{"id":13228,"date":"2019-12-18T17:56:52","date_gmt":"2019-12-18T12:26:52","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=13228"},"modified":"2021-07-02T15:35:55","modified_gmt":"2021-07-02T10:05:55","slug":"2nd-puc-statistics-question-bank-chapter-3","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-statistics-question-bank-chapter-3\/","title":{"rendered":"2nd PUC Statistics Question Bank Chapter 3 Time Series"},"content":{"rendered":"

You can Download Chapter 3 Time Series 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 3 Time Series<\/h2>\n

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

Question 1.
\nDefine time series\/what is time-series? Give an example
\nAnswer:<\/p>\n

    \n
  • A set of figures relating to a variable according to a time is called Time series OR chronological arrangements of the statistical data is called Time series<\/li>\n
  • Production of a firm arranged from the year 2000 to 2008, Sales statistics of a certain article for the year 1998 to 2005.<\/li>\n<\/ul>\n

    Question 2.
    \nWhat do you meant by trend?
    \nAnswer:
    \nTrend is the overall change taking place in the series of the data over a given period.<\/p>\n

    Question 3.
    \nWhat do you mean by Secular trend \/ Seasonal variation \/ cyclical variation \/ Irregular variations?
    \nAnswer:<\/p>\n

      \n
    • Secular trend\/Trend refers to the tendency of the variable to increase, decrease, or remain steady over a given period.<\/li>\n
    • Seasonal variations refer to the variations caused annually by the seasons of the year. Also includes the variations of any kind which are periodic in nature and whose period is shorter than one year. ( t < 1 year)<\/li>\n
    • Cyclical variations are fluctuations spread over a period of more than one year. Most of the Time series relating to Economics and Business show some kind of cyclical variations. Cyclical variation is an oscillatory variation, which occurs in four stages, such as (1) Prosperity (2) Decline (3) Depression and (4) Improvement.<\/li>\n
    • Irregular \/ Erratic variations are those changes of time series, which are irregular in nature and do not show any pattern. The causes of irregular variations are due to accidental happenings such as wars, earth quacks, floods, famine, fire, strikes, etc.,<\/li>\n<\/ul>\n

      Question 4.
      \nGive a difference between ‘cyclical’ and irregular variations in a time series.
      \nAnswer:<\/p>\n

        \n
      • Secular trend\/Trend refers to the tendency of the variable to increase, decrease, or remain steady over a given period.<\/li>\n
      • Seasonal variations refer to the variations caused annually by the seasons of the year. Also includes the variations of any kind which are periodic in nature and whose period is shorter than one year. ( t < 1 year)<\/li>\n
      • Cyclical variations are fluctuations spread over a period of more than one year. Most of the Time series relating to Economics and Business show some kind of cyclical variations. Cyclical variation is an oscillatory variation, which occurs in four stages, such as (1) Prosperity (2) Decline (3) Depression and (4) Improvement.<\/li>\n
      • Irregular \/ Erratic variations are those changes of time series, which are irregular in nature and do not show any pattern. The causes of irregular variations are due to accidental happenings such as wars, earth quacks, floods, famine, fire, strikes, etc.,<\/li>\n<\/ul>\n

        Question 5.
        \nGive an example for seasonal variation.
        \nAnswer:
        \nMore sales of woolen clothes in winter season or there is more sales of Ice creams and cool drinks in summer season.<\/p>\n

        Question 6.
        \nGive an example for upward trend in time series.
        \nAnswer:
        \nPrices of petroleum products\/Population of India.<\/p>\n

        \"KSEEB<\/p>\n

        Question 7.
        \nMention the factors causing seasonal variation
        \nAnswer:
        \nClimatic and whether conditions are responsible for the seasonal variation<\/p>\n

        Question 8.
        \nWhat are the stages\/Phases of a cyclical trend\/Business cycle?
        \nAnswer:
        \n(1) Prosperity (2) Decline (3) Depression and (4) Improvement.<\/p>\n

