{"id":13047,"date":"2019-12-18T15:07:29","date_gmt":"2019-12-18T09:37:29","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=13047"},"modified":"2021-07-02T15:35:57","modified_gmt":"2021-07-02T10:05:57","slug":"2nd-puc-statistics-question-bank-chapter-2","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-statistics-question-bank-chapter-2\/","title":{"rendered":"2nd PUC Statistics Question Bank Chapter 2 Index Numbers"},"content":{"rendered":"

You can Download Chapter 2 Index Numbers Questions and Answers, Notes, 2nd PUC Statistics Question Bank with Answers<\/a>\u00a0Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Statistics Question Bank Chapter 2 Index Numbers<\/h2>\n

2nd PUC Statistics Index Numbers One and Two Marks Questions and Answers<\/h3>\n

Question 1.
\nWhat do you mean by an index number?\/ Define index numbers.
\nAnswer:
\nAn index number is a statistical measure designed to show an average change in a variable or group.of related variables with respect to Time, Geographical location or Income group etc.<\/p>\n

Question 2.
\nDefine\/what are the conditions for an Index number to satisfy TRT and FRT.
\nAnswer:
\nTime Reversal Test requires that the product of P01<\/sub> (price index number computed time backward) and P10<\/sub> (price index number computed time forward) should be equal to one [1]; ie P01<\/sub> \u00d7 p10<\/sub> = 1.<\/p>\n

Factor Reversal Test requires that the product of P01<\/sub> (price index number) and Q01<\/sub> (quantity index number) should be equal to the net changes occurring in between the current year and the base year (V01<\/sub> )
\nie. P01<\/sub> \u00d7 Q01<\/sub> = \\(\\frac{\\sum p_{1} q_{1}}{\\sum p_{0} q_{0}}\\);(Except the factor 100)<\/p>\n

Question 3.
\nDefine Unit Test
\nAnswer:
\nThis test requires that the index number used should be independent of the units of measurement.<\/p>\n

Question 4.
\nDefine Circular test
\nAnswer:
\nThis requires that the index number is to work in a circular manner and this property enables us to find the index numbers from period to period without referring back to the original base each time. For 3 years 0(1998), 1(2005) and 2(2010):
\nCircular test is said to be satisfied if: P01<\/sub> \u00d7 P12<\/sub> \u00d7 P20<\/sub> = 1<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nWhat is a price relative?
\nAnswer:
\nPrice Relative is the price in the current year expressed as percentage of the price in the base
\nP = \\(\\frac{p_{1}}{p_{0}}\\) \u00d7 100<\/p>\n

Question 6.
\nWrite the formula for unweighted geometric mean index number .
\nAnswer:
\n\"2nd<\/p>\n

Question 7.
\nThe sum of the price relaives of 5 different is 220. Find suitable Unweighted price index number
\nAnswer:
\nHere Unweighted price Index number: P01 = = 40<\/p>\n

Question 8.
\nIf cost of living Index number of 2005 is 225 with 1995 as a base year, what is the change in the Index?
\nAnswer:
\nThe percentage change in consumer prices is 125%<\/p>\n

Question 9.
\nDefine consumer price\/cost of living index number.
\nAnswer:
\n“Cost of living index number is the index number of the cost met by a Specified class of consumers in buying a basket of goods and services.”<\/p>\n

Question 10.
\nWhy Index numbers are called ‘Economic Barometers’?
\nAnswer:
\nA Barometer measures the pressure of the atmosphere. An index number indicates the changes occurring in Economic field such as variations in price, costs, growth rate, imports, exports of certain commodities etc.<\/p>\n

Question 11.
\nTheoretically which best average is used in the construction of Index Number?
\nAnswer:
\nGeometric mean<\/p>\n

Question 12.
\nPrice index number for the current is 200, give your conclusion.
\nAnswer:
\nThere is a net increase of prices by 100% in the current year as compared to base year<\/p>\n

Question 13.
\nMention any two steps in the construction of Index Number.
\nAnswer:
\nAny two of the following :<\/p>\n

    \n
  1. Purpose and the scope<\/li>\n
  2. Selection of base period or<\/li>\n
  3. Selection of commodities or items<\/li>\n
  4. Obtaining price quotations<\/li>\n
  5. Choice of an average<\/li>\n
  6. 6. Selection of weights<\/li>\n
  7. Selection of suitable formula<\/li>\n<\/ol>\n

    \"KSEEB<\/p>\n

    Question 14.
    \nName the 2 methods of computing Consumer price Index (cost of living Index) Number?
    \nAnswer:
    \nAggregative expenditure method(AEM) & Family Budget method (FBM).<\/p>\n

    Question 15.
    \nWhat do you mean by ‘Family Budget Survey’ conducted while constructing consumer price index number?
    \nAnswer:
    \nA detailed enquiry\/survey regarding the consumption pattern and the average expenditure spent on various item under the heads-Food, Cloth, Rent, Fuel & Lighting, Education, Entertainment, & Miscellaneous, required for day to day living of the consumers is conducted.<\/p>\n

    Question 16.
    \nWhy Fisher’s Index number is called an Ideal Index Number?
    \nAnswer:
    \nFisher’s Index Number is called as ideal because, it is free from bias in use of weights ie. it takes both current and base year quantities as weights.<\/p>\n

