Explanation: To solve this problem, we need to understand the concept of averages and how to calculate the average of a subset of numbers when the overall average and the average of another subset are known.
First, let's define the given information:
- The average of 22 numbers is 11.
- The average of the last two numbers is 16.
The formula for the average of a set of numbers is:
\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}} \]
Using this formula, we can find the total sum of the 22 numbers:
\[ \text{Sum of 22 numbers} = \text{Average} \times \text{Count} = 11 \times 22 = 242 \]
Next, we need to find the sum of the last two numbers. Since their average is 16:
\[ \text{Sum of last two numbers} = \text{Average} \times \text{Count} = 16 \times 2 = 32 \]
Now, we can find the sum of the remaining 20 numbers by subtracting the sum of the last two numbers from the total sum:
\[ \text{Sum of remaining 20 numbers} = \text{Total sum} - \text{Sum of last two numbers} = 242 - 32 = 210 \]
Finally, we can find the average of the remaining 20 numbers:
\[ \text{Average of remaining 20 numbers} = \frac{\text{Sum of remaining 20 numbers}}{\text{Count of remaining numbers}} = \frac{210}{20} = 10.5 \]
Therefore, the average of the remaining 20 numbers is 10.5, which corresponds to option A.
This problem demonstrates the importance of understanding how to manipulate sums and counts to find averages of subsets of numbers. It also highlights the need to carefully apply the average formula and avoid common misconceptions, such as assuming that the average of a subset is the same as the overall average.