If the mean and the mode of a moderately skewed frequency distribution are 90 and 96 respectively, then the median is

Options

A. 93
B. 92
C. 98
D. 88

Answer

To find the median of a moderately skewed frequency distribution when the mean and mode are given, we can use the relationship between mean, median, and mode.

### Step-by-step Solution:

1. **Identify the given values:**
- Mean (M) = 90
- Mode (Mo) = 96

2. **Use the formula relating mean, median, and mode:**
The formula is:
\[ Mo = 3 \times \text{Median} - 2 \times M \]
Rearranging this formula to find the median gives:
\[ \text{Median} = \frac{Mo + 2M}{3} \]

3. **Substitute the known values into the formula:**
\[ \text{Median} = \frac{96 + 2 \times 90}{3} \]

4. **Calculate the value:**
- First, calculate \(2 \times 90\):
\[ 2 \times 90 = 180 \]
- Now add this to the mode:
\[ 96 + 180 = 276 \]
- Finally, divide by 3:
\[ \text{Median} = \frac{276}{3} = 92 \]

5. **Conclusion:**
The median of the frequency distribution is 92.