      \n
    • It is based on geometric mean which is considered as best average<\/li>\n
    • It satisfies both time reversal tests and factor reversal tests<\/li>\n<\/ul>\n

      Question 17.
      \nWrite the uses of Index numbers.
      \nAnswer:
      \nIndex numbers are useful to governments in formulating Economic policies, such as Taxation, imports, exports, granting of licenses to new firms, fixation of Bank rates, salary and grants to employees. Also, in comparing variations in production, prices, shares, Demand, supply, and measurement of real Rupee.<\/p>\n

      Question 18.
      \nThe average price level of a commodity in the year 2000 is times of what it was in 1990. Express the change by means of Index number.
      \nAnswer:
      \nThe average price in 1990 is 100, so the Index number should be 100 \u00d7 2 1\/2 = 250 in 2000<\/p>\n

      Question 19.
      \nWhich prices of the commodities is useful (used) in the construction of cost of living Index Number?
      \nAnswer:
      \nRetail prices of the commodities is used in the construction of consumer price Index Number.<\/p>\n

      \"KSEEB<\/p>\n

      Question 20.
      \nIf the price index for the current year is 125 what is your conclusion?
      \nAnswer:
      \nThe prices have increased by 25% .<\/p>\n

      Question 21.
      \nThe price index for the current year is 121. Give your conclusion.
      \nAnswer:
      \nThe prices have increased by 21%<\/p>\n

      Question 22.
      \nWhat weights are used in Laspeyre’s, Paasche’s, Marshall-Edgeworth’s Price Index Numbers?
      \nAnswer:
      \nBase year, Current year & Arithmetic mean of Base year and Current year Quantities are used as weights.<\/p>\n

      Question 23.
      \nwhich average is preferred in the construction of an index number? why
      \nAnswer:
      \nA.M or GM. Is used because AM us very easy to calculate where as geometric mean is considered as most appropriate and better method for averaging the ratios.<\/p>\n

      Question 24.
      \nWhich weights are used in Paasche’s Quantity Index No.?
      \nAnswer:
      \nBase year prices (P0<\/sub>).<\/p>\n

      \"KSEEB<\/p>\n

      Question 25.
      \nWhat is the Index number during the base year?
      \nAnswer:
      \n100<\/p>\n

      Question 26.
      \nIf P01(L) for the year 2006 with base year 2000 is 225, what is the Index Number for 2000?
      \nAnswer:
      \n100 .<\/p>\n

      Question 27.
      \nWhich test is satisfied by Marshall-Edgeworths’s Index number?\/Does Marshall- Edgeworths’s Index number satisfies time reversal test?
      \nAnswer:
      \nTime Reversal Test\/Yes.<\/p>\n

      \"KSEEB<\/p>\n

      Question 28.
      \nGive any two Limitations of Price Index Number.
      \nAnswer:<\/p>\n

        \n
      1. Many formulae are used and they give different answers for the index.<\/li>\n
      2. As the customs and habits change from time to time, the uses of commodities also vary.<\/li>\n
      3. There is ample scope for bias in the construction of Index numbers.<\/li>\n<\/ol>\n

        Question 29.
        \nWhat are the points to remember while selecting the Base Year?AVrite two norms for selecting the base year in the construction Index number
        \nAnswer:
        \nBase year selected<\/p>\n

          \n
        • should be the Normal one<\/li>\n
        • should not be too long or too short period .<\/li>\n
        • is a fixed or chain base year method<\/li>\n<\/ul>\n

          Question 30.
          \nShow that Laspeyre’s price index number does not satisfy time reversal test.
          \nAnswer:
          \n\"2nd<\/p>\n

          Question 31.
          \nIf a price of a commodity is Rs.10 in 2002 aiid Rs.35 in 2008, then compute the index no. of price.
          \nAnswer:
          \nPrice Index No.[price relativel = \\(\\frac{P_{1}}{P_{0}}\\) \u00d7 100 = \\(\\frac{35}{10}\\) \u00d7 100 = 350<\/p>\n

          Question 32.
          \nIf Laspeyre’s price index number and paasche’s price index numbers are 210 and 208, then find Dorbish-Bowle’s price index no.
          \nAnswer:
          \nThe relation between Laspeyre’s ,Paasche’s and Dorbish-bowley price index number is :
          \nD – B = \\(\\frac{L+P}{2}\\) \u00d7 100; D-B = \\(\\frac{210 + 208}{2}\\) = 209<\/p>\n

          Question 33.
          \nGiven \u03a3 p1<\/sub>q0<\/sub> = 100 and \u03a3 p0<\/sub>q0<\/sub> = 102 find a suitable index no.
          \nAnswer:
          \n\"2nd<\/p>\n

          \"KSEEB<\/p>\n

          Question 34.
          \nIf \u03a3 p1<\/sub>q1<\/sub> and \u03a3 p0<\/sub>q1<\/sub> = 120 find a suitable index number.
          \nAnswer:
          \n\"2nd<\/p>\n

          Question 35.
          \nIf PL<\/sup>01<\/sub> for the year 2006 with base year 2000 is 225, what is the index number for 2000?
          \nAnswer:
          \nThe index number for the year 2000 is ‘100’<\/p>\n