        Question 9.
        \nWhich components of time series are applicable in case of
        \nAnswer:<\/p>\n

          \n
        1. Fire accident in a factory<\/li>\n
        2. Increase of woolen goods during winter<\/li>\n
        3. Fall in the death rate due to advances in Science<\/li>\n
        4. An era of Prosperity<\/li>\n
        5. An increase in employment during harvest season.
          \n– (1) Random, (2) Seasonal, (3) Secular, (4) Cyclical variations (5) Seasonal variation<\/li>\n<\/ol>\n

          Question 10.
          \nWith which components of a time series would you mainly associated each of the following?
          \n(a) Increase in money in circulation for the last 10 years
          \n(b) Rain fall in Bangalore that occurred for a week in December 2007.
          \nAnswer:
          \n(a) Secular trend
          \n(b) Irregular variations<\/p>\n

          Question 11.
          \nMention the type of component (T-S) seen in the following :
          \n“Increase in the number of deaths of piligrims due to floods and landslides in the Uttarkhand recently”
          \nAnswer:
          \nIrregular variations<\/p>\n

          Question 12.
          \nWhat is the name given to the line, which is obtained under method of least squares?
          \nAnswer:
          \nLinear\/Straight line trend\/line<\/p>\n

          Question 13.
          \nWhat is a Historigram? \/Name the graph of time series.
          \nAnswer:
          \nThe graph of time series is called Historigram.<\/p>\n

          Question 14.
          \nGive any two uses of Analysis of Time Series.
          \nAnswer:
          \nAnalysis of Time series helps to understand the past behavior of the data \/ to predict the future trend.<\/p>\n

          Question 15.
          \nWhat is the duration of seasonal variation?
          \nAnswer:
          \nWithin one year (t < 1 year)<\/p>\n

          Question 16.
          \nMention the conditions to be followed in the method of least squares. \/Principles of Method of least squares.
          \nAnswer:
          \nThe sum of the deviations obtained from the actual and trend values is Zero ie. \u03a3(Y – Y\u0304)=0 and The sum of the squares of the deviations obtained from the actual and trend values is least.
          \ni.e., \u03a3(Y – Y\u0304)2<\/sup> is least<\/p>\n

          Question 17.
          \nWhat do you mean by moving averages?
          \nAnswer:
          \nMoving averages are the averages obtained by finding the arithmetic means of successive values of the time series by taking say 3\/4\/5 years at a time by leaving the first and adding the next; this is to eliminate short-term variations\/fluctuations that are present in the time series.<\/p>\n

          Question 18.
          \nWrite any merit and demerit of moving average methods.
          \nAnswer:
          \nThe merit is it is simple and easy;
          \nDemerit is that, not all trend values can be obtained by this method<\/p>\n

          \"KSEEB<\/p>\n

          Question 19.
          \nMention a merit and demerit of least square method
          \nAnswer:
          \nIt can be used for predicting future trend\/Trend values can be obtained for all time points.<\/p>\n

          Question 20.
          \nWrite down the equation for method of least square with the Normal equations.
          \nAnswer:
          \n* The equation is y = a + bx; Normal equations are
          \nna + b\u03a3x = \u03a3y;
          \na\u03a3x + b\u03a3x2<\/sup> = \u03a3xy
          \n* Quadratic\/second degree equation\/parabolic trend equation is:
          \ny = a + bx + cx2<\/sup> : Normal equations are: na + b\u03a3x + c\u03a3x2<\/sup> = \u03a3y;
          \na\u03a3x + b\u03a3x2<\/sup> + c\u03a3 = \u03a3xy ; a\u03a3x2<\/sup> + b\u03a3x3<\/sup> + c\u03a3x4<\/sup> = \u03a3x2<\/sup>y.<\/p>\n

