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Statistics 5 Mark Each

PART 1 : INDEX NUMBER · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 8 questions.

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Question 15 Marks
Among the different groups ofcost of living expenditure, the price of food increased by $60 \%$ in the year $2018$ as compared to the base year. The index number of clothing is $190.$ The price of fuel decreased by $10 \%,$ the expense on rent increased by $1.7$ times and the miscellaneous expenses increased from ? $2000$ to ? $4000.$ If the percentage of total expenditure for the first four groups are $40 \%, 12 \%, 20 \%$ and $10 \%$ respectively, find the cost of living index number for the year $2018$ and interpret it.
Answer
Cost of living index number $=167.80$ Interpretation: There is a rise by $67.80 \%$ in the expenditure in comparison to base year.
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Question 25 Marks
Find the ideal index number from the data given below.
Item Current year   Base year  
  Quantity Price $(₹)$ Quantity Price $(₹)$
$A$ $11$ $20$ $10$ $10$
$B$ $30$ $22$ $20$ $8$
$C$ $25$ $8$ $11$ $2$
$D$ $20$ $16$ $13$ $7$
$E$ $10$ $3$ $6$ $5$
Answer
Ideal index number $I_F=239.53$
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Question 35 Marks
Find index number by total expenditure method and by family budget method from the data given below.
Item Unit $2000$   $2018$
    Quantity Price $(₹)$ Price $(₹)$
$A$ Quintal $35 \ kg$ $400$ $600$
$B$ Gram $20$ gram $5$ $8$
$C$ Dozen $24$ pieces $14$ $21$
$D$ Box $30$ pieces $250$ $300$
$E$ Tin $25 \ kg$ $120$ $180$
$F$ Litre $40$ litre $14$ $22.4$
$($Note : $1$ Box : $50$ pieces and $1$ tin : $20 \ kg)$
Answer
Index number by total expenditure method $=151.86$, Index number by family budget method $=151.86$
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Question 45 Marks
Find the ideal index number for the year $2018$ from the data given below.
Item Unit $2013$   $2018$  
    Price $(₹)$ Quantity Price $(₹)$ Quantity
$A$ $1\ kg$ $4$ $3000$ gram $8$ $4\ kg$
$B$ $20 \ kg$ $120$ $10 \ kg$ $280$ $15 \ kg$
$C$ $5$ dozens $120$ $3$ dozens $140$ $48$ pieces
Answer
Ideal index number $I_F=173.73$
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Question 55 Marks
Find Laspeyre’s, Paasche’s and Fisher’s index numbers using the following data for the year $2018$ by taking the year $2014$ as the base year.
Item Unit Price $(₹)$   Quantity  
    $2014$ $2018$ $2014$ $2018$
$A$ $20 \ kg$ $80$ $120$ $5\ kg$ $7\ kg$
$B$ Quintal $500$ $700$ $10 \ kg$ $15 \ kg$
$C$ Kg $10$ $14$ $1200$ gram $2000$ gram
$D$ Dozen $36$ $60$ $20$ pieces $25$ pieces
Answer
$I_L=152.68, I_P=151.52, I_F=152.10$
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Question 65 Marks
The quantity consumed and total expenditure of four different items are given below. Find Paasche’s and Fisher’s index numbers for the year $2016$ with respect to the year $2013.$
Item Year $2013$   Year $2016$  
  Total Expenditure $(₹)$ Quantity Total Expenditure $(₹)$ Quantity
$A$ $180$ $60 \ kg$ $187.5$ $25 \ kg$
$B$ $80$ $10\ litre$ $208$ $20\ litre$
$C$ $240$ $15 \ kg$ $306.6$ $66 \ kg$
$D$ $168$ $3\ kg$ $200$ $2.5 \ kg$
Answer
$I_P=191.53, I_F=211.52$
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Question 75 Marks
Find Laspeyre’s, Paasche’s and Fisher’s index numbers for the year $2018$ from the data given below.
Item Year $2012$   Year $2018$  
  Price $(₹)$ Total Expenditure $(₹)$ Price $(₹)$ Total Expenditure $(₹)$
$A$ $5$ $50$ $8$ $160$
$B$ $20$ $60$ $22$ $110$
$C$ $10$ $80$ $15$ $150$
$D$ $25$ $500$ $50$ $1500$
$E$ $200$ $1000$ $300$ $1800$
Answer
$I_L=163.67, I_P=165.33, I_F=164.5$
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Question 85 Marks
Find Laspeyre’s, Paasche’s and Fisher’s index numbers for the year $2018$ from the data given below.
Item Quantity   Price $(₹)$  
  $2016$ $2018$ $2016$ $2018$
$A$ $4$ $10$ $10$ $20$
$B$ $7$ $8$ $11$ $13$
$C$ $10$ $9$ $15$ $14$
$D$ $6$ $15$ $7$ $10$
Answer
$I_L=120.06, I_P=135.51, I_F=127.55$
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