Median

Median. 

Median of a distribution is the value of the variable which divides it into two equal parts. It is the value which exceeds and is exceeded by the same number of observations, i.e., it ,is the value such that the number of observations above it is equal to the number of observations below it The median
is thus a positional average.
In case of ungrouped data, if the rumber of observations is odd then median
is the middle value after the values haye been arranged in ascending or descending
order of magnitude. In case of even number of observations, there are two middle
terms and median is obtained by taking the arithmetic mean of the middle terms.
For example, the median of the value 25, 20,15,35,18, i.e., 15, 18, 20, 25; 35 is
20 and the median of 8, 20, 50, 25, 15, 30, i.e., of 8, 15, 20, 25, 30, 50'
is 1/2( 20 -25 ) = 22·5 .

Remark

In case of even number of observations, in fact any value lying between the two middle values can be taken as median but conventionally we take it to be the mean of the middle terms.
In case of discrete frequency distribution median is obtained by considering
the cumulative frequencies. The steps for calculating median are given below: