If mode and mean of data are found 28 and 24 respectively, find median using empirical formula.

Answer

To find the median using the empirical formula given the mode and mean, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the empirical formula**:
The empirical formula relating mode (Mo), median (Me), and mean (A) is:
\[ Mo = 3 \times Me - 2 \times A \]

2. **Substitute the known values**:
We are given:
- Mode (Mo) = 28
- Mean (A) = 24

Substitute these values into the empirical formula:
\[ 28 = 3 \times Me - 2 \times 24 \]

3. **Simplify the equation**:
Calculate \(2 \times 24\):
\[ 2 \times 24 = 48 \]
Now substitute this back into the equation:
\[ 28 = 3 \times Me - 48 \]

4. **Rearrange the equation to isolate the median**:
Add 48 to both sides:
\[ 28 + 48 = 3 \times Me \]
\[ 76 = 3 \times Me \]

5. **Solve for the median**:
Divide both sides by 3:
\[ Me = \frac{76}{3} \]
Now calculate \( \frac{76}{3} \):
\[ Me = 25.33 \]

### Final Answer:
The median is approximately \( 25.33 \).

---