Question

Thirty pairs of values of two variables X and Y are given below. Form a bivariate frequency table. Also, find marginal frequency distributions of X and Y.

X	110	88	91	115	97	85	85	91	120	95
Y	500	800	870	599	625	650	905	700	850	824
X	82	105	99	90	108	124	90	90	111	89
Y	970	609	990	735	600	735	729	840	999	780
X	112	100	87	92	91	82	96	120	121	122
Y	638	850	630	720	695	923	555	810	805	526

Answer 1

Bivariate frequency table can be prepared by taking class intervals 80 – 90, 90 – 100, …, etc for X and 500 – 600, 600 –700, …., etc for Y.
Bivariate frequency distribution is as follows:

Y/X	80 – 90	90 – 100	100 – 110	110 – 120	120 – 130	Total (fy)
500 – 600	–	I (1)	–	II (2)	I (1)	4
600 – 700	II (2)	II (2)	II (2)	I (1)	–	7
700 – 800	I (1)	IIII (4)	–	–	I (1)	6
800 – 900	I (1)	III (3)	I (1)	–	III (3)	8
900 – 1000	III (3)	I (1)	–	I (1)	–	5
Total (fx)	7	11	3	4	5	30

Marginal frequency distribution of X:

X	80 – 90	90 – 100	100 – 110	110 – 120	120 – 130	Total
frequency	7	11	3	4	5	30

Marginal frequency distribution of Y:

Y	500 – 600	600 – 700	700 – 800	800 – 900	900 – 100	Total
Frequency	4	7	6	8	5	30