Median

Posted in Statistics, Total Reads: 729
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Definition: Median

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)

 

Example:

 

Median for even no. of observations

Suppose the data set is

14, 11,16,8,6,3,22,28

No. of observations= 8

 

Step 1: Arrange in ascending order

3,6,8,11,14,16,22,28

 

Step 2:

The middle nos. are 11 and 14

Median= (11+14)/2= 12.5

 

Median for odd no. of observations

Suppose the data set is

14, 11, 16, 8, 6, 3, 22

No. of observations= 7

 

Step 1: Arrange in ascending order

3, 6, 8, 11, 14, 16, 22

 

Step 2:

The middle no. is 11

Median= 11


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