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)_ 5  23 $$||$$(2)_ $$|$$(1) $$|$$(1) 4 24 $$|$$(1) $$||$$(2) $$||$$(2) $$||$$(2) 7  $$f_x$$5 5 6 4 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 TotalF 4 5 4 7 20(ii) Conditional frequency distribution of $$X$$ when $$Y=23$$ X 10111213 TotalF 22114(iii) Conditional frequency distribution of $$Y$$ when $$X=11$$ X21222324 TotalF 03025Mathematics

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