Which one of the following nunbers can be removed from the set S = {0, 2, 4 ,5 9} without changing the average of set S?
Average (mean) = Sum of all numbers / Total number of numbers
Average = (0 + 2 + 4 + 5 + 9) / 5 = 20 / 5 = 4
The average of the set S is 4. Now, let's consider each number one by one:
If we remove 2, the new set becomes {0, 4, 5, 9}, and the average is (0 + 4 + 5 + 9) / 4 = 18 / 4 = 4.5, which is not the same as the original average of 4.
If we remove 4, the new set becomes {0, 2, 5, 9}, and the average is (0 + 2 + 5 + 9) / 4 = 16 / 4 = 4, which is the same as the original average.
If we remove 5, the new set becomes {0, 2, 4, 9}, and the average is (0 + 2 + 4 + 9) / 4 = 15 / 4 = 3.75, which is not the same as the original average of 4.
If we remove 9, the new set becomes {0, 2, 4, 5}, and the average is (0 + 2 + 4 + 5) / 4 = 11 / 4 = 2.75, which is not the same as the original average of 4.
So, the number that can be removed from the set S without changing the average is 4.
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