          Question 21.
          \nMention any one of use of analysis of time series.
          \nAnswer:
          \nAnalytical study of the time series will helps to predict \/ plan for future.<\/p>\n

          Question 22.
          \nName the methods of measurement of trend in time series.
          \nAnswer:<\/p>\n

            \n
          1. Method of moving averages and<\/li>\n
          2. Method of least squares.<\/li>\n<\/ol>\n

            Question 23.
            \nWhat do you mean by secular trend?
            \nAnswer:
            \nThe term secular trend refer to the tendency of a variable to increase or decrease or to remain constant over a period of time.<\/p>\n

            Question 24.
            \nGive an example of cyclical variation in a time series.
            \nAnswer:
            \nExamples of Business and Economics such as price, sales, production etc.<\/p>\n

            Question 25.
            \nWrite the equation of parabolic trend in measuring the trend.
            \nAnswer:
            \nThe second degree\/parabolic trend\/ equation is y = a + bx + cx2<\/sup><\/p>\n

            Question 26.
            \nWhich component of the time series is associated with deaths due to tsunami?
            \nAnswer:
            \nIrregular\/random variation.<\/p>\n

            Question 27.
            \nWhich component of Time series is observed in \u2018Increase in passengers in train during April and May\u2019?
            \nAnswer:
            \nSeasonal Variation.<\/p>\n

            Question 28.
            \nWhat is time series? Give an example.
            \nAnswer:
            \nChronological arrangement of statistical data is called time series.
            \nEg: Arrangement of population of India from 1941-2001
            \n\"2nd<\/p>\n

            Question 29.
            \nMention the components of time series.
            \nAnswer:
            \nThe components of time series are:<\/p>\n

              \n
            1. Secular trend.<\/li>\n
            2. Seasonal trend.<\/li>\n
            3. Cyclical trend.<\/li>\n
            4. Irregular \/ Random Variations.<\/li>\n<\/ol>\n

              Question 30.
              \nWhat do you mean by moving average method?
              \nAnswer:
              \nThe method of moving average is a simple arithmetic mean calculated successively by taking some specified number of values at a time (m) say 3, 4, or 5 years. The aim of averaging is to remove short term variations in the time series.<\/p>\n

              Question 31.
              \nWhat do you mean by method of least squares?
              \nAnswer:
              \nIn this method a mathematical relation is developed between the time (x) and the values (y). The relation may be used to fit (a) Linear\/straight line trend (6) Quadratic trend (c) Exponential trend. Such that \u201cthe sum of the squares of the deviations obtained from actual and trend vales is least\u201d.
              \nAnd these relations are used for computing the trend values in the time series.<\/p>\n

              Question 32.
              \nName two methods of measuring secular trend in time series.
              \nAnswer:<\/p>\n

                \n
              • Method of moving averages.<\/li>\n
              • Method of least squares.<\/li>\n<\/ul>\n

                \"KSEEB<\/p>\n

                Question 33.
                \nWhich component of time series are applicable in case of
                \n(a) Fire accident in a factory
                \n(b) Increase of woollen goods during winter
                \n(c) Fall in the death rate due to advances in science
                \n(d) An era of prosperity.
                \nAnswer:
                \n(a) Random \/ irregular
                \n(b) seasonal,
                \n(c) secular and
                \n(d) cyclical variations.<\/p>\n

                Question 34.
                \nLet y = a+bx, if a = 25, b = 3.5 findy when x = 4.
                \nAnswer:
                \nBy substituting a = 25, b = 3.5 and x = 4.
                \nwe get y = 15 + 3.5 (4) = 25 + 14 = 39.<\/p>\n

                Question 35.
                \nIn the analysis of time series the fitted Linear trend equation is y = 75.3 – 2.75x estimate trend value when x = 5.
                \nAnswer:
                \nBy substituting the value of x = 5 in the equation.
                \nWe get y = 75.3 – 2.75 (5) = 75.3 – 13.75
                \n\u2234 y = 61.55.<\/p>\n

