Question

Construct a bivariate frequency distribution table of the marks obtained by students in English (X) and Statistics (Y).

Marks in Statistics (X)	37	20	46	28	35	26	41	48	32	23	20	39	47	33	27	26
Marks in English (Y)	30	32	41	33	29	43	30	21	44	38	47	24	32	21	20	21

Construct a bivariate frequency distribution table for the above data by taking class intervals 20 – 30, 30 – 40, ...... etc. for both X and Y. Also find the marginal distributions and conditional frequency distribution of Y when X lies between 30 – 40.

Answer 1

Let X: Marks in Statistics
Y: Marks in English
Bivariate frequency table can be prepared by taking class intervals 20 – 30, 30 – 40,…, etc for both X and Y. Bivariate frequency distribution is as follows:

Y/X	20 – 30	30 – 40	40 –50	Total (fy)
20 – 30	II	II	I	5
30 – 40	III	II	II	7
40 – 50	II	I	I	4
Total (fx)	7	5	4	16

Marginal frequency distribution of X:

X	20 – 30	30 – 40	40 – 50	Total
Frequency	7	5	4	16

Marginal frequency distribution of Y:

Y	20 – 30	30 – 40	40 – 50	Total
Frequency	5	7	4	16

Conditional frequency distribution of Y when X lies between 30 – 40:

Y	20 – 30	30 – 40	40 –50	Total
Frequency	2	2	1	5