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Statistics 5 Mark Each

‘Board Question Paper : March 2022 · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 6 questions.

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Question 15 Marks
Find the trend using four monthly moving averages for the following data showing monthly sales $($in lakhs $₹)$ of a shop.
month Sales $($lakh $₹)$
march $5$
April $3$
May $7$
June $6$
July $4$
August $8$
September $9$
October $10$
November $8$
December $9$
Answer
self practice
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Question 25 Marks
The information about death rate of a state in different years is given in the following table. Fit a linear equation to find trend and hence estimate the death rate for the year $2023.$
year $2015$ $2016$ $2017$ $2018$ $2019$ $2020$ $2021$
Death rate $7.6$ $6.9$ $7.1$ $7.3$ $7.2$ $6.9$ $6.9$

 
Answer
$\hat{y}=6.78$
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Question 35 Marks
The monthly sale of different types of laptops $($in hundred units$)$ and its profit $($in lakh $₹)$ for the last six months for a company is given below :
month $1$ $2$ $3$ $4$ $5$ $6$
Number of laptops sold $($hundred units $x)$ $5$ $7$ $5$ $12$ $8$ $3$
Profit $($lakh $₹ y)$ $8$ $9$ $10$ $15$ $10$ $6$
Obtain the regression line of $Y$ on $X$. Also, estimate $Y$ for $X =7$.
Answer
$9.97$
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Question 45 Marks
From the following information of heights of husband and wife, Calculate the rank correlation coefficient between their heights.
Height of husband $(cms)$ $156$ $153$ $185$ $157$ $163$ $191$ $162$
Weight of wife $( cms )$ $154$ $148$ $162$ $157$ $162$ $170$ $154$
Answer
$r \cong 0.91$
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Question 55 Marks
From the following information, find correlation coefficient between heights and weights.
Height $(cm) x$ $155$ $165$ $158$ $162$ $153$ $160$
Weight $(cm) y$ $53$ $63$ $56$ $60$ $52$ $60$
Answer
$r \cong 0.98$
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Question 65 Marks
Compute the Laspayre's, Paasche's and Fisher's index numbers for the year $2021$ from the data given below :
Item Quantity price $(₹)$
Year $2021$ Year $2020$ Year $2021$ Year $2020$
$A$ $25 \ kg$ $32 \ kg$ $42$ $45$
$B$ $15$ 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
$I _{ L }=90.67 ; I _{ P }=91.31 ; I _{ F }=90.99$
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