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Statistics 3 Marks Each

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

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12 questions · timed · auto-graded

Question 13 Marks
The following information is obtained for monthly advertisement cost and the sales of the last year for a company providing online shopping.
particulars Advertisement cost $($Ten thousand$)$ Sales $($Lakh $₹)$
mean $10$ $90$
Standard deviation $3$ $12$
$r = 0.8$
Obtain the regression line of the sales on the advertisement cost.
Answer
$\hat{y}=58+3.2 x$
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Question 23 Marks
The details of expenditure on clothing for the worker class of a region are as follows. Find the index number for clothing by Family Budget Method.
Item Saree Dhoti shirting other
Unit Piece piece meter Meter
Quantity in year $2020$ $5$ $8$ $20$ $15$
Price in year $2020 (₹)$ $300$ $70$ $32.40$ $20.90$
Price in year $2021 (₹)$ $400$ $100$ $38$ $23.80$
Answer
$129.64$
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Question 33 Marks
The probability that a bomb dropped from a plane over a bridge will hit the bridge is $\frac{1}{5}$. Two bombs are enough to destroy the bridge. If $6$ bombs are dropped on the bridge, find the probability that the bridge will be destroyed.
Answer
$0.3446$
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Question 43 Marks
For three mutually exclusive and exhaustive events $A , B$ and $C$ in the sample space of a random experiment $2 P ( A )=3 P ( B )=4 P ( C )$. Find $P ( B \cup C )$.
Answer
$\frac{7}{13}$
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Question 53 Marks
If two balanced coins are tossed, then find the probability of $(1)$ getting one head and one tail $(2)$ getting at least one head.
Answer
$P ( B )=\frac{m}{n}=\frac{3}{4}$
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Question 63 Marks
Obtain the linear equation for trend for a Time Series with $n=8$, $\Sigma y=344, \Sigma t y=1342$.
Answer
$65.05-4.9 t$
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Question 73 Marks
If $b_{y x}=0.8$ then find the value of by for the following $u$ and $v$.
$(i)\ u=x-105$ and $v=y-90$
$(ii)\ u=\frac{x-1400}{100}$ and $v=\frac{y-750}{50}$
$(iii)\ u=10( x -4.6)$ and $v=y-75$.
Answer
$(i)\ 0.8\ (ii)\ 1.6\ (iii)\ 0.08$
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Question 83 Marks
Year201620172018201920202021
Average Monthly Wages ₹15,00018,00019,00020,00022,00025,000
Cost of living Index Number
(Base Year 2014)		120180205220235260
Answer
2016=12,500 ; 2017=10,000 ; 2018=9268.29 ; 2019=9090.91 ; 2020= 9361.7 ; 2021=9615.38
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Question 93 Marks
If $y=\frac{2 x^2+3 x+4}{x^2+5}$ the find $\frac{d y}{d x}$.
Answer
$\frac{-3 x^2+12 x+15}{\left(x^2+5\right)^2}$
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Question 113 Marks
A number of selected from the natural number 1 to 100 . Find the probability of the event that the selected number is a multiple of 3 or 5.
Answer
0.47
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Question 123 Marks
Ten students were ranked on the basis of their proficiency in sports and general knowledge. The rank correlation coefficient obtained from the data was found to be 0.2 later on, it was noticed that the difference in the ranks of the two attributes for one of the students was taken as 3 instead of 2. Find the correct value of rank correlation coefficient.
Answer
$\Sigma d ^2=127=0.23 ; r \cong 0.23$
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3 Marks Each - Statistics STD 12 Commerce Questions - Vidyadip