Median refers to the middle number separating the lower half of the set of numbers from the greater half of the set of the numbers in a sorted list of all the data points.
It gives a better picture about the data set compared t the mean in the presence of some outliers, which may increase or decrease the mean to a huge extent.
To calculate the median of a set of numbers, the following steps are followed:
a) The numbers are arranged in ascending order
b) If the no. of data points is odd, then median is the middle number. ((n-1)/2 th observation)
c) If the no. of data points is odd, the median is the average of the two middle nos.
(avg of n/2 and (n-1)/2 th observation)
Median for even no. of observations
Suppose the data set is
No. of observations= 8
Step 1: Arrange in ascending order
The middle nos. are 11 and 14
Median= (11+14)/2= 12.5
Median for odd no. of observations
14, 11, 16, 8, 6, 3, 22
No. of observations= 7
3, 6, 8, 11, 14, 16, 22
The middle no. is 11