Question
The median for a set of 10 numbers is 10. An even number is added, and the median is now 11 and the range is now 4. What number was added?
Answers
Steve
If the numbers are x1-x10, then the median is
(x5 + x6)/2 = 10
Since the range was less than 4, that means that the numbers in order were
8 x x x 9 11 11 11 11 11
or
9 9 9 9 9 11 x x x 12 12
The median moved upward, so the even number was added on the top side, so it must have been 12.
(x5 + x6)/2 = 10
Since the range was less than 4, that means that the numbers in order were
8 x x x 9 11 11 11 11 11
or
9 9 9 9 9 11 x x x 12 12
The median moved upward, so the even number was added on the top side, so it must have been 12.