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Question 11 Mark
What is implicit weight ?
Answer
The weights are included in the selection of items and they cannot be expressed numerically, then this indirect method of assigning weight is called implicit weight.
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Question 21 Mark
What is weight ?
Answer
In the construction of index number, the number associated with the selected items in proportion to their importance is called weight of that item.
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Question 31 Mark
Define the cost of living index number.
Answer
The number showing the percentage of relative changes in the cost of living of the people of a certain section of the society in the current year $($period$)$ as compared to the base year $($period$)$ is called the cost of living index number.
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Question 41 Mark
Define the index number.
Answer
The percentage change in the value of variable with any item for the given $($current$)$ period compared to its value in a fixed $($base$)$ period is called an index number.
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Question 51 Mark
Write the formula for the conversion of chain base index number into fixed base index number.
Answer
The formula for the conversion of chain base index number into fixed base index number is as follows: Fixed base index number:$= ($Current year’s chain base index number * Previous year’s fixed base index number$)/100$
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Question 61 Mark
What is a base year ?
Answer
When the price of an item is compared with the price of the same item in some specific (fixed) year of the past, then that specific year is called the base year.
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Question 71 Mark
If the quantity index number of an item for $9$ certain year is $130,$ interpret it.
Answer
The quantity index number of an item for a certain year is $130$ means as compared to base year there is $30 \%$ increase in the quantity of an item.
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Question 81 Mark
Which method is more suitable to compare the changes in a variable at two different time period ?
Answer
Two compare the changes in a variable at two different time period, method of relative measure (ratio) is more suitable.
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Question 91 Mark
How should be the base year in the calculation of index number ?
Answer
In the calculation of index number, the year selected as base year should be standard or normal. It should be free from natural calamities like floods, drought, earthquake, abnormal man-made events like war, revolt, riot, strike, agitation, political events, economic disturbance or any unusual events. And it is also necessary that the base year should not be from a distant past.
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Question 101 Mark
Which is the appropriate average for the construction of index number ?
Answer
The Weighted mean is the appropriate average for the construction of index number.
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Question 111 Mark
In which method does the base year change each year ?
Answer
In chain base method, the base year changes each year.
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Question 121 Mark
State the main difference between fixed base method and chain base method and chain base method.
Answer
In fixed base method a stable period or year with usual events or situation is selected as a normal year or base year. In chain base method, for every current year, its preceding year is taken as a base year.
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Question 131 Mark
Which index number is used in India to find the rate of dearness allowance ?
Answer
Cost of living Index Number is used in India to find the rate of dearness allowance.
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Question 141 Mark
Which index number is used to find the rate of inflation ? Write the formula to find the rate of inflation.
Answer
Wholesale price index number is used to find the rate of inflation. it's formula is as follows :Rate of inflation $=\frac{\left(\begin{array}{c}\text { Wholesale price } \\ \text { index number of } \\ \text { current year }\end{array}\right)-\left(\begin{array}{c}\text { Wholesale price } \\ \text { index number of } \\ \text { preceding year }\end{array}\right)}{\text { Wholesale price index number of preceding year }} \times 100$
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Question 151 Mark
The price index number of oil is $Rs. 500.$ State whether this statement is true or false and if false, correct and rewrite it.
Answer
The price index number of oil is $Rs. 500.$ This statement is false. Index number if free from the unit as it is a relative measure. The price index number of oil is $500.$
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Question 161 Mark
What is a chain base index number ?
Answer
Taking preceding year as a base year of a variable quantity for the price of variable quantity for whom index number is obtained then it is called chain base index number. Here base year is repeatedly changed.
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Question 171 Mark
Name the important basic tests of index numbers.
Answer
Following are the important basic tests of index numbers. $(i)$ Time Reversal test $(ii)$ Factor reversal test
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Question 181 Mark
What is a price relative ?
Answer
A ratio of price of the commodity in the current year with the price in the base year means price relative.
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Question 191 Mark
The price of commodity increases $1.5$ times the base year. Then what will be the index number of price?
Answer
The index number of price $= 2.5 \times 100=250$
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Question 201 Mark
If the daily wage of a worker is $500$ in the year $2017$ and the cost of living index number for the year is $130,$ find the real daily wage of the worker.
Answer
Real daily wage of the worker $= Rs.384.62$
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Question 211 Mark
As compared to the year $2015,$ there is $80 \%$ increase in the sales of cotton for the year $2017.$ What Is the index number of sales of cotton in the year $2017?$
Answer
Index number of sales of cotton in the year $2017=100 + 80 = 180.$
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Question 221 Mark
The price of an item is $Rs. 570$ which becomes $Rs. 1140$ in the current year. Find index number and state the percentage increase or decrease in the price.
Answer
Hence, there is $(200-100)= 100\%$ increase in the price of the item.
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Question 231 Mark
For a data to construct the index number of price, $ {∑p_1q_1} =240, {∑p_0q_0}  = 120, {∑P_0q_1}=125.$ Find paasche’s index number.
Answer
$I_P= 192$
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Question 251 Mark
If the price of an item in the current year is $ 3/4$ times the price of base year, then obtain the index numbers of base year and current year.
