This document discusses a quantitative techniques course covering bi-variate frequency distribution tables. It provides two examples of creating bi-variate tables using students' exam marks and husbands and wives ages. The first example uses data on 20 students' marks in two subjects to create a table grouping the marks into class intervals of 10. The second example uses ages of 22 husbands and wives, creating a table grouping both spouses' ages into class intervals of 5 years. The document ends with multiple choice questions to test understanding of frequency distributions, classifications and bi-variate tables.

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 14

2. RECAP
• Bi-Variate Frequency Distribution Table Meaning &
Problems-------- 01

3. LEARNING OBJECTIVES
• The aim of the chapter is to make students to
present data in textual and Tabular format including
the technique of creating frequency distribution
and working out bi-variate distribution table

4. LEARNING OUTCOMES
• After the Chapter, The Students Shall be able to
Describe and Understand the Rules & Types of
Classification, Frequency Distribution, Class Interval
& its Types, Basic Principles Tabulation and The
Sorting of Data.

5. SESSION - 14
• Bi-Variate Frequency Distribution Table Problems - 02

6. EXAMPLE 1
Prepare a bivariate frequency distribution table with
regard to marks scored by 20 students in two subjects
i.e., Marks in F.A and Q.T, With class interval 10
F.A 36 29 31 19 41 46 28 37 53 39
Q.T 57 43 41 31 61 63 19 53 75 61
F.A 41 39 36 36 71 18 43 47 36 36
Q.T 61 57 53 49 81 19 59 66 49 51

7. CONTD
BI-VARIATE FREQUENCY DISTRIBUTION
Q.T
F.A
15-25 25-35 35-45 45-55 55-65 65-75 TOTAL
15-25 I I -- -- -- -- 2
25-35 I -- -- -- -- -- 1
35-45 -- II -- -- -- -- 2
45-55 -- -- IIII I -- 5
55-65 -- -- IIII I I -- 7
65-75 -- -- -- I -- 1
75-85 -- -- -- I -- I 2
TOTAL 2 3 11 3 -- 1 20

8. EXAMPLE 2
Prepare a bivariate frequency distribution table with
regard to the ages of 22 husbands and wives are given
below, taking class intervals for both ages, 20-25,25-30,
30-35 etc. Age of husband as X , age of wives as Y
X 29 38 43 26 30 47 38 36 24 42 43
Y 24 35 40 27 26 46 36 36 23 40 33
X 28 40 24 34 37 33 23 30 39 49 36
Y 25 35 21 32 30 36 24 28 35 48 20

9. CONTD
Classification of Ages of Husbands and Wives
Y
X
20-25 25-30 30-35 35-40 40-45 45-50 TOTAL
20-25 III I -- I -- -- 5
25-30 -- II II -- -- -- 4
30-35 -- -- I I I -- 3
35-40 -- -- I IIII I -- 6
40-45 -- -- -- -- II -- 2
45-50 -- -- -- -- -- II 2
TOTAL 3 3 4 6 4 2 22

10. SUMMARY
As we already discussed and learnt today on
Classifications and Tabulation as below
• Bi-Variate Frequency Distribution Table Problems - 02

11. MCQs
1 . A grouping of data into mutually exclusive classes
showing the number of observations in each class is;
(a) Frequency polygon
(b) Relative frequency
(c) Frequency distribution
(d) Cumulative frequency
2 . The class frequency divided by the total number of
observations is called:
(a) Percentage frequency
(b) Relative frequency
(c) Cumulative frequency
(d) Bivariate frequency

12. MCQs
3 . The following frequency distribution
Classes 10----20, 20----30, 30----40, 40----50, 50----60
Frequency 2 4 6 4 2
is classified as:
(a) Exclusive classification
(b) Inclusive classification
(c) Geographical classification
(d) Two-way classification

13. MCQs
4 . The following frequency distribution
Classes 0----4, 5----9, 10----14, 15----19, 20----24
Frequency 2 3 7 5 3
is classified as:
(a) Multiple classification
(b) Qualitative classification
(c) Inclusive classification
(d) Exclusive classification

14. MCQs
5 . The following frequency distribution
Classes; Less than 2, Less than 4, Less than 6, Less than 8
Frequency; 2 6 16 19
is classified as:
(a) Inclusive classification
(b) Exclusive classification
(c) Discrete classification
(d) Cross classification

15. CONTD
ANSWERS
1. C
2. B
3. A
4. C
5. B

16. REFERENCES
• S.P. Gupta, Sultan Chand and Sons Publications, 2017
• S. C. Gupta, Himalaya Publishing House,
Fundamentals of Statistics, 2018
• R.S.N Pillai and Bagavathi, S.Chand publications, 2010

17. THANK YOU