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 - Mathematics and Statistics

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Sum

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
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Solution

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
Concept: Classification and Tabulation of Bivariate Data - Marginal Frequency Distributions
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Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic - Miscellaneous Exercise 4 [Page 54]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic
Miscellaneous Exercise 4 | Q 5 | Page 54

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