Answer
index number of base year $= 100$
Current years index number $= 100 \times 3/4 = 75$
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Question 261 Mark
The production of an Item is $20$ tons in $2017$ and $15$ tons in $2016.$ Find the percentage change in $2016$ in relation to $2017.$
Answer
Hence, there was $(100—75 =) 25 \%$ less production of the item In the year $2016$ as compared to the year $2017.$
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Question 271 Mark
The index number of sales of an Item for the year $2017$ in relation to the year $2015$ is $140.$ State the percentage change in the sales of the item.
Answer
As compared to $2015,$ the index number of sales of an item is $140.$ So, it can be said that the sales of the item is increased by $40 \%.$
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Question 281 Mark
In the total expenditure method for giving weights, write down the formula of index number in the following cases: $(i )$ When the quantity of base year is taken as weight. $(ii)$ When the quantity of current year Is taken as weight.
Answer
$(i)$ index number: $I_{l}=\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100$
$(ii)$ index number: $I_{P}=\sum_{\sum p_{0} q_{1}} \times 100$
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Question 291 Mark
Explain the selection of average for the construction of index number.
Answer
In the construction of index number, the ideal average is the geometric mean while the popular average is the weighted mean.
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Question 301 Mark
Write down the formula for Laspeyre’s and Paasche’s index number.
Answer
Laspeyre's index number $I_{l}=\sum_{\sum p_{1} q_{0}}^{p_{1} q_{0}} \times 100$
Paasche's index number $I_{P}=\sum_{\sum_{p q 1} q_{1}} \times 100$
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Question 311 Mark
State the formula showing the relation among Laspeyre’s, Paasche’s and Fisher’s index numbers.
Answer
$I_f =$ Laspeyre’s index number; $I_P =$ Paasche’s index number and = Fisher’s index number, then the formula showing the relation among them is $I_F =(I_L\times I_P)$
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Question 321 Mark
What is taken as weight of price relative in family budget method?
Answer
In family budget method, base year expenditure of an item Is taken as the weight of price relative of that item.
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Question 331 Mark
State the formula to determine the real wage.
Answer
Real wage $= ($Wage $\times\ 100)/$Cost of living index number
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Question 341 Mark
“In cost of living index number four varieties of wheat is selected in food group. So the explicit weight of wheat is $4.$” Rewrite this statement with correction.
Answer
The statement with correction is rewritten as follows “In cost of living index number four varieties of wheat is selected in food group. So the implicit weight of wheat is $4.$”
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Question 351 Mark
State main steps involved in the construction of the cost of living index number.
Answer
$(1)$ Purpose, $(2)$ Family budget Inquiry, $(3)$ Price quotations of the commodities, $(4)$ Selection of the base year, $(5)$ Selection of the average and $(6)$ Selection of the weights.
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Question 361 Mark
State the formula to convert the fixed base index number into chain base index number.
Answer
Chain base index number $($Fixed base index number for current year $\times \ 100) / $ Fixed base index number for preceding year
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Question 371 Mark
“In the construction of an index number the Ideal, average is arithmetic mean,” Is It true? If no, write the correct statement.
Answer
The given statement is not true. The correct statement Is as follows:“In the construction of an index number the Ideal average is geometric mean.”
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Question 381 Mark
Which number is taken as the index number of base year?
Answer
The number $100$ is taken as the index number of base year.
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Question 391 Mark
Why is the index number considered as the barometer of nation’s economy?
Answer
The index number reflects the changes in all the economic conditions of the country and it also compares the values or conditions of two different time intervals. Thus, it works as a barometer for the socio-economical conditions of a country. Hence, the index number is considered as the barometer of nation’s economy.
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Question 401 Mark
State the popular average in the construction of an index number.
Answer
In the construction of an index number the popular average is weighted mean.
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Question 411 Mark
State the main difference between explicit weight and implicit weight.
Answer
Explicit weight is assigned according to the Importance of the item while implicit weight is implied in the selection of the item.
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Question 421 Mark
State two popular methods of assigning explicit weight.
Answer
Explicit weight is assigned by two popular methods: $(1)$ Total expenditure method and $(2)$ Family budget method.
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Question 431 Mark
State the types of weight.
Answer
The two types of weight are: $(1)$ Implicit weight and $(2)$ Explicit weight.
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Question 441 Mark
Write the main characteristic of fixed base method.
Answer
In fixed base method, the base year is constant, So uniformity is maintained in calculation and comparison of the relative changes in the values of the variable.
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Question 451 Mark
State the main merit of chain base method.
Answer
In chain base method new items can be included according to the taste and choice of the consumers.
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Question 461 Mark
State the methods of selecting base year.
Answer
The two methods of selecting base year are: $(1)$ Fixed base method and $(2)$ Chain base method.
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Question 471 Mark
How should be the base year in the construction of an index number?
Answer
In the construction of an index number the base year should be normal; free from natural calamities, abnormal man-made events, political events arid economic disturbances.
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Question 491 Mark
Which average is considered as an ideal average for the construction of index number?
Answer
Geometric mean is considered as an ideal average for the construction of index number.
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Question 501 Mark
What is the purpose of index number?
Answer
The purpose of index number is to measure and compare the change observed in the value of any time variable.
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1 Marks Each - Statistics STD 12 Commerce Questions - Vidyadip