This document discusses bi-variate frequency distribution tables. It begins with recapping univariate frequency distributions and introducing bi-variate distributions, which involve classifying data based on two variables simultaneously. The steps for creating a bi-variate frequency distribution table are described, including determining class intervals for each variable and placing them on the table axes to create cells for tallying observations. An example of population height and weight data classified into a bi-variate table is shown. Multiple choice questions reviewing key concepts of frequency distributions are also presented.

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 13

2. RECAP
• Preparation of Frequency Distribution Table -
Continuous Series(Inclusive) Problems -03

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 - 13
• Bi-Variate Frequency Distribution Table Meaning &
Problems-------- 01

6. Bi-Variate Frequency Distribution Table
Meaning;
• Frequency distributions involving one variable are
called univariate frequency distribution. In many
situations it may be necessary to study two variables
simultaneously.
• For example, we want to study the age of wives and
husbands, height and weight of students.
• The data classified on the basis of two variables is
called a Bi-Variate Frequency Distribution Table.

7. CONTD
• STEPS OF BI-VARIATE FREQUENCY DISTRIBUTION
Determine the suitable class interval of each
variable
Write one of class interval vertically on the left
hand side of the table and other at the top
horizontally
A tally mark has to be put in the cell where the
variables intersect in both class intervals
Repeat the procedure till to exhaust all the
variables or observations
Total the tally marks of the column and keep at the
bottom. Similarly, rows tally marks total it and keep
at the right side of the table

8. EXAMPLE 1
• The given below data related to the height and weight
of 20 persons. You are required to form a Bi-variate
frequency table with class intervals 62-64, 64-66 for
height and 115-125, 125-135 for weight
Weight 169 134 135 136 147 124 117 127 143 129
Height 69 64 64 65 68 63 64 70 71 62
Weight 162 140 122 133 140 133 120 148 128 151
Height 69 67 64 68 67 68 65 67 66 66

9. CONTD
BI-VARIATE FREQUENCY DISTRIBUTION
WEIGHT
HEIGHT
62-64 64-66 66-68 68-70 70-72 TOTAL
115-125 I III -- -- -- 4
125-135 I I I II I 6
135-145 -- II II -- I 5
145-155 -- -- II I -- 3
155-165 -- -- -- I -- 1
165-175 -- -- -- I -- 1
TOTAL 2 6 5 5 2 20

10. SUMMARY
As we already discussed and learnt today on
Classifications and Tabulation as below
• Bi-Variate Frequency Distribution Table Meaning &
Problems-------- 01

11. MCQs
1 . The class marks are given below: 10,12,14,16,18. The
first class of the distribution is:
(a) 9----12
(b) 10.5----12.5
(c) 9----11
(d) 10----12
2 . If the midpoints are 10, 15, 20, 25 and 30. The last
class boundary of the distribution is:
(a) 25----30
(b) 27.5----32.5
(c) 20----35
(d) 30----35

12. MCQs
3 . The number of classes depends upon:
(a) Class marks
(b) Frequency
(c) Class interval
(d) Class boundary
4 . The class interval is the difference between:
(a) Two extreme values
(b) Two successive frequencies
(c) Two successive upper limits
(d) Two largest values

13. MCQs
5 . When the classes are 40----44, 45----49, 50----54, ...
the class interval is:
(a) 4
(b) 6
(c) 100
(d) 5

14. CONTD
ANSWERS
1. C
2. B
3. C
4. C
5. D

15. 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

16. THANK YOU