5 Mark Each

Question 15 Marks

Find Spearman's correlation coefficient from the data given below for the temperature $\left({ }^{\circ} C \right)$ on a certain day of a month and number of tourists visiting on that day to various hill stations of a mountainous region and interpret it.

Weekly income $(100 ₹)$	$20$	$25$	$30$	$28$	$27$	$30$	$29$	$28$	$24$	$22$
Weekly expenditure $(00 ₹)$	$18$	$20$	$27$	$27$	$25$	$29$	$27$	$28$	$22$	$20$

Answer

$r=-0.57$, partial negative correlation

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Question 25 Marks

Find Spearman's correlation coefficient from the data given below for the weekly income $( 100 ₹)$ and weekly expenditure $( 100 ₹ ).$

Weekly income $(100 ₹)$	$20$	$25$	$30$	$28$	$27$	$30$	$29$	$28$	$24$	$22$
Weekly expenditure $(00 ₹)$	$18$	$20$	$27$	$27$	$25$	$29$	$27$	$28$	$22$	$20$

Answer

$r=0.87$

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Question 35 Marks

The following information is obtained for two related variables $X$ and $Y$.
$n=6, \Sigma x=40, \Sigma y=58, \Sigma x^2=316, \Sigma y^2=606$ and $\Sigma x y=431$
Later on, it was found that one pair of observations was taken as $(10,13)$ instead of $(11,14)$ and one pair of observations $(9,11)$ was not taken. Find the correct correlation coefficient and interpret it.

Answer

$r=0.94$, high degree of positive correlation

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Question 45 Marks

Find correlation coefficient from the data given below for the temperature $\left({ }^{\circ} C \right)$ on different days and the sale of woollen coats $($in pieces$)$ during a week of the month of December.

Temperature $(@)x$	$-4$	$-3$	$-2$	$0$	$1$	$3$	$5$
Sale of woollen coats $($pieces$) y$	$19$	$15$	$12$	$10$	$8$	$5$	$4$

Answer

$r=-0.97 \quad$

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Question 55 Marks

Find correlation coefficient from the data given below for the price $($in thousand $₹) X$ of different models of two wheelers and their annual sales $(100$ units$) Y$ of a company and also interpret it.

Price of vehicle $($thousand $₹) x$	$60$	$58$	$70$	$75$	$65$	$80$	$63$
Annual sales $(100$ units$) y$	$4$	$3$	$10$	$12$	$8$	$18$	$7$

Answer

$r=0.98$, high degree of positive correlation

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Question 65 Marks

The data regarding sales $($in lakh $₹ )$ and the profit $($in thousand $₹ )$ of a company for different years are as follows. Find the correlation coefficient.

Sales $($lakh $₹) x$	$2.1$	$1.5$	$2.2$	$1.8$	$1.6$	$2.3$	$2$
Profit $($thousand $₹) y$	$7.8$	$7.6$	$8$	$7.4$	$7.6$	$8$	$8.4$

Answer

$r=0.61$

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Question 75 Marks

The following data is obtained while studying the relationship between annual administrative cost $X ($in lakh $₹)$ and annual profit $Y ($in lakh $₹)$ of various companies. Find the correlation coefficient and interpret.

Annual administrative cost of company $($lakh $₹) X$	$30$	$23$	$34$	$26$	$18$	$24$	$15$
Annual profit of company $($lakh $₹) Y$	$80$	$60$	$90$	$70$	$55$	$65$	$35$

Answer

$r=0.98$

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Question 85 Marks

Find correlation coefficient for the data given below for the height $( cms )$ and weight $( kg )$ of seven students.

Height $(cms)x$	$130$	$143$	$138$	$132$	$142$	$144$	$139$
Weight $(kg)y$	$45$	$50$	$48$	$46$	$50$	$52$	$48$

Answer

$r=0.97$

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Question 95 Marks

The information of families collected to study the relationship between the income of a family and its expenditure on food items in the percentage of their incomes are as follows. Find the correlation coefficient between the income of a family and its expenditure on food items in percentage of income.

Income of a family $($thousand $₹) x$	$8$	$20$	$45$	$5$	$25$	$30$	$21$
Expenditure on food items in percentage of the income $y$	$60$	$50$	$40$	$65$	$42$	$30$	$28$

Answer

$r=-0.69$

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