Maharashtra State BoardHSC Commerce 12th Board Exam
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Construct a bivariate frequency distribution table of the marks obtained by students in English (X) and Statistics (Y). Marks inStatistics(X) 37 20 46 28 35 26 41 48 Marks inEnglish(Y) 30 32 4 - Mathematics and Statistics

Sum

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.

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Solution

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
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic
Exercise 4.1 | Q 4 | Page 49
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