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Question

Following data gives age($$X$$ in years) of students in a particular school and their marks in G. K. test. Prepare a bivariate frequency distribution.
$$X$$: $$11$$ $$11$$ $$10$$ $$13$$ $$12$$ $$10$$ $$12$$ $$12$$ $$13$$ $$10$$ $$11$$ $$13$$ $$12$$ $$12$$ $$11$$ $$13$$ $$10$$ $$10$$ $$11$$
$$Y$$: $$22$$ $$24$$ $$23$$ $$21$$ $$24$$ $$21$$ $$22$$ $$23$$ $$24$$ $$24$$ $$22$$ $$23$$ $$21$$ $$24$$ $$21$$ $$22$$ $$24$$ $$22$$ $$23$$ $$24$$
Also obtain
(i) Marginal frequency distributions of age and marks in G.K.
(ii) Conditional frequency distribution of age when marks in G.K. are $$23$$.
(iii) Conditional frequency distribution of marks in G.K. when the age is $$11$$ years.


Solution

Write values of $$X$$ horizontally and $$Y$$ vertically.
$$X$$ takes values from $$10$$ to $$13$$ and $$Y$$ takes values from $$21$$ to $$24$$. Therefore the two way table will contain $$16$$ cells.
The first student is $$11$$ years old and has $$22$$ marks in G.K.
Therefore, we put tally mark in the cell corresponding to $$X=11$$ and $$Y=22$$ etc.
Bivariate frequency distribution table of $$X$$ and $$Y$$.
 Y $$\downarrow$$ / X$$\to$$ 1011 12 13 $$f_y$$ 
 21 $$| $$
(1)
 _ $$||$$
(2)
$$|$$
(1) 
 4
 22 $$|$$
(1)
$$|||$$
(3) 
 $$|$$
(1)
 23 $$||$$
(2)
$$|$$
(1) 
$$|$$
(1) 
24 $$|$$
(1) 
$$||$$
(2) 
$$||$$
(2) 
$$||$$
(2) 
 $$f_x$$20 
(i a.) Marginal frequency distribution of $$X$$:
 X 10111213 Total
 F5564 20
(i b.) Marginal frequency distribution of $$Y$$:
 X 21 22 23 24 Total
F 4 5 4 7 20
(ii) Conditional frequency distribution of $$X$$ when $$Y=23$$
 X 10111213 Total
F 22114
(iii) Conditional frequency distribution of $$Y$$ when $$X=11$$
 X21222324 Total
F 03025

Mathematics

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