# Formula for Median with Examples

Here you will learn what is the formula for median of grouped and ungrouped data and how to find median with examples.

Let’s begin –

## What is Median ?

Median is defined as the measure of central term when they are arranged in ascending or descending order of magnitude.

## Formula for Median :

(i) For ungrouped distribution : Let n be the number of variate in a series then

Median = $$({n + 1\over 2})^{th}$$ term, (when n is odd)

Median = Mean of $$({n\over 2})^{th}$$ and $$({n\over 2} + 1)^{th}$$ terms, (where n is even)

Example : Find the median of 6, 8, 9, 10, 11, 12 and 13.

Solution : Total number of terms = 7

Here, n is odd.

The middle term = $$1\over 2$$(7 + 1) = 4th

Median = Value of the 4th term =10

Hence, the median of the given series is 10.

(ii) For ungrouped frequency distribution : First we prepare the cumulative frequency(c.f.) column and Find value of N then

Median = $$({N + 1\over 2})^{th}$$ term, (when N is odd)

Median = Mean of $$({N\over 2})^{th}$$ and $$({N\over 2} + 1)^{th}$$ terms, (where n is even)

(iii) For grouped frequency distribution : Prepare c.f. column and find value of $$N\over 2$$ then find the class which contain value of c.f. is equal or just greater to N/2, this is median class

Median = $$l$$ + $$({N\over 2} – F)\over f$$$$\times$$h

where  $$l$$ – lower limit of median class

f – frequency of median class

F – c.f. of the class preceding median class

h – class interval of median class

Example : Find the median of the following frequency distribution.

 class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 $$f_i$$ 8 30 40 12 10

Solution :

 class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 $$f_i$$ 8 30 40 12 10 c.f. 8 38 78 90 100

Here $$N\over 2$$ = $$100\over 2$$ = 50 which lies in the value of 78 of c.f. hence corresponding class of this c.f. is 20 – 30 is the median class, so

$$l$$ = 20, f = 40, f = 38, h = 10

$$\therefore$$ Median = $$l$$ + $$({N\over 2} – F)\over f$$$$\times$$h = 20 + $$(50 – 38)\over 40$$$$\times$$10 = 23