# How to calculate median of grouped data if group size is variable

• alokmahor

#### alokmahor

I learned in school that Median = L + (n/2-cf)*h/f
where L = lower limit of median class
n = no. of observations
cf = cumulative frequency of class preceding the median class,
f = frequency of median class,
h = class size (assuming class size to be equal).

I used to use this formula for grouped data of fix width like
marks ... no. of student
0 - 10 ... 5
10 - 20 ... 3
20 - 30 ... 4 and so on.
here grouped data is of fixed width 10=10-0=20-10=30-10 ans so on

BUT how will I calculate median if width is not fixed like

population ... no. of town
5 - 10 .... 500
10 - 20 .... 100
20 - 50 ..... 50
50 - 100 .... 30
100 - 200 .... 20
200 - 500 ... 10
500 - 1000 ..... 3
1000 and above .... 2

how will I calculate median in this case

## Answers and Replies

Start counting from both ends and find the place where both sums are as close to equal as possible. For example, in your second illustration, there are 500 in the first batch, which is more than all the others together, therefore the median is in the first batch.

thanks mathman,
I got the solution both type of problem will be solved by the same method