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Statistics 3 Marks Each

PART 1 : INDEX NUMBER · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 16 questions.

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16 questions · timed · auto-graded

Question 13 Marks
Calculate index number by total expenditure method from the following data.
Item Quantity Price $(₹)$
Year $2014$ Year $2014$ Year $2018$
$A$ $4$ $10$ $11$
$B$ $7$ $5$ $13$
$C$ $10$ $3$ $12$
$D$ $3$ $20$ $24$
$E$ $2$ $13$ $26$
Answer
Index number by total expenditure method $=198.43$
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Question 23 Marks
The prices of five food items for the year $2012$ and $2017$ are given below. Find general price index number for the items by taking the year $2012$ as the base year.
Item Price per kg $(₹)$  
  Year $2012$ Year $2017$
$A$ $8$ $10$
$B$ $12$ $18$
$C$ $10$ $7$
$D$ $6$ $9$
$E$ $15$ $21$
Answer
General index number $=127$
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Question 33 Marks
Convert the following fixed base index numbers into chain base index numbers.
Year $2010$ $2011$ $2012$ $2013$ $2014$ $2015$
Index number $130$ $132$ $96$ $144$ $138$ $108$
Answer
Chain base index number $=100,101.54,72.73,150,95.83,78.26$
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Question 43 Marks
From the following data, find index numbers by taking the average price of the year $2013$ and $2015$ as the base year price.
Year $2013$ $2014$ $2015$ $2016$ $2017$ $2018$
Price $(₹)$ $16$ $12$ $20$ $24$ $33$ $30$
Answer
Index number $=88.89,66.67,111.11,133.33,183.33,166.67$
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Question 53 Marks
The prices of three items among five items increased by $40 \%, 50 \%$ and $60 \%$ and prices of the other two items decreased by $20 \%$ and $30 \%$. If the ratio of importance of these items is $4: 3: 7: 9: 2$ respectively, find the general index number for the group of these items.
Answer
Cost of living index number $=119.6$
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Question 63 Marks
The index number for the year $2012$ is $100 .$ It increased by $5 \%$ in the year $2013 ,$ decreased by $10 \%$ in $2014,$ decreased by $5 \%$ in $2015 ,$ increased by $20 \%$ in $2016,$ increased by $25 \%$ in $2017 .$ Find index numbers for these six years. Also convert them into chain base index numbers.
Answer
Chain base index numbers $=100,105,85.71,105.56,126.32,104.17$
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Question 73 Marks
Calculate cost of living index number from the data about the percentage price relatives and their weights for different groups given in the following table.
Year $2012$ $2013$ $2014$ $2015$ $2016$ $2017$ $2018$
Wages $(₹)$ $460$ $500$ $580$ $600$ $620$ $710$ $750$
Cost of living index number $100$ $110$ $118$ $124$ $135$ $135$ $140$
Answer
Cost of living index number $=183.50$
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Question 83 Marks
Find the real wages for the worker class from the following data about their yearly wages.
Year $2012$ $2013$ $2014$ $2015$ $2016$ $2017$ $2018$
Wages $(₹)$ $460$ $500$ $580$ $600$ $620$ $710$ $750$
Cost of living index number $100$ $110$ $118$ $124$ $135$ $135$ $140$
Answer
Real wage $=460,454.55,491.53,483.87,459.26,525.93,535.71$
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Question 93 Marks
Find index numbers by fixed base and chain base method from the following data about the prices.
Year $2011$ $2012$ $2013$ $2014$ $2015$ $2016$
Price $40$ $45$ $48$ $60$ $75$ $90$
Answer
Fixed base index numbers $=100,112.5,120,150,187.5,225$
Chain base index numbers $=100,112.5,106.67,125,125,120$
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Question 103 Marks
$\text { The chain base index numbers are given in the following table. Prepare fixed base index numbers from it. }$
Year $2014$ $2015$ $2016$ $2017$ $2018$
Index number $80$ $110$ $120$ $105$ $200$
Answer
Fixed base index numbers $=80,88,105.6,110.88,221.76$
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Question 113 Marks
The prices of items among the five groups of items of living have become $2, \frac{5}{2}, 3, \frac{9}{4}$ and $\frac{18}{5}$ times in the year $2018$ as compared to the year $2011 .$ If expenditure on these groups are $40 \%, 30 \%, 10 \%$, $15 \%$ and $5 \%$ respectively of the income, find the general price index number for the group of items.
Answer
General price index number $=236.75$
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Question 123 Marks
The prices of three items $A, B, C$ among five items increased by $40 \%, 50 \%$ and $120 \%$ respectively in the year $2018$ as compared to the base year $2017,$ while prices of two items $D$ and $E$ decreased by $10 \%$ and $5 \%$ respectively. Importance of item $A$ is three times than that of item $B$ and the importance of item $C$ is four times than that of item $B.$ If importance of items $D$ and $E$ is $2 \frac{1}{2}$ times than that of item $B,$ find general price index number of the five items for the year $2018.$
Answer
General price index number $=147.12$
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