The two-digit numbers that remain the same when their digits are swapped are known as palindromic numbers. In this case, the only two-digit palindromic numbers are 11, 22, 33, 44, 55, 66, 77, 88, and 99.
Calculating the Average
To find the average of these numbers, we first need to add them together:
- 11
- 22
- 33
- 44
- 55
- 66
- 77
- 88
- 99
The sum is:
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495
Finding the Number of Values
There are a total of 9 two-digit palindromic numbers.
Calculating the Average
Now, we divide the total sum by the number of values:
Average = Total Sum / Number of Values = 495 / 9 = 55
Thus, the average of the two-digit numbers that remain the same when their digits are interchanged is 55. Therefore, the correct answer is C. 55.