Grouped Data
In order to find the median, the median class is to be first located and then interpolation is to be used by assuming that items are evenly spaced over the entire class interval. The formula used for the calculation of median is
Median = W + Lm
Where,
Lm = Lower limit of the median class
fm = Frequency of the median class
F = Cumulative frequency up to the lower limit of the median class
W = Width of the class interval
N = Total frequency.
Example
Let us find median for the following data.
Gross profit as a percentage of sales

010

1020

2030

3040

4050

No. of companies

21

32

43

34

23

Gross profit (%)

No. of Companies (f)

Cumulative Frequency (cf)

010

21

21

1020

32

53

2030

43

96

3040

34

130

4050

23

153

Here the total frequency N = 153. Median is the size of the th item, i.e.th item, i.e. the size of the 77th item. It lies in the class 2030. Hence 2030 is the median class, of which the lower limit is 20.
Thus, Lm = 20, N = 153, F = 53, fm = 43, W =10
Median
= 25.34
Thus 25.34 is the median gross profit percentage of the companies.