OK, so if you are given a Median value, out of a set which contains an EVEN number of values, then how can you have precisely half higher, and half lower, than the median!? This would only be possible if your value set contained an ODD number of entries.
Maybe I'm being too literal? Comments appreciated.
A median of an even cardinality set is defined as the number (m+n)/2 where m and n are the two most "middle" elements of the ordered set. This leads to medians like this:
Let A={1,2,3,4} ⇒ median(A) = (2+3)/2 = 2.5.
Note that half the values are above this number and half are less.
The only downfall of this is when you have something as follows:
Let B={1,2,2,2,3,4} ⇒median(B) = (2+2)/2=2.
Note that not exactly half are above and half are below. There are two ways to "resolve" this paradox in your head:
1)
Just accept it Imagine the median as physically in between the n/2th term and the n/2+1th term so that way you actually "split" the set into two equal magnitude subsets. Imagine this as {1,2,2,
[I'M MR. MEDIAN LOOK AT ME] 2, 3, 4}
2) In the case of the question, the sample size is large enough to assume it is a distribution so the median (one single value) is the term that splits the distribution into 2 evenly sized parts.
