Example: Find out the median of the following items:

    5,         7,         9,         12,       10,       8,         7,        15        21

Solution: These items would first be arranged in ascending order of magnitude. The series then would be as follows:

 

Calculation of Median                       

Serial Number	Size of items
1	5
2	7
3	7
4	8
5	9
6	10
7	12
8	15
9	21

If M represents the median and N the number of items, then
         M = Size of (N+1)/2) th  item

        M = Size of (9+1)/2) th or 5th item
        M = 9. In the above example the number of items was odd and there was no difficulty in locating the middle items and its value.

 

Solved Example

Find the value of the median from the following data :

32, 41, 28, 54, 35, 26, 23, 33, 38, 40

 

Solution: These items would be arranged in ascending order; as. follows :                                         

     Calculation of Median                                   

Serial Number	Values
1	23
2	26
3	28
4	32
5	33
6	35
7	38
8	40
9	41
10	54

 

Median is the size of ((N+1)/2) th ((10+1)/2) th or 5.5th item

M or size of 5.5th item = (size of 5^th  item+ size of 6^th  item)/2

M=33+35 /2 =34