The values of the mode and median are 7.52 and 9.06. respectively, in a moderately asymmetrical distribution. The mean of the distribution is:

Options

A. 9.83
B. 8.67
C. 10.23
D. 9.5

Answer

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Mode (Mo) = 7.52
- Median (Me) = 9.06

2. **Use the empirical relationship**:
In a moderately asymmetrical distribution, the relationship between the mean (M), median (Me), and mode (Mo) can be approximated by the formula:
\[ M = \frac{Mo + 2 \times Me}{3} \]

3. **Substitute the values into the formula**:
\[ M = \frac{7.52 + 2 \times 9.06}{3} \]

4. **Calculate the value inside the parentheses**:
- First, calculate \(2 \times 9.06\):
\[ 2 \times 9.06 = 18.12 \]
- Now, add the mode:
\[ 7.52 + 18.12 = 25.64 \]

5. **Divide by 3 to find the mean**:
\[ M = \frac{25.64}{3} \approx 8.5467 \]

6. **Final result**:
The mean of the distribution is approximately 8.55 (rounded to two decimal places).