3 Marks Each

Question 13 Marks

The coefficient of rank correlation between two related variables for $8$ pairs is $0.6$. Later on, it was found that one of the difference of ranks was taken as $-3$ instead of $5 .$ Find the correct rank correlation coefficient.

Answer

$r=0.41$

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Question 23 Marks

Find Spearman's rank correlation coefficient from the following data of the time of usage of cars $($years$)$ and their annual maintenance expenditure $($thousand $₹ )$ for different models of a car manufacturing company.

Time of usage of cars $($years$) x$	$4$	$4.5$	$5$	$6.8$	$4.7$
Maintenance expenditure $($thousand $₹) y$	$3.5$	$3.5$	$3.5$	$3.5$	$3.5$

Answer

$r=0$

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Question 33 Marks

A test of students is conducted to know the relation between the understanding of English $\operatorname{grammar}(X)$ and Gujarati grammar $(Y)$. The marks obtained in this test are as follows. Find rank correlation coefficient.

Marks of understanding English grammar $(x)$	$28$	$15$	$5$	$10$	$15$	$25$	$15$	$20$
Marks of understanding Gujaratigrammar $(y)$	$27$	$10$	$22$	$20$	$6$	$14$	$10$	$8$

Answer

$r=0$

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Question 43 Marks

Ranks given by two judges to seven competitors $A , B , \ldots ., G$ in a patriotic song competition are as follows.
Find correlation coefficient.

Rank	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Judge $I$	$C$	$F$	$A$	$B$	$E$	$D$	$G$
Judge $II$	$B$	$D$	$F$	$A$	$C$	$E$	$G$

Answer

$r=0.21$

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Question 53 Marks

Ranks given by two judges to ten competitors in a dance competition are as follows. Find Spearman's rank correlation coefficient.

Rank by judge $(I)$	$1$	$6$	$5$	$10$	$3$	$2$	$4$	$9$	$7$	$8$
Rank by judge$(II)$	$3$	$5$	$8$	$4$	$7$	$10$	$2$	$1$	$6$	$9$

Answer

$r=-0.21$

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Question 63 Marks

A study conducted to know the relationship between the number of family members and the consumption of milk in families shows the following results. Find correlation coefficient between the number of family members and the consumption of milk $($in litres$)$ in families.

Number of family members	$3$	$5$	$2$	$5$	$4$	$6$	$3$
Consumption of milk $($litre$)$ in family	$1.5$	$2.5$	$0.5$	$2$	$1.5$	$2$	$1$

Answer

$r=0.88$

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Question 73 Marks

The data collected from a sample taken to know the relation between the usage $($in years$)$ of trucks of a transport company and their annual maintenance expenditure $(10,000 ₹)$, provided the following information.$n=6, \Sigma x=16, \Sigma y=51, \Sigma x y=154, \Sigma x^2=52$ and $\Sigma y^2=478$Later on, it was found that one pair of observations was taken as $(3,8)$ instead of $(5,10)$. Find the correct value of the correlation coefficient.

Answer

$r=0.83$

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Question 83 Marks

The following data is obtained to study the relation between annual income $(X)$ and investment in shares $(Y)$ of some families.$\bar{x}=13.5, \bar{y}=16.5, \Sigma(x-12)(y-15)=80, \Sigma(x-12)^2=400, \Sigma(y-15)^2=80$ and $\Sigma(x-12)=12$ Where $X=$ Annual income $($lakh $₹) Y=\text { Share investment (thousand ₹) } $ Find the correlation coefficient and interpret it.

Answer

$r=0.40$

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Question 93 Marks

The following results are obtained for the consumption of fertilizer $($tons$)$ and production of wheat $($tons$)$ in nine districts. Find the correlation coefficient and interpret it. $\Sigma x=18, \Sigma y=504, \Sigma(x-2)^2=60, \Sigma(y-55)^2=480$ and $\Sigma(x-2)(y-55)=121$

Answer

$r=0.72$

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Question 103 Marks

Find the value of correlation coefficient from the following results.$\operatorname{Cov}(x, y): S_y^2=S_x: S_y=2: 3$

Answer

$r=1$

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Question 113 Marks

The data of marks of the first test of $10$ students of the $12th$ standard class for Statistics and Economics are as follows. Find the value of correlation coefficient. $ \bar{x}=64, \bar{y}=56, \Sigma x^2=50780, \Sigma y^2=32010 \text { and } \Sigma x y=36120 $

Answer

$r=0.11$

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Question 123 Marks

If $n=5, \Sigma x=25, \Sigma y=15, \Sigma x^2=180, \Sigma y^2=90$ and $\Sigma x y=75$, find the value of correlation coefficient.

Answer

$r=0$

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Statistics 3 Marks Each

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