Median of two sets.

[goelmohit2002]

Hi All,

When two sets A and B are combined, then median of set C lies between median of set A and B.

E.g. if median of set A = 2
if median of set B = 5
then 2 <= Median of C <= 5.

Can someone please tell why ? Why median lies between these two figures ?

Thanks
Mohit

[goelnikhils]

Mohit,
I think it can lie in between as Median is always a middle value . so if you 2 have sets the median is bound to come in between if you join these sets as the number of elements will either be evenly distirbuted.

This is just my guess.

[Ben Ku]

Mohit,
One way to see this is to take sample sets. Let's suppose we have the following sets (elements are listed in increasing order):
A = {J, K, 2, L, M}
B = {P, Q, 5, R, S}

If we were to combine the sets, the median would be between the 5th and 6th elements in the combined set.

Let's try to find out where the HIGHEST median might be. To do this, we want to make the unknown values as high as possible. In this case, L and M can be greater than 5, but the maximum for P and Q is 5. One possible combined set is:
A+B = {J, K, 2, P, Q, 5, L, M, R, S}
Here you see that the median is between Q and 5, which must be less than or equal to 5.

We can find the LOWEST possible median by minimizing the unknown values. Here, P and Q can be less than 2, but the minimum for L and M is 2. One possible combined set is:
{J, K, P, Q, 2, L, M, 5, R, S}
Here you see the median is between 2 and L, which must be greater than or equal to 2.

So the median must be between 2 and 5.