                Question 36.
                \nWhich index is used for the measurement of seasonable variation?
                \nAnswer:
                \nSeasonal Indices are used for the measurement of seasonal variation.<\/p>\n

                Question 37.
                \nWhich variation is un predrestable and which variation is prediatable?
                \nAnswer:
                \nIrregular variations are unprediatable and secular and seasonal variations are predretable.<\/p>\n

                Question 38.
                \nDiagrammatically represent ‘Business cycle’ with stages.
                \nAnswer:
                \n\"2nd<\/p>\n

                Question 39.
                \nWhat is graphical \/ pree – hand method of measurement of trend?
                \nAnswer:
                \nIn this method the actual values are plotted on a graph and smoth line or curve is drawn.
                \nAgain a line or curve is drawn a long the actual line which covers majority of the points according to personal judgment. This line is called line of best fit, is the trend line.<\/p>\n

                Question 40.
                \nWhat is semi-average method of measurement of trend?
                \nAnswer:
                \nThe original values of time series are divided in to two equal parts (if odd number ignoring the middle value) and averages are calculated both the parts, are called semi averages the two points and extending the line which gives the trend of the time series.
                \nActual values are plotted on a graph which is a history gram and by plotting the semi-averages on a graph joining the two points and extending the line which gives the trend of the time series.<\/p>\n

                \"KSEEB<\/p>\n

                2nd PUC Statistics Time Series Five Marks Questions and Answers<\/h3>\n

                Question 1.
                \nMention and explain the components of time series in brief.
                \nAnswer:
                \nThe components\/variations of time series are :<\/p>\n

                  \n
                1. Secular trend<\/li>\n
                2. Seasonal trend .<\/li>\n
                3. Cyclical variations<\/li>\n
                4. Irregular\/ Random variations.<\/li>\n<\/ol>\n

                  (1) Secular trend: – ‘The term secular trend\/ ‘Trend’ refers to the tendency of the variable to Increase or decrease or to remain steady over a period of time’, e.g. The values of population, prices, sales, literacy etc. are all increasing. As against the death rate, illiteracy, travel by bullock carts is decreasing. The rise or fall may be steep or gradual. But they show increasing trend, if we observe over a sufficiently long period of time.(Here the time ‘t\u2019 > lyear)<\/p>\n

                  (2) Seasonal trend: – The term seasonal variations basically refer to the variations caused annually by the seasons of the year. But also includes the variations of any kind which are periodic in nature and whose period is shorter than one year (Here the time’t’ Ex:-<\/p>\n

                    \n
                  • Sales of cool drinks, ice creams are more in the summer season<\/li>\n
                  • Sale of stationery will be more in June, July.<\/li>\n
                  • The business commercial Bank may reach a peak around the first week of every month.<\/li>\n
                  • Sales of coconuts are always high on Saturday etc.<\/li>\n<\/ul>\n

                    Hence a clever Businessman will arrange for the production or to maintain stock accordingly to the needs of the season and will earn maximum profit.<\/p>\n

                    (3) Cyclical Variations:- Cyclical variations are the fluctuations spread over a period of more than one year. (Here time ‘t'< lyear). Most of the Time series relating to Economics and Business show some kind of cyclical variations.<\/p>\n

                    Hence ‘cyclical variation is an oscillatory variation which occurs in four stages, such as (1) Prosperity (2) Decline\/Recession (3) Depression and (4) Improvement\/Recovery<\/p>\n

                    The business cycle is:-
                    \n\"2nd
                    \nIn Prosperity, the curve increases, the business is in boom, the transaction are much more than expected. After reaching the peak of activities the business declines, the curve slopes down. This is called the period of Decline, in Depression the business activities are at the lowest. Then follows a period of improvement in activities and the curve again starts to rise. In this manner the cycle repeats. The interval of time from one prosperity to the other is called the period of cycle. (Here the time ‘t ‘> OR < 1 year) .<\/p>\n

