Which one of the following numbers can be removed from the set S = {2, 4, 5, 9} without changing the average of set S?

Question: Which one of the following numbers can be removed from the set S = {2, 4, 5, 9} without changing the average of set S?

Solution:
- S = {2, 4, 5, 9}
- Number of elements 4,
- Total = (2+4+5+9)= 20.
∴ Average = 20/ 4= 5

Try removing each number and check if the new average is still 5,
After removing 2, we get S = {4,5,9}
- Summation = 18
- Number of elements = 3
∴ Average = 18/3 =6. Which is not equal to 5.

Again, removing 4 from set S, we get S = {2,5,9}
- Summation = 16
- Number of elements = 3
- Average = 16/3 = 5.33

Again, removing 5 from set S, we get S = {2,4,9}
- Summation = 15
- Number of elements = 3
- Average = 15/3 = 5.

- Final Answer: 5 can be removed without changing the average.