Maharashtra State BoardHSC Commerce 11th
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Following data gives the age in years and marks obtained by 30 students in an intelligence test. Age 16 17 22 19 21 16 Marks 16 19 39 50 48 41 Age 21 20 20 23 22 19 Marks 59 44 42 62 37 67 Age 23 20 - Mathematics and Statistics

Sum

Following data gives the age in years and marks obtained by 30 students in an intelligence test.

Age 16 17 22 19 21 16
Marks 16 19 39 50 48 41
Age 21 20 20 23 22 19
Marks 59 44 42 62 37 67
Age 23 20 22 22 23 22
Marks 45 57 35 37 38 56
Age 17 18 16 21 19 20
Marks 54 61 47 67 49 56
Age 17 18 23 21 20 16
Marks 51 42 65 56 52 48

Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20, … etc. for age and 10 – 20, 20 – 30, ... etc. for marks. Find marginal frequency distributions.

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Solution

Let
X = Age in years
Y = Marks
Bivariate frequency table can be prepared by taking class intervals 16 – 18, 18 – 20, … etc for X and 10 – 20, 20 – 30, … etc for Y.
Bivariate frequency distribution is as follows:

Marks (Y)/Age in years (X) 16 – 18 18 – 20 20 – 22 22 – 24 Total (fy)
10 – 20 II (2) 2
20 – 30 0
30 – 40 IIII (5) 5
40 – 50 III (3) II (2) III (3) I (1) 9
50 – 60 II (2) I (1) IIII (5) I (1) 9
60 – 70 II (2) I (1) II (2) 5
Total (fx) 7 5 9 9 30

Marginal frequency distribution of X:

X 16 – 18 18 – 20 20 – 22 22 – 24 Total
Frequency 7 5 9 9 30

Marginal frequency distribution of Y:

Y 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 Total
Frequency 2 0 5 9 9 5 30
Concept: Classification and Tabulation of Bivariate Data - Marginal Frequency Distributions
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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
Miscellaneous Exercise 4 | Q 2. (i) | Page 53
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