5 Mark Each

Question 15 Marks

Find the trend using five yearly moving averages from the following data of profit $($in lakh $₹),$ of a trader, in different years.

Year	$2012$	$2013$	$2014$	$2015$	$2016$	$2017$	$2018$	$2019$	$2020$
Profit $($in lakh $₹)$	$15$	$14$	$18$	$20$	$17$	$24$	$27$	$25$	$23$

Answer

$2012=-; 2013=-; 2014=16.8 ; 2015=18.6 ;=21.2 ;=22.6 ; 2018=23.2 ; 2019=-; 2020=-$

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Question 25 Marks

The profit earned $($in lakh $₹)$ by a company making computers is as follows. Find the linear equation for the trend from this data by least square method and estimate the profit for the year $2020 .$

Year	$2014$	$2015$	$2016$	$2017$	$2018$
Profit $($in lakh $₹)$	$31$	$35$	$39$	$41$	$44$

Answer

$\hat{y}=\operatorname{Rs} 50.8$ lakh

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Question 35 Marks

To know the relationship between the height of father and son, obtain the regression line of height of son on the height of father from the following information of eight pairs of fathers and adult sons :

Height of father $(cm)x$	$167$	$169$	$171$	$168$	$173$	$166$	$167$	$165$
Height of son $(cm ) y$	$158$	$170$	$169$	$172$	$170$	$168$	$164$	$167$

Estimate the height of a son whose father's height is $170 \ cm$.

Answer

$\hat{y}=168.44 \ cm$

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Question 45 Marks

From the following information of a sample of Ten students of a school regarding their marks in two subjects Accountancy and Statistics, find the coefficient of correlation between the marks of two subjects :

Marks in Accountancy	$60$	$80$	$50$	$80$	$95$	$40$	$70$	$40$	$35$	$90$
Marks in Statistics	$50$	$75$	$60$	$85$	$90$	$40$	$65$	$30$	$45$	$70$

Answer

$r \cong 0.90$

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Question 55 Marks

For six different cities of Gujarat state, the approximate figures regarding their density of population $($per square $km)$ and the death rate $($per thousand$)$ are as given below :

City	$A$	$B$	$C$	$D$	$E$	$F$
Density $($per sq.km$.)$	$250$	$500$	$450$	$700$	$600$	$300$
Death rate$($per thousand$)$	$10$	$12$	$10$	$15$	$9$	$12$

Answer

$r \simeq 0.45$

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Question 65 Marks

Compute the Laspeyre's, Paasche's and Fisher's index number for the year $2020$ from the data given below :

Items	Quantity		Price $(₹)$
Items	$2019$	$2020$	$2019$	$2020$
$A$	$25$	$32$	$42$	$45$
$B$	$15$	$20$	$28$	$30$
$C$	$10$	$20$	$30$	$36$
$D$	$8$	$15$	$20$	$25$
$E$	$30$	$36$	$60$	$65$

Answer

$I _{ L }=109.52,I_p=110.29,I _{ F }=109.90$

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Statistics 5 Mark Each

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