Mean and Median: ACT Math Practice Question

Try the following ACT math practice question that tests your understanding of what happens to the mean and median of a list of values when the value of the items in the list are changed.

There are $19$ numbers in a list. If the $6$ smallest of these numbers are decreased by $1$ each and the $4$ greatest of these numbers are increased by $2$ each, which of the following statements must be true?

1. $\quad \textrm{The median does not change.}$
2. $\quad \textrm{The median decreases.}$
3. $\quad \textrm{The median increases.}$
4. $\quad \textrm{The average (arithmetic mean) decreases.}$
5. $\quad \textrm{The average (arithmetic mean) does not change.}$

Choice A

Video Explanation