3 Marks Each

Question 13 Marks

If the daily cost of production for $x$ tons of a commodity is $10 x^2-1000 x+50,000$ then how many units should be produced for the minimum cost? Also, find the minimum cost.

Answer

$2500$

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Question 23 Marks

Normally, $40 \%$ students fail in one examination. Find the probability that at least $4$ students in a group of $6$ students pass in this examination.

Answer

$0.54432 \approx 0.5443$

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Question 33 Marks

Fit a linear equation from the following data for variable $(y)$ of a time series. $n=6, \Sigma y=501, \Sigma t y=1762$

Answer

$\hat{y}=81.79+0.49 t$

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Question 43 Marks

The following information is obtained to study the relationship between average rainfall $($in $cm.)$ and the yield of maize $($in quintal per hectare$)$ in different talukaa of Gujarat.

Particulars	Rainfall (cm) x	Yield of maize (quintal per hectare) y
mean	$82$	$180$
variance	$64$	$225$
Correlation coefficient $0.82$

Estimate the yield of maize when the rainfall is $60 \ cm$.

Answer

$\hat{y}=146.12 ($quintal per hectare$)$

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Question 53 Marks

Obtain the regression line of Yon $X$ from the following data
$n =6, \Sigma x=1020, \Sigma y =990, \Sigma(x-170)^2=60$
$\Sigma( y -165)^2=105, \Sigma(x-170)(y-165)=45 .$

Answer

$\hat{y}=37.5+0.75 t$

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Question 63 Marks

To know the relationship between the abilities of the students of a school in the subjects of Statistics and Accountancy, the teachers of both the subjects have taken a sample of eight students and the following information was collected.

Students	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Marks in Statistics (X)	$79$	$37$	$99$	$26$	$76$	$83$	$91$	$63$
Marks inAccountancy (Y)	$86$	$53$	$93$	$62$	$70$	$64$	$88$	$57$

Calculate the rank correlation co-efficient between the marks of statistics and the marks of accountancy.

Answer

$r \cong 0.86$

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Question 73 Marks

Find the index number for the year $2019$ with the base year $2014$ by weighted average method from the following data of price and weights of five different items.

Item	Weight	Price (₹)
Item	Weight	Year $2014$	Year $2019$
$A$	$40$	$160$	$200$
$B$	$25$	$400$	$600$
$C$	$5$	$50$	$70$
$D$	$20$	$10$	$18$
$E$	$10$	$2$	$3$

Answer

$145.50$

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Question 83 Marks

The chain base index numbers for sales of a certain type of scooter from the year $2015$ to $2020$ are as follows. Find fixed base index numbers.

years	$2015$	$2016$	$2017$	$2018$	$2019$	$2020$
Index numbers of sale	$110$	$112$	$109$	$108$	$105$	$111$

Answer

$2016=110 ; 2016=123.20 ; 2017= 134.29 ; 2018=145.03 ; 2019=152.28 ;2020=169.03$

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Statistics 3 Marks Each

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