Which removement doesn't change the average?

7. \(\left \{16,\;17,\;19,\;20,\;26,\;28 \right \} \)
The average (arithmetic mean) of the 6 numbers above is 21. Of the following, which pair of numbers could be removed from the list without changing the average?

  1. 16 and 28
  2. 17 and 20
  3. 19 and 20
  4. 16 and 26
  5. 20 and 26

We can guess to remove 16 and 26 because they are equally spaced from the mean and the difference between any of them and the mean is equal to the difference between them.

Let us see if the new mean will be the same: $$\frac{17+19+20+28}{4}=21$$


Answer: (D)