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2.7 Bivariate Frequency Distribution

In table 7, we have classified students according to their marks in one subject. Suppose we have marks of a number of students in two subjects, say statistics and physics and we want to consider the variation of marks in both the subjects simultaneously. Then we have to prepare a table (known as a bivariate table) for the following data:

 No. of students 1 2 3 4 5 6 7 8 9 10 11 12 Marks in statistics 60 56 42 33 40 13 27 12 19 50 23 16 Marks in physics 50 45 53 54 49 23 50 24 31 41 47 20 No. of students 13 14 15 Marks in statistics 32 42 30 Marks in physics 38 21 45

Table - 8

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Procedure :

We have to consider a pair of data of observations.

We mark one stroke ( the tally mark ) for one pair.

Now consider the case of the 1st student.

Marks in statistics = 60

Marks in physics = 50

See the row along 50 - 60 ® 5th row

and the column along 50 - 60 ¯
5th column

Therefore the stroke is marked in the cell ( box ) where the 5th row and the 5th column intersect each other.

In this way we mark the strokes for 15 pairs of marks for 15 students and we get the table - 8.

Example: Make a table showing the frequencies, cumulative frequencies ( both less than and more than type ) for the words having different numbers of letters in the following passage (ignore the punctuation marks).

"In Asia the complications are likely to be greater still. There will be four major powers in the Asian balance: Russia, China, Japan and the United States. To some extent, this increases the chance that the forces will emerge sufficient to contain China and it may lead to a real reapproachment between Russia and the West. But who knows, with so many factors, what the pattern will be like, ten years from now ?"

From the Times of India

Solution : We find that the smallest word ' a ' has one letter; and the longest word "re-approachment" has 14 letters. We prepare a tally sheet by writing the number of letters in the first column from 1 to 14. The table is as follows :

Table - 9

Index

2.1 Introduction
2.2 Tabulation
2.3 Classification
2.4 Methods of classification
2.5 Relative frequency distribution
2.6 Cumulative frequency
2.7 Bivariate frequency distribution

Chapter 3