If the mean of a data is 27 and its median is 33 then the mode is

Options

A. 30
B. 43
C. 45
D. 47

Answer

To find the mode of the data given that the mean is 27 and the median is 33, we can use the relationship between mean, median, and mode. 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:**
- Mean = 27
- Median = 33

2. **Substitute the values into the formula:**
\[ \text{Mode} = 3 \times 33 - 2 \times 27 \]

3. **Calculate \(3 \times 33\):**
\[ 3 \times 33 = 99 \]

4. **Calculate \(2 \times 27\):**
\[ 2 \times 27 = 54 \]

5. **Subtract the two results:**
\[ \text{Mode} = 99 - 54 \]

6. **Perform the subtraction:**
\[ 99 - 54 = 45 \]

7. **Conclusion:**
The mode of the data is 45.

### Final Answer:
Mode = 45

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