                    (4) Irregular or Random variations: – Irregular variations are those changes of time series which are irregular in nature and do not show any pattern. The causes of irregular variations are due to accidental happenings such as wars, earth quacks, floods, famine, fire, strikes, etc. These factors are unpredictable. Generally such variations last for a short period.<\/p>\n

                    Question 2.
                    \nFor the following time series calculate the trend by the method of 3 yearly moving averages.
                    \n\"2nd
                    \nAnswer:
                    \n\"2nd
                    \nIn 3 yearly moving averange there are no trend values in 1st and last time points
                    \nHere \u0177 – trend values.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 3.
                    \nFit a trend line to the following data by graphical method.
                    \n\"2nd
                    \nAnswer:
                    \n\"2nd<\/p>\n

                    Question 4.
                    \nDraw a trend line by th\u00e7 method of semi-averages for the following time series.
                    \n\"2nd
                    \nAnswer:
                    \n\"2nd
                    \nCompute averages for the first half and second half values, are the semi-averages
                    \nactual and semi-averages on a graph to trend line
                    \nGraph of time series.
                    \n\"2nd<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 5.
                    \nFor the following time series, calculate the trend by the method of 3 yearly moving averages. Show a trend on agraph.
                    \n\"2nd
                    \n\"2nd<\/p>\n

                    Answer:
                    \nComputation of 3 yearly moving averages.
                    \nLet x and y be the year and values of the time series.
                    \n\"2nd
                    \n\"2nd
                    \nFrom the graph the time series shows decreasing tendency.<\/p>\n

                    Question 6.
                    \nFor the following time series, calculate the trend by the method of 3 yearly moving averages. Plot the trend values on a graph.
                    \n\"2nd
                    \nAnswer:
                    \nCalculation of trend values by 3 yearly moving averages. (Let x and y be the year and values.)
                    \n\"2nd
                    \n\"2nd<\/p>\n

                    Question 7.
                    \nCalculate the trend values by finding three yearly moving averages.
                    \n\"2nd
                    \nAnswer:
                    \nLet X and Y be the year and sales. Here the period of moving average \u2018m\u2019 = 3
                    \n\"2nd<\/p>\n

                    Question 8.
                    \nFor the following time series, conipute the trend by five yearly moving averages.
                    \n\"2nd
                    \nAnswer:
                    \nComputation of 5 yearly moving averages. Let x and y be the year and values.
                    \n\"2nd
                    \nThere are no trend values for the first 2 times points and last 2 times point.
                    \n(\u0177) {5 yearly moving average} trend values.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 9.
                    \nFor the following time series, compute the trend values by the method of five yearly moving averages.
                    \n\"2nd
                    \nAnswer:
                    \nLet x and y be the year and Index of the time series.
                    \n\"2nd<\/p>\n

                    Question 10.
                    \nFor the following time series, compute the trend by 5 yearly moving averages.
                    \n\"2nd
                    \nAnswer:
                    \nComputation of trend values by the method of 5 yearly moving averages.
                    \nLet x and y be the year and values.
                    \n\"2nd<\/p>\n

                    Question 11.
                    \nObtain the trend values for the following time series by the method of four yearly centered moving averages.
                    \n\"2nd
                    \nComputation o \u2018 4 year y centered moving average. Let x and y be the year and values.
                    \nHere there are no trend values for the first 2 time points and last 2 time points.
                    \n\"2nd<\/p>\n

                    Question 12.
                    \nObtain the trend values for the fo centered averages.
                    \n\"2nd
                    \nAnswer:
                    \nCalculation of trend by 4 yearly moving averages. Let x and y be the year and values.
                    \n\"2nd
                    \nFrom above, the time series shows a decreasing tendency.<\/p>\n