          Question 36.
          \nIf PL<\/sup>01<\/sub>, = 135 and Pp<\/sup>01<\/sub>= 138, find P01<\/sub> [F].
          \nAnswer:
          \n\"2nd<\/p>\n

          Question 37.
          \nIf Laspeyre’s and Fisher’s indices are 110 and 110.5 respectiely, find Paasche’s index number.
          \nAnswer:
          \nP01<\/sub> [F] = \\(\\sqrt{\\mathrm{P}_{01}(\\mathrm{L}) \\times \\mathrm{P}_{01}(\\mathrm{P})}\\) ; 110.5 = \\(\\sqrt{110 \\times \\mathrm{P}_{01}(\\mathrm{P})} \\)
          \n(110.52<\/sup> = 110 \u00d7 P01(P); P01(P) = 12210.25\/110 = 111.0023<\/p>\n

          \"KSEEB<\/p>\n

          Question 38.
          \nIf \u03a3 p0<\/sub>q1 <\/sub>= 250 and \u03a3 p1<\/sub>q1<\/sub> = 400, compute suitable price index no.
          \nAnswer:
          \nPaasche’s price index number p01 = <\/sub>\\(\\frac{\\sum p_{1} q_{1}}{\\sum p_{0} q_{1}}=\\frac{400}{250}\\) = 160<\/p>\n

          Question 39.
          \n\u03a3 q1<\/sub>p0<\/sub> = 180 and \u03a3 q0<\/sub>p0<\/sub> = 150 then find suitable quantity index number.
          \nAnswer:
          \nQ01 <\/sub>= \\(\\frac{\\sum q_{1} p_{0}}{\\sum q_{0} p_{0}}=\\frac{180}{150}\\) = 120<\/p>\n

          Question 40.
          \nCalculate cost of living index number from the following data.
          \n\"2nd
          \nAnswer:
          \nI01<\/sub> = \\(\\frac{\\Sigma p w}{\\Sigma w}\\) = (110 \u00d7 3 + 120 \u00d7 8 + 112 \u00d7 4 + 108 \u00d7 6 + 105 \u00d7 9)\/(3 + 8 + 4 + 6 + 9) = 104.466<\/p>\n

          Question 41.
          \nCalculate ‘P01<\/sub>‘ by simple average of price relative method, using Arithmetic Mean
          \n\"2nd
          \nAnswer:
          \nP = \\(\\frac{\\mathrm{P}_{1}}{\\mathrm{P}_{2}}\\) \u00d7 100 = [l 12.5,94.44,100,120]; \u03a3 P = 426.94;
          \n\u2234 P01<\/sub> = \\(\\frac{\\Sigma P}{n}\\) = 106.73<\/p>\n

          Question 42.
          \nFind V01<\/sub>, given \u03a3 p0<\/sub>q0<\/sub> = 382 and \u03a3 p1<\/sub>q1<\/sub>\u00a0= 424
          \nAnswer:
          \n\"2nd<\/p>\n

          Question 43.
          \nConstruct consumer price Index number from the following data.
          \n\"2nd
          \nAnswer:
          \nI01<\/sub> = \\(\\frac{\\Sigma p w}{\\Sigma w}\\) =\u00a0 [100 \u00d7 1 + 120 X 3 + 130 \u00d7 4 + 110 \u00d7 2]\/[1 + 3 + 4 + 2] = 1200\/10 = 120<\/p>\n

          Question 44.
          \nHow Laspeyre’s , Paasche’s and Dorbish Index numbers are related?.
          \nAnswer:
          \nArithmetic mean of Laspeyr’s and Paasche’s Index numbers
          \nD – B = \\(\\frac{\\mathrm{L}+\\mathrm{P}}{2}\\)<\/p>\n

          Question 45.
          \nWho are specific consumers considered in the construction of Index Number?
          \nAnswer:
          \nHere the specific class consumers means group of consumers who are having similar pattern of consumption. Generally those of factory workers, government employees, and the consumers who belonging to a particular community etc.<\/p>\n

          \"KSEEB<\/p>\n

          Question 46.
          \nWhat is meant by simple index number?
          \nAnswer:
          \nThe index number being constructed for a single item is a simple or Univar rate index number.<\/p>\n

          Question 47.
          \nWhat is meant by composite index number?
          \nAnswer:
          \nThe index number being constructed for group of items is a composite index number.<\/p>\n

          Question 48.
          \nMention the characteristics of index number.
          \nAnswer:
          \nIndex numbers:<\/p>\n

            \n
          • Are specialised averages.<\/li>\n
          • Are expressed in ratios but expressed in percentages.<\/li>\n
          • Study the effect of factors which cannot be measured directly.<\/li>\n
          • Facilitates comparision.<\/li>\n<\/ul>\n

            Question 49.
            \nWhat is meant by fixed base and chain base in index number?
            \nAnswer:
            \nIf the period of comparision is fixed for any current year, is called as fixed base year.
            \nIf the. period of comparision is immediate preceeding period for any current year, is called chain base year.<\/p>\n

            Question 50.
            \nWhat are quantity weights and value weights?
            \nAnswer:
            \nA quantity weight is the amount of commodity used or produced during a period.
            \nA value weight is the product of price and quantity used during a period.<\/p>\n

