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Statistics 5 Mark Each

Board Question Paper : March 2019 · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 4 questions.

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4 questions · timed · auto-graded

Question 15 Marks
The data about goods transported in different years by a division of railway are given below. Fitting a linear equation find the estiamte for the year $2017:$
Year $2011$ $2012$ $2013$ $2014$ $2015$
Good transported $180$ $192$ $195$ $204$ $202$
OR
The quantity index numbers consumption of édible oil in a state are given in the following table. Find the trend using five yearly moving averages :
Year $2005$ $2006$ $2007$ $2008$ $2000$ $2010$ $2011$ $2012$ $2013$ $2014$ $2015$
Index No. $115$ $121$ $119$ $120$ $117$ $119$ $120$ $118$ $116$ $124$ $125$
Answer
$\hat{y}=217$ Ton; $a=177.8$ OR $118.4 ; 119.2 ; 119 ; 118 ; 119.4 ; 120.6$
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Question 25 Marks
In order to study the relationship between the repairing time of accident damaged cars and the cost of repair, the fullowing 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$)$ and $X ($repairing time$).$ If the time taken to repair a car is $50$ hours, find an estimate of the repairing cost.
Answer
$50$ hours; $\hat{y}=52.2$
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Question 35 Marks
Find the correlation co-efficient between the density of population and death rate from the following information
$($Use Karl Pearson's method$) :$
Density $($Per Sq.Km.$) x$ $200$ $500$ $400$ $700$ $600$ $300$
Death rate $($per thousand$) y$ $10$ $12$ $10$ $15$ $9$ $12$
Answer
$r=0.45$
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Question 45 Marks
Compute the Laspayre's, Paasche's and Fisher's index numbers for the year $2016$ from the data given below :
Item Quantity price
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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5 Mark Each - Statistics STD 12 Commerce Questions - Vidyadip