Answer :
Step-by-step explanation:
To find the new average after adding 16 to the existing set of 10 numbers, we can follow these steps:
Given:
- Average of 10 numbers = 15
First, calculate the sum of the 10 numbers:
\[ \text{Sum of 10 numbers} = \text{Average} \times \text{Number of numbers} = 15 \times 10 = 150 \]
Now, add 16 to the sum of these 10 numbers:
\[ \text{New sum} = 150 + 16 = 166 \]
Next, calculate the new average:
\[ \text{New average} = \frac{\text{New sum}}{\text{Number of numbers}} = \frac{166}{11} \]
Now, divide 166 by 11 to find the new average:
\[ \text{New average} = \frac{166}{11} = 15.09 \]
Therefore, the new average of the 11 numbers (after adding 16) is \( \boxed{15.09} \).
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