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Introduction to Index Number Test - 10

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Introduction to Index Number Test - 10
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  • Question 1
    1 / -0
    Calculate the index number for the year 2006 with 1996 as the base year by the weighted average of price relatives method from the following data.
    CommodityABCDE
    Weight402552010
    Price(Rs) per unit 19963280110.244
    Price(Rs) per unit 200640120115.363
    Solution
     CommodityCommodityWeightWeight 
    ww
    Pricein1996Price\,in\,1996
    (Rs.)  P0(Rs.)\,\,P_0 
    Pricein2006Price\,in\,2006
    (Rs.)  P1(Rs.)\,\,P_1 
    PricerelativePrice\,relative
    I=P1P0×100I=\dfrac{P_1}{P_0}\times 100 
    I.wI.w 
    AA 4040 3232 4040 125125 50005000 
    BB 2525 8080 120120 150150 37503750 
    CC 55 11 11 100100 500500 
    DD 2020 10.2410.24 15.3615.36 150150 30003000 
    EE 1010 44 33 7575 750750 
     TotalTotal 100100   1300013000
    \Rightarrow  P01=Iww=13000100=130P_{01}=\dfrac{\sum Iw}{\sum w}=\dfrac{13000}{100}=130
  • Question 2
    1 / -0
    When the price of a divided by the price of the preceding year, we, get:
    Solution
    \Rightarrow  When the price of divided by the price of the preceding year, we get : Link  relative.Link\,\,relative.
    \Rightarrow  This method is based on the assumption that the trend is linear and cyclical variations are of uniform pattern. 
    \Rightarrow  The link relatives are percentages of the current period (quarter or month) as compared with the previous period. With the computations of the link relatives and their average, the effect of cyclical and the random components is minimized. Further, the trend gets eliminated in the process of adjustment of chain relatives
    \Rightarrow  This method is less complicated than the ratio to moving average and the ratio to trend methods.However, this method is based upon the assumption of a linear trend which may not always hold true.
  • Question 3
    1 / -0
    When the price of a year is. divided by the price of a particular year we get:
    Solution
    \Rightarrow  When the price of year is divided by the price of particular year we get : Simple  relative.Simple\,\,relative.
    \Rightarrow  Under this method, the price Index for a given year is calculated as the simple average of the price relatives of the different items included in the index numbers. 
    \Rightarrow  The simple average used, here, may be of any type viz. arithmetic mean, geometric mean, harmonic mean, median or mode, but arithmetic mean is usually preferred to, for its simplicity in calculation and geometric mean for its ability of measuring the relative changes which is the inherent feature of an index number.
  • Question 4
    1 / -0
    The current price of a soap is Rs 10.  The base price is 4. Find price relative.
    Solution
    Price relative == Base Price // Current Price
                           =410=0.25=\dfrac{4}{10} = 0.25
  • Question 5
    1 / -0
    If all the values are not of equal importance the index number is called: 
    Solution
    \Rightarrow  If all the values are not of equal importance the index number is called : WeightedWeighted
    \Rightarrow  The ratio of the sum of weighted prices of current and base time periods multiplied by 100 is called weighted aggregate price index.
    \Rightarrow  This index is calculated after allocating weight to each commodity on the basis of their relative importance.
    \Rightarrow  Weight of these commodities are then multiplied by the prices of base and current time periods. these prices are called weighted price.

  • Question 6
    1 / -0
    A weighted aggregate price index where the weight for each item is its base period quantity is known as the
    Solution
    A weighted aggregate price index where the weight for each item is its base period quantity is known as the Laspeyres Index.
  • Question 7
    1 / -0
    The current price of a soap is Rs 11.  The base price is 3, find price relative.
    Solution
    \Rightarrow   Current price of soap is Rs.11.Rs.11.
    \Rightarrow   Base price of soap is Rs.3Rs.3
    \Rightarrow   PricerelativePrice\, relative = CurrentpriceBaseprice=113=3.6\dfrac{Current\,price}{Base\,price}=\dfrac{11}{3}=3.6
  • Question 8
    1 / -0
    Which of the following statement is incorrect?
    Solution
    Step 1: Check whether the given statements are correct or not.\textbf{Step 1: Check whether the given statements are correct or not.}

                   Most index numbers are subjected to revision from time to time due to different reasons.\text{Most index numbers are subjected to revision from time to time due to different reasons.}
                   In most cases it becomes compulsory to change the base year because numerous changes\text{In most cases it becomes compulsory to change the base year because numerous changes}
                   took place with the passage of time. For example change may happen due to disappearance\text{took place with the passage of time. For example change may happen due to disappearance}
                   of old items, inclusion of new ones, change in weights of commodities or changes in conditions,\text{of old items, inclusion of new ones, change in weights of commodities or changes in conditions,}
                   habits and standard of life etc.\text{habits and standard of life etc.}

    Hence, Option D is answer\textbf{Hence, Option D is answer}
  • Question 9
    1 / -0
    Construct a composite index number as a weighted mean from the following data:
    Index Number12214510198137116
    Weight724165
    Solution
     IndexnumberIndex\,number
            II
    WeightWeight
    ww 
    I.wI.w 
     12212277 854854 
    145145 22 290290 
    101101 44 404404 
    9898 11 9898 
    137137 66 822822 
    116116 55 580580 
    TotalTotal w=25\sum w=25 Iw=3048\sum Iw=3048 
    \Rightarrow  Composite index number = Iww=304825=121.92122\dfrac{\sum Iw}{\sum w}=\dfrac{3048}{25}=121.92\approx 122.
  • Question 10
    1 / -0
    If all the values are not of equal importance the index number is called:
    Solution
    If all the values are not of equal importance, the index number is called Weighted.
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