Carcass wrote:
9, 9, 9, 7, 7, 15, 11, x
The eight numbers shown represent the weight, in pounds, of eight cats in a pet store. What is the median weight, in pounds, of the eight cats in the pet store?
The logical reasoning for this problem is as follows.
We should divide into some cases after we put numbers in ascending order.
We have numbers \(7, 7, 9, 9, 9, 11, 15\) and \(x\).
Case 1) \(x \le 7\)
Then we have \(x, 7, 7, 9, 9, 9, 11, 15\) in ascending order and their median is \(9\).
Case 2) \(7 < x \le 9\)
Then we have \(7, 7, x, 9, 9, 9, 11, 15\) in ascending order and their median is \(9\).
Case 3) \(9 < x \le 11\)
Then we have \(7, 7, 9, 9, 9, x, 11, 15\) in ascending order and their median is \(9\).
Case 4) \(11 < x \le 15\)
Then we have \(7, 7, 9, 9, 9, 11, x, 15\) in ascending order and their median is \(9\).
Case 5) \(15 < x\)
Then we have \(7, 7, 9, 9, 9, 11, 15, x\) in ascending order and their median is \(9\).
All cases tell \(9\) is their median, whatever \(x\) is.