                    Question 13.
                    \nPopulation figures of a city (in Lakhs) are as given below. Fit a exponential curve of the type y = abx and estimate the pupulation for the year 213.
                    \n\"2nd
                    \nAnswer:
                    \nThe exponential. Logarithmetic equation isy = abx<\/sup> taking lagarithm on both side logy – log at x. log b.
                    \nThe normal equations are:-
                    \nn log a + log b . \u03a3x = \u03a3 log y (1) log a lx + log b . \u03a3x2 = \u03a3x logy \u2014>(2)
                    \nuse deviation method and \u03a3x = 0
                    \nlet x and y be the year and population.
                    \n\"2nd
                    \nFrom (1) since \u03a3x = 0:
                    \n\"2nd
                    \nloga =1.0076
                    \na = Antilog (1.0076)= 10.1765.
                    \n\"2nd
                    \nlog b = 0.08684
                    \nb = A.L(0.0868) = 1.2212
                    \nThe exponential trend equation is:-
                    \ny = abx<\/sup>
                    \n\u0177 = 10,1765(1.2212)x<\/sup>
                    \n\u0177(2013)= 10.1-765 (1-.2212)4<\/sup>
                    \nHere x = 4 for the projected value for 2013
                    \n\u0177(2013) = 10.1765(2.2240) = 22.63 Lakhs.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 14.
                    \nThe production of wheat in Punjab in metric tons in a certain locality are given below. Fit a logarithmetic trend of the type y = abx and estimate the production for the year 2006.
                    \n\"2nd
                    \nAnswer:
                    \nThe exponential \/ logarithmic equation is
                    \ny = abx<\/sup> by taking logarithms
                    \nWe get log y = log a + x log b
                    \nThe normal equations are:-
                    \nn log a + log b \u03a3x = \u03a3 logy \u2014> (1)
                    \nlog a \u03a3x + log b . \u03a3x2<\/sup> = \u03a3x log y -\u00bb (2)
                    \nUsing deviation method \u03a3x = 0
                    \nLet x and y be the year and production of wheat.
                    \n\"2nd
                    \nFrom equation (1); since Sx = 0
                    \n\"2nd
                    \nSimilarly from (2)
                    \n\"2nd
                    \nThe fitted legarithmic \/ Exponential trend equation is; logy = log a + x log b.
                    \ni.e., logy= 1.0725 + x(0.0093)
                    \nEstimation for the year 2006; x = 6
                    \nlogy = 1.0725 + 0.0093(6)
                    \n= 1.0725 + 0
                    \nlogy =1.0725
                    \nand y = Anti log (log y)
                    \n= A.L (1.0725)
                    \ny = 11.82 metric tons.<\/p>\n

                    Question 15.
                    \nThe sales statistics of a certain company for the years 2005 2011 are given below:
                    \n\"2nd
                    \nAnswer:
                    \nLet x and y be the year and sdes.
                    \nthe equation is : y = abx<\/sup>
                    \nlogarithmic term: log y = log y = log a + x log b
                    \nThe normal equations are:
                    \nn log a + log b \u03a3x = \u03a3 log y -> (1)
                    \nlog a . \u03a3x + log b . \u03a3x2<\/sup> = lx . log y \u2014> (2)
                    \n\"2nd
                    \nFrom equation (1) since Ex = 0
                    \n\"2nd
                    \nloga= 1.9136 a = AL(1.9136) = 81.9596
                    \n\"2nd
                    \nlog b = 0.1483 b = AL (0.1483) = 1.407
                    \nThe fitted exponential equation is:-
                    \ny = abx<\/sup>
                    \n\u0177 = 81.9596(l.407)x<\/sup>
                    \nEstimation for the year 2012; x = 4
                    \n\u0177(2012)= 81.9596(1.407)4<\/sup>
                    \n= 81.9596 x 3.919 = 321.199 units.<\/p>\n

