5 Mark Each

Question 15 Marks

The dropout rate of students of standard $1$ to $5$ from primary schools of a district is as follows

year	$2009-10$	$2010-11$	$2011-12$	$2012-13$	$2013-14$	$2014-15$	$2015-16$
Dropout rate	$3.24$	$2.98$	$2.29$	$2.20$	$2.09$	$2.07$	$2.04$

Estimate the dropout rate for students from standard $1$ to $5$ for the year $2016-17$ and $2017-18$ by fitting a linear equation for trend.
OR Find the trend using four monthly moving averages for the following data showing monthly sales $($in lakh $₹)$ of a shop.

month	Sales (lakh ₹)
march	$5$
April	$3$
May	$7$
June	$6$
July	$4$
August	$8$
Sept.	$9$
Oct.	$10$
Nov.	$8$
Dec.	$9$

Answer

$1.62$ and $1.42$ OR $5.13 ; 5.63 ; 6.5 ; 7.25 ; 8.25 ; 8.88$

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Question 25 Marks

In order to study the relationship between the repairing time of accidentally damaged cars and the cost of repair, the following information is collected.

Repairing time of a car $($man hours$)$	$32$	$40$	$25$	$29$	$35$	$43$
Repairing cost $($thousand $₹)$	$25$	$35$	$18$	$22$	$28$	$46$

Obtain the regression line of $Y ($repairing cost$)$ on $X ($repairing time$).$ If the time taken to repair a car is $40$ hours, find an estimate of the repairing cost. Also find its error.

Answer

$\hat{y}=52.2$

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Question 35 Marks

To know the relation between the heights and weights of the students of a school, a sample of six students is taken and the following information is obtained. Find the Correlation coefficient between the heights and weights of the students.

Height $( cm.) x$	$155$	$165$	$158$	$162$	$153$	$160$
Weight $(kg.) y$	$53$	$63$	$56$	$60$	$52$	$60$

Answer

$r \simeq=0.98$

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Question 45 Marks

Find the Laspeyre's and Paasche's index numbers using the following data for the year $2017$ by taking the year $2016$ as the base year. Also find the Fisher's index number.

Item	Base year $2016$		Current year $2017$
Item	Per unitPrice $(₹)$	TotalExpenditure $(₹)$	Per unitPrice $(₹)$	TotalExpenditure $(₹)$
Wheat	$16$	$224$	$18$	$270$
Rice	$35$	$140$	$40$	$200$
Tuver Dal	$100$	$200$	$120$	$360$
Oil	$108$	$432$	$120$	$600$

Answer

$I _{ L }^{\prime}=113.65 ; I _{ P }=113.94 ; I _{ F }=113.79$

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Statistics 5 Mark Each

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