'Median' is a value in the middle of the distribution, dividing the distribution in such a way that there are an equal number of values above and below the median.
In order to find the median for a set of ungrouped values, as a first step, the N values should be ordered in an increasing order. If N is odd, the value at the position (N+1)/2 is the median value. If N is even, the median is the average of the two values at the positions N/2 and N/2 + 1.
For grouped data, median is that value at or below which 50th percentile of the values lie. The median is therefore also, the 50th %ile for grouped data.
For a given data, median is a single value. Further, it takes into account the frequencies of all values in the data but not the values per se. However, median is non-algebraic, as its calculation requires that the values be ordered, which requires comparisons of logical nature.
Frank, H. and Althoen, S.C. "The mean." žB.2 in Statistics: Concepts and Applications Cambridge, Great Britain: Cambridge University Press, pp. 28-37, 1995.
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Dogra, Shaillay K., "Median" From QSARWorld--A Strand Life Sciences Web Resource.