5 Mark Each

Question 15 Marks

The birth rates of a state in different year are given in the following table. Fit a linear tread for these data. Also find the estimate of birth rate for the year $2020:$

year	$2012$	$2013$	$2014$	$2015$	$2016$	$2017$	$2018$
Birth rate	$22.2$	$21.8$	$21.3$	$20.9$	$20.6$	$20.2$	$19.9$

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

Year	$2009$	$2000$	$2011$	$2012$	$2013$	$2014$	$2015$	$2016$	$2017$	$2018$	$2019$
Production	$112$	$106$	$93$	$90$	$114$	$159$	$170$	$130$	$108$	$113$	$115$

Answer

$2020$ is $19.04$ OR $103,112.4 ; 125.2 ; 132.6 ; 136.2 ; 136 ; 127.2$

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Question 25 Marks

From the following information, obtain the regression line of monthly expenditure on monthly income. If Namrata's monthly income is $₹ 75$ thousand estimate her monthly expenditure :

Monthly income $($thousand$)$	$60$	$70$	$64$	$68$	$62$	$65$	$72$
Monthly Expenditure $($thousand$)$	$50$	$59$	$57$	$50$	$53$	$58$	$60$

Answer

$60.77$

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Question 35 Marks

From the following information obtained from a sample of $7$ families of a society regarding height of father $($in $cms)$ and height of his adult son $($in $cms ),$ calculate the correlation coefficient:

Height of father $(cm )$	$170$	$169$	$168$	$167$	$166$	$165$	$164$
Height of son $(cm )$	$172$	$168$	$170$	$168$	$165$	$167$	$166$

Answer

$r =0.81$

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Question 45 Marks

Compute the Laspeyre's. Paasche's and Fisher's index numbers for the year $2019$ from the data given below:

Item	Quantity		price
Item	Year $2015$	Year $2016$	Year $2015$	Year $2016$
$A$	$25 \ kg$	$32 \ kg$	$42$	$45$
$B$	$15$ litre	$20$ litre	$28$	$30$
$C$	$10$ pieces	$20$ pieces	$30$	$36$
$D$	$8$ meter	$15$ meter	$20$	$25$
$E$	$30$ litre	$36$ litre	$60$	$65$

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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