Which one of the following numbers can be removed from the set S = {0, 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 = {0, 2, 4, 5, 9} without changing the average of set S?

Solution:
Total sum of the elements in set S = 0 + 2 + 4 + 5 + 9 = 20
Number of elements = 5
Average of set S = 20/5 = 4

A number can be removed without changing the average only if it equals the mean.
Here, the average or mean = 4.

Checking the set S = {0, 2, 4, 5, 9}, we see that 4 is an element of the set.
If we remove 4:
New sum = 20 - 4 = 16
New number of elements = 4
New average = 16/4 = 4

Since the average remains unchanged, the number to be removed is 4.

∴ The correct answer: গ) 4.