the formula:

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Mean (\( \bar{x} \)) = 5
- Median (M) = 6

2. **Substitute the values into the formula:**
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
\[ \text{Mode} = 3 \times 6 - 2 \times 5 \]

3. **Calculate \( 3 \times \text{Median} \):**
\[ 3 \times 6 = 18 \]

4. **Calculate \( 2 \times \text{Mean} \):**
\[ 2 \times 5 = 10 \]

5. **Subtract the two results:**
\[ \text{Mode} = 18 - 10 = 8 \]

6. **Final Result:**
The mode of the distribution is \( 8 \).