A set of data is given. The mean of the set is 35 while the median is set as 60. Find the mode of the data.

Options

A. 25
B. 30
C. 20
D. 110

Answer

To find the mode of the data given the mean and median, we can use the relationship between mean, median, and mode. The formula we can use is:

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Mean (M) = 35
- Median (Med) = 60

2. **Substitute the values into the formula:**
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
\[ \text{Mode} = 3 \times 60 - 2 \times 35 \]

3. **Calculate \(3 \times 60\):**
\[ 3 \times 60 = 180 \]

4. **Calculate \(2 \times 35\):**
\[ 2 \times 35 = 70 \]

5. **Subtract the two results:**
\[ \text{Mode} = 180 - 70 = 110 \]

6. **Final result:**
The mode of the data is **110**.