I guess the hard part of this problem is to come up with two instances to show the median may or may not be 20
Bunuel has these two sets as the solutions, but how did he come up with such numbers? Lets try to find out...
{14,18,24,24}. The median is 21;
{18,18,22,22}. The median is 20.
I guess he started with an easy set, {18,18,22,22}. Mean=20, median =20, easy!
Now our goal is to get to a set which has a mean=20 but median is NOT 20.
Step I: I want to space the last two elements a bit further off,
{18,18,24,24}, here the sum=84 (and the goal is to keep the sum=80, so that the mean is 20)
Step II: I want to compensate the extra 4 in the sum in the first two elements
{16,16,24,24}, now my mean =20, but my median is also 20
Step III: I want to finally change the second term, such that the median is NOT 20 anymore
{14,18,24,24}, so now my mean is still 20, but my median is 21
I think this is how
Bunuel was thinking when he came up with these numbers. Of course we can make more such cases.
Answer:
E