Question

The following data gives the marks of 20 students in mathematics (X) and statistics (Y) each out of 10, expressed as (x, y). construct ungrouped frequency distribution considering single number as a class.
Also prepare marginal distributions :

(2, 7) (3, 8) (4, 9) (2, 8) (2, 8) (5, 6) (5 , 7) (4, 9) (3, 8) (4, 8) (2, 9) (3, 8) (4, 8) (5, 6) (4, 7) (4, 7) (4, 6 ) (5, 6) (5, 7 ) (4, 6 )

Answer 1

We can tublate the bi- variate frequency
distribution in a table shown below :

x →	2	3	4	5	Total
y↓
6	-	-	| | (2)	| | | (3)	5
7	| (1)	-	| | (2)	| | (2)	5
8	| | (2)	| | (3)	| | (2)	-	7
9	| (1)	-	| | (2)	≠	3
Total	4	3	8	5	20

Marginal distribution of X :

X	2	3	4	5	Total
Frequency	4	3	8	5	20

Marginal distribution of y :

Y	6	7	8	9	Total
Frequency	5	5	7	3	20