The Median by definition denotes to the middle value in a distribution. In case of the median one-half of the items in the distribution have a value the size of the median value of smaller and one-half have a value the size of the median value or bigger. The median is just the 50th percentile value below which 50 percent of the values in the sample fall. It divides the observation into two halves.

As differ from the arithmetic mean which is calculated from the value of each item in the series, the median is what is known as a positional average. The term position denotes  the place of a value in a series. The place of the median in the series is such that an equal number of items lie on either side of it.

For e.g. if the income of five employees are  $ 5, 900, 6,950, 7,020. 7,200 &  8,280 the median will  be 7,020.

5,900, 6,950, 7,020,(value at middle position of the array), 7,200, 8,280

For the  example above the calculation of median was simple as  of odd number of observations. When even numbers of observations are listed, then there is no single middle position value and then the median is taken to be the arithmetic mean of two middle most items. For e.g., if in the case above we are given the income of six employees as 5900, 6950, 7020, 7200, 8280, 9300, the median income would be:

5900, 6950, 7020 (there are two middle position values), 7200, 8280, 9300  

Median = 7020 + 7200/2 = 14220/2 = $7110.

Illustration: - From the following data of the wages of 7 workers, compute the median wage:

Wages (in $) 4100, 4150, 6080, 7120, 5200, 6160, 7400

Solution:

Calculation of median

Median = size of N+1 /2 the item = 7+1 /2= 4th item = $ 6080.
                                                        
The size of 4th item = 6080. And hence the median wage = $ 6080

We thus find that the median is the middlemost item: 3 persons get a wage less than $ 6080 and equal number, & 3 get more than $ 6080