5 Mark Each

Question 15 Marks

The number of two wheelers reigstered $($in thousand$)$ in a city in different years is as follows. Use the method of fitting linear equation to these data to obtain the estimates for the number of vehicles registered in the year $2016$ and $2017 :$

Year	$2010$	$2011$	$2012$	$2013$	$2014$	$2015$
No. of vehicles$(‘000)$	$69$	$75$	$82$	$91$	$101$	$115$

OR Find the trend using five yearly moving averages for the following data about yearly production $($in tons$)$ of a factory :

Year	$2006$	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$	$2015$	$2016$
Production $($tons$)$	$212$	$206$	$193$	$190$	$214$	$259$	$230$	$270$	$230$	$213$	$115$

Answer

$129.60$ OR $2008=203 ; 2009=212.4 ;2010 = 225.2 ; 2011=232.6$ and $2014= 227.2 .$

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Question 25 Marks

The following data gives the experience of machine operators and their performance ratings :

Operator	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Experience $($years$) x$	$12$	$5$	$10$	$3$	$18$	$4$	$12$	$16$
Performance rating $y$	$82$	$74$	$79$	$77$	$88$	$67$	$87$	$86$

Answer

$\hat{y}=77.61$

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Question 35 Marks

Find Karl Pearson's correlation coefficient between density of population $($per square $km)$ and death rate $($per thousand$)$ from the following data:

City	$A$	$B$	$C$	$D$	$E$	$F$	$G$
Density $($per sq.km$.)$	$750$	$600$	$350$	$500$	$200$	$700$	$850$
Death rate$($per thousand$)$	$30$	$20$	$15$	$20$	$10$	$25$	$50$

Answer

$r=0.88$

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Question 45 Marks

The quantity consumed and total expenditure of four different items are as gien below. Find Paasche's, Laspeyre's and Fisher's index numbers for the year $2015$ with respect to the year $2013 .$

items	Base year $2013$		Current year $2015$
	Total Expenditure $(r)$	Consumption $($Quantity$)$	Total Expenditure $(r)$	Consumption $($Quantity$)$
$A$	$420$	$60 \ kg.$	$375$	$25 \ kg.$
$B$	$170$	$10\ litre$	$416$	$20\ litre$
$C$	$525$	$15 \ kg.$	$613.2$	$6 \ kg.$
$D$	$345$	$3 \ kg.$	$400$	$2.5.kg$

Answer

$I_L=213.77, I_P=178.19, I_F=195.17$

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Statistics 5 Mark Each

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