The mean of 20 numbers is 9. If 3 is added to every number what will be the new mean?

Options

A. 9
B. 12
C. 27
D. 15

Answer

To find the new mean after adding 3 to each of the 20 numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
- The mean of 20 numbers is 9.

2. **Calculate the sum of the original numbers**:
- The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Number of numbers}} \]
- Rearranging this formula to find the sum gives:
\[ \text{Sum of numbers} = \text{Mean} \times \text{Number of numbers} \]
- Substituting the given values:
\[ \text{Sum of numbers} = 9 \times 20 = 180 \]

3. **Determine the new sum after adding 3 to each number**:
- If we add 3 to each of the 20 numbers, the total increase in the sum will be:
\[ \text{Increase} = 3 \times 20 = 60 \]
- Therefore, the new sum of the numbers will be:
\[ \text{New sum} = \text{Old sum} + \text{Increase} = 180 + 60 = 240 \]

4. **Calculate the new mean**:
- The new mean can be calculated using the new sum:
\[ \text{New Mean} = \frac{\text{New sum}}{\text{Number of numbers}} = \frac{240}{20} = 12 \]

5. **Conclusion**:
- The new mean after adding 3 to each number is **12**.