If the mode of a data is 45 and mean is 27 , then the median is

Options

A. 30
B. 27
C. 33
D. none of the above

Answer

To find the median when the mode is 45 and the mean is 27, we can use the relationship between mode, median, and mean. The formula we will use is:

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Mode = 45
- Mean = 27
- Median = x (we need to find this)

2. **Substitute the known values into the formula:**
\[ 45 = 3x - 2 \times 27 \]

3. **Calculate \(2 \times \text{Mean}\):**
\[ 2 \times 27 = 54 \]
So the equation becomes:
\[ 45 = 3x - 54 \]

4. **Rearrange the equation to isolate \(3x\):**
\[ 3x = 45 + 54 \]

5. **Calculate \(45 + 54\):**
\[ 45 + 54 = 99 \]
Now we have:
\[ 3x = 99 \]

6. **Solve for \(x\) (Median):**
\[ x = \frac{99}{3} \]

7. **Calculate \(\frac{99}{3}\):**
\[ x = 33 \]

8. **Conclusion:**
The median is \(33\).

### Final Answer:
The median is \(33\).