                    Question 16.
                    \nFor the given time series, fit a straight line trend of the type y = a + bx by the method of least squares.
                    \n\"2nd
                    \nAnswer:
                    \nLet x and y be the year and production.
                    \nThe straight line equations y = a+bx
                    \nNormal equations are.
                    \nna + b \u03a3x = \u03a3 y ……..(1)
                    \na \u03a3x + b \u03a3x2<\/sup> = \u03a3xy……..(2)
                    \nHere x = X – x\u0304( odd time points)
                    \nx\u0304 = 1996
                    \n\"2nd
                    \nFrom (1) 5a + b. 0 = 289
                    \n\u2234 a = \\frac{289}{5} = 57.8
                    \nFrom (2) a.0 + b.10 = 35
                    \n\u2234b = \\frac{35}{10} = 3.5
                    \nHence the fitted straight line trend equation is \u0177 = 57.8 + 3.5x<\/sup>
                    \nNote: The trend values for the givjgn years can be obtained by substituting the values of x as -2, -1, 0, 1, 2 if n is odd and -5, -3, -1, 1, 3, 5 if n is even.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 17.
                    \nFit an equation of the type y = a + bx to the following Time-series data.
                    \n\"2nd
                    \nAnswer:
                    \nThe straight line equation is y = a + bx
                    \nThe normal equations are na + b \u03a3x = \u03a3y
                    \na \u03a3x+b \u03a3x2<\/sup>= \u03a3 xy
                    \nHere n = 8, even,
                    \ntake x=2 (x- x\u0304); x\u0304 = 2001.5
                    \nLet X be the year and Y be the imports.
                    \n\"2nd
                    \nThe fitted straight line equation is : \u0177 = 30.875 -0.375x<\/p>\n

                    Question 18.
                    \nCompute 4 yearly moving averages for the following data :
                    \n\"2nd
                    \nAnswer:
                    \nLet X and Y be the years and values
                    \n\"2nd<\/p>\n

                    2nd PUC Statistics Time Series One and Ten Marks Questions and Answers<\/h3>\n

                    Question 1.
                    \nFit a straight line to the following time series, show the trend line on a graph
                    \n\"2nd
                    \nAnswer:
                    \nLet x and y be the year and values The Straight line equation is
                    \ny = a + bx
                    \nNormal equations are –
                    \nna + b\u03a3x = \u03a3y ………… (1)
                    \na\u03a3x + b\u03a3x2<\/sup> = \u03a3xy ………….(2)
                    \nHere x\u0304 = 1992
                    \n\"2nd
                    \nFrom (1) 7a + b.O = 3106
                    \n\u2234 a = 443.71
                    \nFrom (2) a.O + b.28 = 2045
                    \n\u2234 b= 73.04
                    \n\u2234 The fitted straight line trend equation is
                    \n\u0177 = 443.71 + 73.04x
                    \nTrend value (\u0177) for 1989; Here x = -3
                    \n\u2234 \u0177 1989<\/sub> = 443.71 + 73.04 (-3) = 443.71 – 219.12
                    \n\u0177 89<\/sub> = 224.50
                    \nTrend value for 1990 ; Here x = -2
                    \n\u0177 90<\/sub> = 443.71 + 73.04(-2) = 297.63
                    \nSimilarly all remaining trend values can be obtained by substituting x= -1,0,1,2 and 3 Straight line trend:
                    \n\"2nd<\/p>\n