            Question 51.
            \nDefine base year and current year in index number.
            \nAnswer:
            \nThe year selected for comparision is the base year and the year for which comparisons are required is the current year.<\/p>\n

            Question 52.
            \nIf the general price level goes up by 80% between 2002 and 2012, What is the index number for 2012 with base 2000?
            \nAnswer:
            \nIndex number for the year 2012 = 180. .<\/p>\n

            Question 53.
            \nwhich averages are commonly used in the construction of index number?
            \nAnswer:
            \nSimple Arithmetic Means (x\u0304), weighted. An (x\u0304w<\/sub>) an<\/p>\n

            Question 54.
            \nIf total value in base year and current year are respectively 800, and 1000, compute value Index number.
            \nAnswer:
            \nValue I.NO. V01<\/sub> = \\(\\frac{\\Sigma p_{1} q_{1}}{\\Sigma p_{0} q_{0}}\\) \u00d7 100
            \n\\(\\frac{1000}{800}\\) \u00d7 1000 = 125<\/p>\n

            Question 55.
            \nWhat is the relation between Laspeyre\u2019s, Paasche\u2019s and Fishers Index numbers?
            \nAnswer:
            \n\\(\\sqrt{L \\times p}\\)<\/p>\n

            \"KSEEB<\/p>\n

            Question 56.
            \nGive the meaning of Base year.
            \nAnswer:
            \nThe year against which comparisions are made is called base year<\/p>\n

            Question 57.
            \nWhat is normal Base year?
            \nAnswer:
            \nNormal Base year is the year in which in that year there are no accidents \/ natural calamities occurred, which affect the business and economic activities.
            \n(OR)
            \nNormal base year is the year in which in that year there are no wars, floods, famine, tsunami, strikes etc.<\/p>\n

            Question 58.
            \nDefine price Index numbers.
            \nAnswer:
            \nPrice Index numbers indicates the general level of prices of articles over a period of time<\/p>\n

            Question 59.
            \nDefine value Index number.
            \nAnswer:
            \nValue Index number indicate the effect of combination of price and quantity changes in between the two periods.<\/p>\n

            Question 60.
            \nWhat test is satisfied by Marshall-Edge worth\u2019s Index number?
            \nAnswer:
            \nTimer reversal test..<\/p>\n

            Question 61.
            \nIf Index number in 2005 is 225 with base as 1995, what is the change in the Index?
            \nAnswer:
            \nThe percentage change is 125%.<\/p>\n

            Question 62.
            \nThe average price level of a commodity in the year 2000 is 2\\(\\frac{1}{2}\\) times of what it was in 1990. Express the change by means of Index number.
            \nAnswer:
            \nThe average price in 1990 is 100, so, the Index number in 2000 should be 100 \u00d7 2\\(\\frac{1}{2}\\) = 250.<\/p>\n

            Question 63.
            \nGive the formula for constructing weighted geometric niean price index number.
            \nAnswer:
            \nP01<\/sub> = Antilog{ \\(\\frac{\\sum w \\log p}{\\sum w}\\) } ,Where w is weight and \\(\\frac{P_{1}}{P_{0}}\\) \u00d7 100<\/p>\n

            Question 64.
            \nWrite the expression for Marshall-Edgeworth\u2019s Quantity Index Number.
            \nAnswer:
            \n\"2nd<\/p>\n

            Question 65.
            \nGiven \u03a3 p1<\/sub>q0<\/sub> =100 and \u03a3 p0<\/sub>q0<\/sub> =102 find a suitable index number.
            \nAnswer:
            \nLaspeyre\u2019s Price Index Number
            \nP01<\/sub> = \\(\\frac{\\sum p_{1} q_{0}}{\\sum p_{0} q_{0}}\\) \u00d7 100 = \\(\\frac{100}{102}\\) \u00d7 100 = 98.04 01<\/p>\n

            \"KSEEB<\/p>\n

            Question 66.
            \nDistinguish between weighted and unweighted \/ simple index numbers
            \nAnswer:
            \nIn weighted index numbers due weightage is given to different items in a relative way i.e., equal importance is not given to all items, where as in unweighted index numbers weights used are all uniform.<\/p>\n

            Question 67.
            \nFrom the following data, calculate simple aggregative index number.
            \n\"2nd
            \nAnswer:
            \nSimple Aggregative Index number p01<\/sub> – \\(\\frac{\\sum P_{1}}{\\sum P_{0}}\\) \u00d7 1000
            \nHere P0<\/sub> – Price in in 1990
            \nP1<\/sub>– Price in 2000
            \n\u03a3 p0<\/sub> = 70, \u03a3 p1<\/sub> = 76, p01<\/sub>= \\(\\frac{76}{70}\\) \u00d7 100 = 108.57.<\/p>\n

            \"KSEEB<\/p>\n

            Question 68.
            \nCalculate simple aggregate price index number for the following data.
            \n\"2nd
            \nAnswer:
            \nSimple aggregative price index number,
            \n\"2nd<\/p>\n

            Question 69.
            \nShow that Marshall – Edgeworth\u2019s Index number satisfies Time reversal lest.
            \nAnswer:
            \nMarshall-Edgeworth\u2019s Price Index number,
            \n\"2nd<\/p>\n

