Relative frequency distribution,Relative cumulative frequency distribution and Bivariate frequency distribution

Relative frequency distribution:

A table in which the frequency of each class is divided by the total frequency of all the classes is called relative frequency distribution. When the relative frequencies are expressed as a percentage, than it is called percentage relative frequency distribution. It is important to note that the sum of the relative frequencies of all classes should equal to one 1 or 100%.

Relative cumulative frequency distribution:

A table in which the cumulative frequency of each class is divided by the total frequency of all classes is called relative cumulative frequency distribution. Or %age relative cumulative frequency distribution. It is to be noted that relative cumulative frequency of last class should equal 100.

Question:

From the data given below construct relative frequency distribution and percentage relative frequency distribution.

Marks:          10 – 20   20 – 30   30 – 40   40 – 50   50 – 60   60 – 50   

Frequency:       5             16            31            28            19           10 

Sol:

marks	F	%age relative frequency
10 – 20	5	5/109 x 100 = 4.6
20 – 30	16	16/109 x 100 = 1.7
30 – 40	31	31/109 x 100 = 28.4
40 – 50	28	28/109 x 100 = 25.4
50 – 60	19	19/109 x 100 = 17.4
60 – 70	10	10/109 x 100 = 9.2
	109	100

From the above table we can read that 4.6% of the students obtained 10 or more but less than 20 marks 25.7% of the students obtained 40 or more but less than 50 marks etc.

Question:

Construct the relative cumulative frequency distance and %age relative cumulative frequency distribution from the following data.

Marks:                      0 - 10 10 – 20   20 – 30   30 – 40   40 – 50   50 – 60  

Frequency:                 8            12            24            18           10             5

Sol:

Marks	F	Cumulative freq (less than type)
0 - 10	8	8	8 ÷ 77 x 100 = 10.4
10 – 20	12	8 + 12  = 20	20 ÷ 77 x 100 = 25.9
20 – 30	24	8 + 12 + 24 = 44	44 ÷ 77 x 100 = 57.1
30 – 40	18	8 + 12 + 24 + 18  = 62	62 ÷ 77 x 100 = 80.5
40 – 50	10	8 + 12 + 24 + 18 + 10 = 72	72 ÷ 77 x 100 = 93.5
50 – 60	5	8 + 12 + 24 + 18 + 10 + 5 = 77	77 ÷ 77 x 100 = 100
	77

From the above table we can read that 10.4% of the students obtained less than 10 marks, 80.5% of the students obtained less than 40 marks etc.

Bivariate frequency distribution:

The frequency distribution con structured so far for a single variable is called univarite frequency distance. But in many problems we deal with two variables, the frequency distribution con structured for such variables is called the bivariate frequency distribution.

There rules for construction of bivariate frequency distribution is exactly the same as that of univarite frequency distributions. Since two variables are studied at the same time, therefore the classes for one variable are arranged in rows and that of the second variable in columns.