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Median:

Median is the middle value of the series. It is also called 50th percentile or second quartile.

Individual series:

1. First arrange the series the series in ascending or descending order.
2. If the number of values is odd then

If number of values is even then

Where N = number of items

Example: To find the median of 1,2,5,7,3,6,4

Arrange the series in ascending order

1,2,3,4,5,6,7

N = 7

= 4th value = 4.

Discrete series:

1. First arrange the series in ascending or descending order.
2. Find commulative frequency.

N = Number of items

Example: To find the median of

 Value Frequency Commulative frequency 2 1 1 3 5 6 4 10 16 5 15 31

= 16th value

= 4

Continuous Series:

1. First find commulative frequency.
2. Find median class by using the formula N / 2.

Where l1 = lower limit of median class

l2 = upper limit of median class

N = Number of items

c = Commulative frequency of class preceeding median class

f = Frequency of median class.

Example: To find the median of

 Marks Frequency Commulative frequency 10 – 20 10 10 20 – 30 15 25 30 – 40 20 45 40 - 50 30 75

Here N / 2 = 75 / 2 = 37.5

Therefore median class is 30 – 40

l1 = 30, l2 = 40, c = 25, f = 20

= 36.25