            Question 70.
            \nWhat are Simple and Weighted Index numbers ?
            \nAnswer:
            \nIn Simple (unweighted) price Index numbers, an average of price relatives are calculated using Arithmetic mean and Geometric mean.
            \n\"2nd
            \nIn Weighted price Index numbers appropriate weights are assigned to various items, and weighted average of price relatives are calculated using Arithmetic mean ad Geometric mean.
            \n\"2nd
            \nAnd Similarly, Simple and Weighted aggregative Index numbers are computed.<\/p>\n

            Question 71.
            \nCalculate cost of living index number from the following data.
            \n\"2nd
            \nAnswer:
            \nHere, Group index = price relatives = P \\(\\frac{\\mathrm{p}_{1}}{p_{0}} \\times 100\\) and weights – w are given so use Family
            \nBudget Method: Consumer price index number (CPI); CPI =\u00a0 \\(\\frac{\\sum p w}{\\sum w}\\)
            \n\"2nd<\/p>\n

            2nd PUC Statistics Index Numbers Five Marks Questions and Answers<\/h3>\n

            Question 1.
            \nMention the steps involved in the construction of Price Index Number? Explain in brief. (10 Marks)
            \nAnswer:
            \nFollowing are the steps\/stages\/principles\/Fleads. involved:-<\/p>\n

              \n
            1. Purpose and the scope<\/li>\n
            2. Selection of base period<\/li>\n
            3. Selection of commodities or items<\/li>\n
            4. Obtaining price quotations<\/li>\n
            5. Choice of an average<\/li>\n
            6. Selection of weights<\/li>\n
            7. Selection of suitable formula<\/li>\n<\/ol>\n

              1. Purpose and scope:-
              \nAt the very outset the purpose for which the index numbers is being constructed should be clearly defined. Since most of the latter problems will depend upon purpose, because the selection of items, base year, formulae will be different for different purposes. The purpose may be such as cost of living index number for urban areas, rural areas, factory workers etc. should be clearly defined.
              \nAlso, it is necessary to state the scope of the index numbers such as, geographical region, time, Income etc.<\/p>\n

              2. Selection of the Base year: –
              \nIndex numbers are always constructed with reference to some period called base period. The period may be a year, a month, week or a day.
              \nFollowing points are to be considered while selecting the base year.<\/p>\n

                \n
              • The base period selected should be Normal one, that is economically stable. It should be free from wars, floods, famine, booms, depressions, which affects the economic activities.<\/li>\n
              • Also the base year selected should not be too long or too short distance. Since economic activities are always dynamic.<\/li>\n
              • While selecting the base year, decision has to make whether fixed base or chain base year to be selected. In fixed base year, if the period of comparison is kept fixed for all current years, it is called fixed-base period. Where as in chain base year, comparison is made always with the previous year.<\/li>\n<\/ul>\n

                3. Selection of items: –
                \nItems means sample of representative commodities\/ items, required for day to day living, which are included in the construction of index number. According to the tastes, habits, customs and traditions etc., of working class people should be selected. It is also necessary to decide the grade or quality of items.<\/p>\n

                4. Obtaining price quotations: –
                \nAfter selecting the commodities\/ items, the next problem is to fix the prices for the items selected. Since prices vary from place to place, and even from shop to shop in the same market. Hence the suitable way is to obtain the prices ascertained by Marketing inspectors, Super Bazaars, Co-operative Societies or took out the average prices collected by various shops or places where concerned.<\/p>\n

                5. Choice of an average:-
                \nSince index numbers are specialised averages so, in the construction of index numbers, suitable average should be used. The choice is made between Arithmetic mean and Geometric mean. Usually Arithmetic mean with weighted averages is popularly applied, but when accuracy is required Geometric mean is suitable.<\/p>\n

                6. Selection of Weights:-
                \nWeight of the items means, the relative importance of an items used in the construction of index number. Since all items are not equally important in day-to-day usage. Proper weights should be attached to the various items depending on their relative importance, eg: Sugar-Rice, Atta-Salt etc. Mostly these weights are quantities in the base period or . those in the current period are considered. Sometimes a combination of quantities of different time periods may be used as weights.<\/p>\n

                7. Selection of formula:-
                \nA large number of formulae have been devised for construction of Index numbers. Hence a reasonable formula\/ method suitable to the object and the data available should be selected.<\/p>\n

                \"KSEEB<\/p>\n

                Question 2.
                \nWhat are the steps used in the construction of Consumer Price Index Number? Explain in brief. .
                \nAnswer:
                \nHere “Cost of living index number is the index number of the cost met by a specified class of consumers in buying a basket of goods and services.
                \nThe following are the main steps\/stages\/principlps\/points\/Heads involved in the construction of cost of living index numbers: –<\/p>\n

                  \n
                1. Object and scope.<\/li>\n
                2. Conducting family budget survey<\/li>\n
                3. Obtaining the price quotation.<\/li>\n
                4. Method of construction.<\/li>\n<\/ol>\n

                  1. Object and Scope:-
                  \nDecide the class of consumers for which index number is required. Such as whether index number is meant for government employees, bank employees, merchants, farmers, etc. also the geographical location, as that of locality, city or town, or a community of people who are having the similar consumption pattern should be decided.<\/p>\n

