Median for grouped data, Applied Statistics

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 1567_grouped data.png 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

0-10

10-20

20-30

30-40

40-50

No. of companies

21

32

43

34

23

Gross profit
 (%)

No. of Companies
 (f)

Cumulative Frequency
 (cf)

0-10

21

 21

10-20

32

 53

20-30

43

 96

30-40

34

130

40-50

23

153

 Here the total frequency N = 153. Median is the size of the 1504_grouped data1.pngth item, i.e.2102_grouped data2.pngth item, i.e. the size of the 77th item. It lies in the class 20-30. Hence 20-30 is the median class, of which the lower limit is 20.

Thus, Lm = 20, N = 153, F = 53, fm = 43, W =10

Median 

885_grouped data3.png

= 25.34

Thus 25.34 is the median gross profit percentage of the companies. 

Posted Date: 9/14/2012 2:05:46 AM | Location : United States







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