If for a moderately skewed distribution, mode = 60 and mean = 66, then median =

Options

A. 60
B. 64
C. 68
D. none of these

Answer

To find the median of a moderately skewed distribution given the mode and mean, we can use the relationship between mode, median, and mean. The formula is:

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Mode = 60
- Mean = 66

2. **Write the formula**:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

3. **Substitute the known values into the formula**:
\[ 60 = 3 \times \text{Median} - 2 \times 66 \]

4. **Calculate \(2 \times \text{Mean}\)**:
\[ 2 \times 66 = 132 \]

5. **Rearrange the equation**:
\[ 60 = 3 \times \text{Median} - 132 \]

6. **Add 132 to both sides**:
\[ 60 + 132 = 3 \times \text{Median} \]
\[ 192 = 3 \times \text{Median} \]

7. **Divide both sides by 3 to solve for Median**:
\[ \text{Median} = \frac{192}{3} = 64 \]

### Final Answer:
The median is **64**.