                  2. Conducting family budget survey:-
                  \nA sample survey regarding the average expenses of families on various items of consumption is conducted. In the survey, the information regarding commodities consumed by the families, their quality and the respective budget is collected. The items included are under the heads of (i) Food (ii) Clothing (iii) Fuel and lighting and (iv) Miscellaneous. Each of these can be divided into smaller groups, as food may be including Wheat, Rice, Dhal, etc., which are consumed by the people for whom index is meant.<\/p>\n

                  3. Obtaining Price Quotations:
                  \nWhile constructing the cost of living index number, retail prices of commodities\/ items are to be collected. The price lists are obtained from different agencies from different places. Then, they are averaged and these averages are used in the construction of index number. Here price lists of current period as well as base period should be collected.<\/p>\n

                  4. Methods of construction:\u00ac. There are two methods of construction of Consumer price Index Number<\/p>\n

                    \n
                  1. Aggregative Expenditure Method (AEM): In this method base year quantities are considered as weight, i.e. C.P.I = \\(\\frac{\\sum p_{1} q_{0}}{\\sum p_{0} q_{0}}\\) \u00d7 100<\/li>\n
                  2. Family Budget Method (FBM): In this method weighted AM of price relatives are used i.e CPI = \\(\\frac{\\sum p w}{\\sum w}\\) ;Where P = \\(\\frac{p_{1}}{p_{0}}\\) x 100; W = weight (p0<\/sub>q0<\/sub>)<\/li>\n<\/ol>\n

                    Question 3.
                    \nExplain Time Reversal Test and Factor Reversal Tests,
                    \nAnswer:
                    \nTime Reversal Test: (TRT) :
                    \nThis test requires that the index number computed backwards should be the reciprocal of the index number computed forward, except the factor 100.
                    \ni.e. P01<\/sub> = \\(\\frac{1}{\\mathrm{P}_{10}} \\) OR P01<\/sub> \u00d7 P10<\/sub> = 1 (Except the factor 100)<\/p>\n

                    Factor Reversal Test:- This test requires that the product of the Price Index number and the Quantity Index number should be equal to the net change in the value taking place between two periods, except the factor 100.
                    \ni.e. P01 <\/sub>\u00d7 Q01<\/sub> = \\(\\frac{\\sum p_{1} q_{1}}{\\sum p_{0} q_{0}}\\) = V01<\/sub>(Except the factor 100)<\/p>\n

                    Question 4.
                    \nFrom the following data calculate (i) unweighted Arithmetic mean index number (ii) unweighted geometric mean index number.
                    \n\"2nd
                    \nAnswer:
                    \nUnweighted Arithmetic mean index number : P01<\/sub> = \\(\\frac{\\sum P}{n}\\) ; p = price relatives = \\(\\frac{P_{1}}{P_{0}} \\times 100\\)
                    \nUnweighted Geometric mean index number : P01<\/sub> = Antilog \\(\\left\\{\\frac{\\sum \\log p}{n}\\right\\}\\)
                    \n\"2nd
                    \nUnweighted Arithmetic Index number : P01<\/sub> = \\(\\frac{931.39}{4}\\)= 232.85
                    \nUnweighted Geometric mean index number : P01<\/sub> = \\(\\left\\{\\frac{9.4093}{4}\\right\\}\\) = AL(2.3523] = 225.07<\/p>\n

                    Question 5.
                    \nCalculate price index numbers using un weighted aggregatives of prices method for the years 2012 and 2013 with base 2010 from the following data.
                    \n\"2nd
                    \nAnswer:
                    \nUn weightd aggregative price I.NO.
                    \n\"2nd
                    \nHere:
                    \nBase year price of 2010 – P0<\/sub>;
                    \nCurrent year price of 2012 – P1<\/sub>;
                    \nCurrent year price of 2013 – P2<\/sub>;<\/p>\n

                    P01<\/sub> (2012) = \\(\\frac{109}{93} \\) \u00d7 100 = 117.2043 ; P02<\/sub> (2013) = \\(\\frac{127}{93} \\) x 100 = 136.56.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 6.
                    \nCalculate weighted A.M and weighted and G.M. Index number from the following date.
                    \n\"2nd
                    \nAnswer:
                    \nWeighted AM. P.1.NO = \\(\\frac{\\Sigma p w}{\\Sigma w}\\)
                    \nWeighted GM. P.LNO = A.L \\(\\left\\{\\frac{\\Sigma w \\cdot \\log P}{\\Sigma w}\\right\\}\\)
                    \nWhere P = \\(\\frac{P_{1}}{P_{0}} \\times 100\\) – price relatives.
                    \nw – weights \/ Expenses.
                    \n\"2nd<\/p>\n

                    Question 7.
                    \nCompute suitable quantity index number from the following data.
                    \n\"2nd
                    \nAnswer:
                    \nHere base year price are given, use Last eyre\u2019s quantity index number.
                    \n\"2nd
                    \nQ10<\/sub>(L) = \\(\\frac{3810}{2990} \\) \u00d7 100 = 127.42<\/p>\n

                    Question 8.
                    \nCalculate Kelly\u2019s price index number for the following data.
                    \n\"2nd
                    \nAnswer:
                    \n\"2nd
                    \nP01<\/sub> = \\(\\frac{410}{303}\\) \u00d7 100 = 135.31<\/p>\n

