Find the median of the data, using an empirical relation when it is given that Mode = 12.4 and Mean = 10.5.

Answer

To find the median using the empirical relation given the mode and mean, we can use the following formula:

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

### Step-by-Step Solution:

1. **Write down the given values:**
- Mode = 12.4
- Mean = 10.5

2. **Substitute the values into the empirical formula:**
\[ 12.4 = 3 \times \text{Median} - 2 \times 10.5 \]

3. **Calculate \(2 \times \text{Mean}\):**
\[ 2 \times 10.5 = 21 \]

4. **Rewrite the equation:**
\[ 12.4 = 3 \times \text{Median} - 21 \]

5. **Add 21 to both sides of the equation:**
\[ 12.4 + 21 = 3 \times \text{Median} \]
\[ 33.4 = 3 \times \text{Median} \]

6. **Divide both sides by 3 to solve for Median:**
\[ \text{Median} = \frac{33.4}{3} = 11.1333 \approx 11.13 \]

### Final Answer:
The median of the data is approximately **11.13**.