Median of Grouped Data

Median is the value of that item in a distribution which divides it into two equal parts such that the values of one part exceed it and the values of the other are less than this value. In case of frequency distributions, median is the value of the variation under the frequency curve that divides the area under the curve into two equal parts.

 

Cumulative Frequency

 

                 We must construct a cumulative frequency distribution to calculate the median for grouped data. Arrange the data in ascending or descending order of the size. Denote the values as X and frequency with f. prepare the cumulative frequency. Apply the formula: Median size of (n + 1)/ 2nd item, and locate the item in the cumulative frequency column.

 

Procedure to Solve Median for Grouped Data

 

Procedure to Solve Median for Grouped Data are as follows:

(i) First arrange the data in ascending or descending order.

(ii) After arranging the data, obtain the Cumulative Frequency (C.F) by frequency of the values

(iii) After cumulative frequency table is prepared, we apply the following formula to calculate the median for grouped data

i.e. (n + 1)/2

            Where, n = Total number of frequency.

(iv) Then locate the item in the cumulative frequency column.

 

 

Example on Median for Grouped Data

 

Example on Median for Grouped Data are as follows:

Example: - Calculate the median of the following data

Income($)

400

360

300

500

700

860

No. of persons

17

15

9

40

50

12

 

Solution:  We first arrange the data in ascending order.

Income arranged in ascending order ($)

No. of persons

x

f

c.f.

300

9

9

360

15

24

400

17

41

500

40

81

700

50

131

860

12

143

 

n = 143

 


Median for grouped data = size of (n + 1)/ 2nd item, n= 143

Median = size of (143 + 1) / 2nd item = size of 72nd item.

Let us now examine the CF at each successive value in this manner:

CF = 9 is less than 72

Similarly CF = 24 and CF = 41 are less than 72

But CF = 81 is more than 72 against which x is 500. This is the value of the median. Hence median income = $ 500.