Can you tell if z = median of 3 positive integers, x, y, z? If you know that:?

When you arrange the numbers in ascending order, the median is the number in the middle. If y = z, then you have a situation like:

1,4,4

or

4,4,6

In this case, the median is 4. As you can see, regardless of the value of x (bigger or smaller than y and z), the median remains 4. And since y and z are both 4, they would both be medians.

Your teacher is correct.

Answer:

B.

P.S. In the example above 4,4,4 is another possibility, but then the value of the median is obviously 4. I should be complete and mention it though.

The way to prove that y and z will be the median is to assume the opposite. Assume that you could make x the median. In that case, x would have to be between y and z, but not equal to them. Good luck trying to find a value of x that will satisfy that restriction. :-) Since you have an impossible situation, you have proven by contradiction that x can't be the median so y and z are equal to the median value.

Median is the miiddle value when the observations are arranged in order. If y=z, either y or z will always be the second value, no matter what x is.

x=10, y=2,z=2

2,2,10 (after arranging) 2 is the median.

Try it with various numbers.

The answer is (b)