                    Question 9.
                    \nCompute value index number for the year 2012 with respect to base year 2005
                    \n\"2nd
                    \nAnswer:
                    \nValue index number: V01<\/sub> = \\(\\frac{\\Sigma \\mathrm{V}_{0}}{\\Sigma \\mathrm{V}_{0}} \\times 100\\)
                    \nHere – V1<\/sub>, = P1<\/sub>q1<\/sub>; V0<\/sub> = p0<\/sub>q0<\/sub>
                    \n\"2nd
                    \nV01<\/sub> = \\(\\frac{436}{244}\\) \u00d7 100 = 178.7
                    \nComment: There is a net increase of transaction (money and quantity together) by 78.7% in the year 2012 as compared to 2005.<\/p>\n

                    Question 10.
                    \nCompute consumer price index number using aggregative expenditure method.
                    \n\"2nd
                    \nAnswer:
                    \nC.P.I: I01<\/sub>(A.E.M) = \\(\\frac{\\Sigma p_{1} q_{0}}{\\Sigma p_{0} q_{0}} \\times 100\\) ;
                    \nHere budget = p0<\/sub>q0<\/sub>
                    \n\"2nd
                    \n\u2234 I01<\/sub> = \\(\\frac{285}{204} \\times 100\\) = 139.71<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 11.
                    \nFrom the following data construct index fro 2002 taking 2000 as base , by the averange or relative method.
                    \n\"2nd
                    \nAnswer:
                    \nSimple A.M. of price relative Index number.
                    \nP01<\/sub>= \\(\\frac{\\sum p}{n}\\) \u00d7 100; P = price relative = \\(\\frac{P_{1}}{P_{0}} \\times 100\\)
                    \n\"2nd
                    \nP01<\/sub> = \\(\\frac{611.59}{5}\\) = 122.32<\/p>\n

                    Question 12.
                    \nConstruct price Index numbcrs from the following data by applying (a) Laspeyre\u2019s method. (b) Paaschcs method.
                    \n\"2nd
                    \nAnswer:
                    \n\"2nd<\/p>\n

                    Question 13.
                    \nCalculate Paasche’s quantity index number from the following data and give your conclusion.
                    \n\"2nd
                    \nAns.
                    \nPaasche’s Quantity Index number is- Q01<\/sub> = \\(\\frac{\\sum q_{1} p_{1}}{\\sum q_{o} p_{1}}\\) \u00d7 100
                    \n\"2nd
                    \nQ01<\/sub> = \\(\\frac{1260}{1120}\\) \u00d7 100 = 112.5
                    \nConclusion: \u2018[he quantity level in the current year is 112.5% of the quantity level in the base year.<\/p>\n

                    Question 14.
                    \nCalculate Consumer Price Index Number from the following data. Give your conclusion.
                    \n\"2nd
                    \nAnswer:
                    \nBase year quantity (q0<\/sub>) is given, use aggregate expenditure method
                    \nConsumer Price Index \\( \\frac{\\sum p_{1} q_{0}}{\\sum p_{0} q_{0}} \\times 100\\)
                    \n\"2nd
                    \nC.P.I. = \\(\\frac{4700}{3475}\\) x 100 = 135.257
                    \nNet increase of cost of living in the current year\u2019is 35.257% over the base year.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 15.
                    \nCompute Weighted Geometric Mean Index Number from the following data.
                    \n\"2nd
                    \nAnswer:
                    \nWeighted geometric mean index number:
                    \n\"2nd
                    \nwhere p = \\(\\frac{p_{1}}{p_{0}} \\times 100\\) and w = weight
                    \n\"2nd
                    \np = Anti log AL \\(\\left[\\frac{42.7451}{20}\\right]\\) = AL 2.1372 = 137.2<\/p>\n

                    Question 16.
                    \nFor the following data show that Fisher\u2019s Index Number satisfies Factor Reversal Test :
                    \n\"2nd
                    \nAnswer:
                    \nFactor Reversal Test = P01<\/sub> \u00d7 Q01<\/sub> = \\(\\frac{\\Sigma \\mathrm{P}_{1} \\mathrm{q}_{1}}{\\Sigma \\mathrm{P}_{0} \\mathrm{q}_{0}}\\) (V01<\/sub>) – (Except 100)
                    \n\"2nd
                    \nFor Fisher’s index number:
                    \nL.H.S: P01<\/sub> x Q01<\/sub>
                    \n\"2nd
                    \nFisher\u2019s Index number satisfies F.R.T.<\/p>\n

                    Question 17.
                    \nCompute cost of living Index number.
                    \n\"2nd
                    \nAnswer:
                    \nHere Weights are given, use Family budget method. C.P.I = \\(\\frac{\\sum P W}{\\sum W}\\) ; P = \\(\\frac{P_{1}}{P_{0}} \\times 100\\)
                    \n\"2nd
                    \nC.P.I = \\(\\frac{20294.5}{145}\\) = 139.96<\/p>\n

                    Question 18.
                    \nThe following figures relates to the prices and .quantities of certain commodities construct an appropriate Index number.
                    \n\"2nd
                    \nAns.
                    \n\"2nd
                    \n\"2nd<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 19.
                    \nConstruct the cost of living index number by aggregative expenditure method.
                    \n\"2nd
                    \nAnswer:
                    \nCost of living index number by Aggregate expenditure method ; CPI = \\(\\frac{\\sum p_{1} q_{0}}{\\sum p_{0} q_{0}} \\times 100\\)
                    \n\"2nd
                    \nCPI = \\(\\frac{1115.5}{1022}\\) \u00d7 100 = 109.15<\/p>\n

