Statistics. How to find the median of two other medians?

Question

I got median of 226 and another median of 304. Now the question is how to find the overall median? Averaging them is not the correct answer.

Answer 1

It's standard to define the median of an even population with an average between the two "candidates", e.g. the median of 1,3 would be 2. With that definition, the problem is unsolvable even with information about population sizes.

For example, if you know first population has 2 elements and the second had 1, so the second population must be 304.

• If the first one is 226, 226, -- the global median is 226.
• If the first one is 305, 147, -- the global median is 304.

My conjecture is, you will need the entire population to compute the global median (unlike the average, where just the knowledge of the size of each is enough)...

Answer 2

The first median is known to be larger than 8 elements, and the second smaller than 9. So the median certainly lies between 226 and 304.

But this is all you can say ! The median could by any value in between. (Choose a median arbitrarily, you will have all freedom to insert the elements on either side.)