If the ratio of the mode and median of a certain data is 9 : 8, then the ratio of its mean and median is:

Options

A. `15:17`
B. ` 13:15`
C. `15:16`
D. `11:15`

Answer

To solve the problem, we need to find the ratio of the mean and median given the ratio of the mode and median.

### Step-by-Step Solution:

1. **Understanding the Given Ratio:**
We know that the ratio of the mode (Mo) to the median (Me) is given as:
\[ \frac{Mo}{Me} = \frac{9}{8} \]
This implies that we can express the mode and median in terms of a variable \(x\):
\[ Mo = 9x \quad \text{and} \quad Me = 8x \]

2. **Using the Relationship Between Mean, Median, and Mode:**
For a given dataset, there is a known relationship between the mean (M), median (Me), and mode (Mo):
\[ M = \frac{Mo + 2 \cdot Me}{3} \]
Substituting the values of Mo and Me we found:
\[ M = \frac{9x + 2 \cdot 8x}{3} \]

3. **Calculating the Mean:**
Simplifying the expression for the mean:
\[ M = \frac{9x + 16x}{3} = \frac{25x}{3} \]

4. **Finding the Ratio of Mean to Median:**
Now we need to find the ratio of the mean (M) to the median (Me):
\[ \frac{M}{Me} = \frac{\frac{25x}{3}}{8x} \]
Simplifying this ratio:
\[ \frac{M}{Me} = \frac{25x}{3 \cdot 8x} = \frac{25}{24} \]

5. **Final Ratio:**
Therefore, the ratio of the mean to the median is:
\[ \frac{M}{Me} = \frac{25}{24} \]

### Conclusion:
The ratio of the mean and median is \( \frac{25}{24} \).