                    Question 20.
                    \nConstruct the cost of living index number for the year 2006.
                    \n\"2nd
                    \nCost of living index = \\(\\frac{\\sum p_{1} q_{0}}{\\sum p_{0} q_{0}} \\times 100\\) ; Here base year quantities are given.
                    \nSo use Aggregative expenditure method.
                    \n\"2nd
                    \nCost of living index = \\(\\frac{1089}{821} \\times 100\\) = 132.64<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 21.
                    \nCalculate the cost of living index number from the following data.
                    \n\"2nd
                    \nAnswer:
                    \nHere weights = w is given, are family budget method, CPI = \\(\\frac{\\sum p w}{\\sum w}\\)
                    \n\"2nd
                    \nCPI = \\(\\frac{12116.67}{100}\\) = 121.17<\/p>\n

                    Question 22.
                    \nCalculate cost of living index number by aggregative expenditure method:
                    \n\"2nd
                    \nAnswer:
                    \nAggregative expenditure method : C.P.I = \\(\\frac{\\sum p_{1} q_{0}}{\\sum p_{0} q_{0}}\\) x 100.
                    \nHere expenditure = P0<\/sub>q0<\/sub>.
                    \n\"2nd
                    \nCPI = \\(\\frac{979}{527} \\times 100\\) = 185.77<\/p>\n

                    Question 23.
                    \nFrom the following data, construct cost of living index number for the year 1998.
                    \n\"2nd
                    \nAnswer:
                    \nHere expense = weights – w : Cost of living index by family budget method.
                    \n\"2nd<\/p>\n

                    Question 24.
                    \nCompute cost of living Index Number:
                    \n\"2nd
                    \nAnswer:
                    \nLet P and P2<\/sub> be the group index for the year 1990 and 1995 and w-be the weights. Using family budget method:
                    \nCPI (1990) \\(\\frac{13195}{120}\\) = 109.96
                    \nCPI (1995) \\(\\frac{14065}{120}\\) = 117.21<\/p>\n

                    2nd PUC Statistics Index Numbers Ten Marks Questions and Answers<\/h3>\n

                    Question 1.
                    \nCompute Marshall-Edgeworth\u2019s and Dorbish Bowley\u2019s price Index numbers for the following data.
                    \nAnswer:
                    \nCompution of Marshall-Edgeworth\u2019s and Dorbish-Bowley\u2019s numbers:
                    \n\"2nd
                    \n\"2nd
                    \n\"2nd<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 2.
                    \nFrom the data given below construct an Index number of the group of four commodities by using Fisher\u2019s Ideal formula.
                    \n\"2nd
                    \nAnswer:
                    \nFisher’s Index number
                    \n\"2nd
                    \nHere Expenditure = p0<\/sub>q0<\/sub> or p1<\/sub>q1<\/sub>
                    \n\"2nd<\/p>\n

                    Question 3.
                    \nCompute Fisher\u2019s Ideal price and Quantity index numbers for the current year using the following data
                    \n\"2nd
                    \nAnswer:
                    \nComputation of Fisher\u2019s price and quantity index numbers,
                    \n\"2nd<\/p>\n

                    Question 4.
                    \nCalculate Fisher\u2019s Ideal Index number for the following data. Verify that it satisfies time reversal test and factor reversal test.
                    \n\"2nd
                    \nAnswer:
                    \n\"2nd
                    \n\"2nd
                    \nHence Fishers index number satisfies both time reversal test and factor reversal test.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 5.
                    \nCompute \u2018Laspeyre\u2019s, Paasches\u2019, Marshall – Edgeworth\u2019s and Fishers quantity Index numbers from the following data.
                    \nAnswer:
                    \n\"2nd
                    \nLaspeyre’s:
                    \n\"2nd
                    \n\"2nd<\/p>\n

                    Question 6.
                    \nFrom the following data compute
                    \n(i) Fisher\u2019s Price Index number
                    \n(ii) Marshall-Edgeworth\u2019s Price Index number. Also show that Fisher\u2019s Price Index number satisfies TRT.
                    \n\"2nd
                    \nAnswer:
                    \nFisher\u2019s Price Index number
                    \n\"2nd
                    \nMarshall-Edgeworth\u2019s Price Index number
                    \n\"2nd
                    \nT.R.T = P01<\/sub> \u00d7 P10<\/sub> = 1 (Expect the factor 100)
                    \n\"2nd
                    \nFor Fisher\u2019s: T.R.T : P01<\/sub> \u00d7 P10<\/sub> = 1 Expect 100.
                    \n\"2nd<\/p>\n","protected":false},"excerpt":{"rendered":"

                    You can Download Chapter 2 Index Numbers Questions and Answers, Notes, 2nd PUC Statistics Question Bank with Answers\u00a0Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations. Karnataka 2nd PUC Statistics Question Bank Chapter 2 Index Numbers 2nd PUC Statistics Index Numbers One and Two Marks Questions and …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/13047"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=13047"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/13047\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=13047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=13047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=13047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}