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Following tale gives income (X) and expenditure (Y) of 25 families: Y/X 200 – 300 300 – 400 400 – 500 200 – 300 IIII I IIII I I 300 – 400 – IIII IIII I 400 – 500 – – II Find How many families have th - Mathematics and Statistics

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Sum

Following tale gives income (X) and expenditure (Y) of 25 families:

Y/X 200 – 300 300 – 400 400 – 500
200 – 300 IIII I IIII I I
300 – 400 IIII IIII I
400 – 500 II

Find How many families have their income Rs. 300 and more and expenses Rs. 400 and less?

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Solution

Bivariate frequency distribution table for Income (X) and Expenditure (Y) is as follows:

Y/X 200 – 300 300 – 400 400 – 500 Total (fy)
200 – 300 6 6 1 13
300 – 400 0 4 6 10
400 – 500 0 0 2 2
Total (fx) 6 10 9 25

The cells 300 – 400 and 400 – 500 are having income ₹ 300 and more and the cells 200 – 300 and 300 – 400 are having expenditure ₹ 400 and less. Now, the following table indicates the number of families satisfying the above condition.

Y/X 300 – 400 400 – 500 Total
200 – 300 6 1 13
300 – 400 4 6 10
Total 10 7 17

∴ There are 17 families with income ₹ 300 and more and expenditure ₹ 400 and less.

Concept: Statistics (Entrance Exam) - Bivariate Frequency Distribution
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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 1. (iv) | Page 49
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