The average of 6 values is 11.2. If 3 is multiplied to each number then what will be the new average?

Options

A. a) 22.6
B. b) 14.6
C. c) 18.6
D. d) 33.6

Answer

To solve the problem, we will follow these steps:

1. **Calculate the Total of the Original Values**:
The average of the 6 values is given as 11.2. The formula for average is:
\[ \text{Average} = \frac{\text{Total Sum of Values}}{\text{Number of Values}} \]
Rearranging the formula to find the total sum:
\[ \text{Total Sum of Values} = \text{Average} \times \text{Number of Values} \]
Substituting the given values:
\[ \text{Total Sum of Values} = 11.2 \times 6 = 67.2 \]

2. **Multiply Each Value by 3**:
If each of the 6 values is multiplied by 3, the new total sum will be:
\[ \text{New Total Sum} = 3 \times \text{Total Sum of Values} = 3 \times 67.2 = 201.6 \]

3. **Calculate the New Average**:
The new average can be calculated using the new total sum and the number of values:
\[ \text{New Average} = \frac{\text{New Total Sum}}{\text{Number of Values}} = \frac{201.6}{6} \]
Performing the division:
\[ \text{New Average} = 33.6 \]

Thus, the new average after multiplying each number by 3 is **33.6**.