                    Question 2.
                    \nFor the given time series, fit a straight line trend of the type y = a + bx by the method of least squares and find the trend value for the year 1995.
                    \n\"2nd
                    \nAnswer:
                    \nX Here X=2(x-x) \\n = 6 X = 1990.5
                    \n\"2nd
                    \nFrom (1) 6a + b.0 = 620 \u2234 a = 103.33
                    \nFrom (2) a.O + b.70 = 302 \u2234 b = 4.31
                    \nThe fitted straight line trend equation is.
                    \n\u0177 = 103.33 + 0.057x
                    \nEstimation of production for the year 1995
                    \nHere x = 9
                    \n\u01771995<\/sub> = 103.33 + 4.31(9)= 142.09.<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 3.
                    \nFor the following time series fit a curve of the type y = a + bjc + cx2. Estimate the value for 1997.
                    \n\"2nd
                    \nAnswer:
                    \nThe quadratic equation is:
                    \ny = a + bx + cx2<\/sup>
                    \nThe normal equations are
                    \nna + b\u03a3x + c\u03a3x2<\/sup> = \u03a3y ………..(1)
                    \na\u03a3x + b\u03a32<\/sup>+c\u03a3x3<\/sup> = \u03a3xy………..(2)
                    \na\u03a3x2<\/sup> + b\u03a33<\/sup>+c\u03a3x4<\/sup> = \u03a3x2<\/sup>y………..(3)
                    \nHere x = X – X\u0304
                    \nLet x and y be the year and the value
                    \n\"2nd
                    \nFrom (1) 7a + b.0 + c.28 = 261
                    \n7a + 28c = 261 ………….. (4)
                    \nFrom (2) a.0 + b.28 + c.0 = 310
                    \nb= 11.07
                    \nFrom (3) a.28 + b.0 + c.196 = 1216
                    \n28a + 196c = 1216 ………….(5)
                    \nSolving (4) and (5) we get a and c
                    \n4 x (4) – (5)
                    \n\"2nd
                    \n\u2234 c = 2.05
                    \nPut c = 2.05 in (4) we get
                    \n7a + 28(2.05) = 261
                    \n7a = 261 – 57.4
                    \n\u2234 a = 29.09
                    \nThe trend equation is: \u0177 = 29.09 +13.57x+2.05x2<\/sup>
                    \nEstimation for the trend value for 1997
                    \nHere x = 4 ; x2<\/sup> = 16
                    \n\u01771997<\/sub> = 29.09 +11.07 (4) + 2.05(16)
                    \n\u01771997<\/sub> = 106.17.<\/p>\n

                    Question 4.
                    \nFit a quadratic trend of the form y = a + bx + cx2<\/sup> to the following time series.
                    \n\"2nd
                    \nEstimate the probable number of merited students in the college in the year 1995.
                    \nAnswer:
                    \nThe Quadratic equation is y = a + bx + cx2<\/sup>
                    \nThe normal equations are – na + b\u03a3x + c\u03a3x2<\/sup> = \u03a3y
                    \na\u03a3x + b\u03a3x2<\/sup> + c\u03a3x3<\/sup> = \u03a3xy
                    \na\u03a3x2<\/sup> + b\u03a3x3<\/sup> + c\u03a3x4<\/sup> = \u03a3x2<\/sup> y
                    \nLet x and y be the year and no. of merited students X\u0304 = 1992
                    \n\"2nd
                    \nFrom (1) 5a + B.0 + c.10 =40
                    \ni.e. 5a + 10c = 40 (4)
                    \nFrom (2) a.0 + B.10 + c.0 = -1
                    \n\u2234 b = – 0.1
                    \nFrom (3) a.l0 + B.0 + c.34 = 95
                    \ni.e. 10a + 34c = 95………….(5)
                    \nSolving (4) and (5) we get a and c ;(4) x 2 – (5)
                    \n\"2nd
                    \n\u2234c = 1.07
                    \nSubstituting c = 1.07 in (4)
                    \nwe get 5a+10(i.07) = 40
                    \n\u2234 a = 0.17
                    \nThe fitted quadratic trend equation is
                    \ny\u0304 = 0.17 – 0.1x + 1.07x2<\/sup>
                    \nEstimation for 1995 Here x = 3, x2<\/sup> = 9
                    \ny\u030495<\/sub> =0.17 \u2014 0.1(3) +1.07(9)
                    \n\u2234 y\u030495<\/sub> = 9.5<\/p>\n

                    \"KSEEB<\/p>\n

                    Question 5.
                    \nFit a quadratic trend for the following time series. Estimate the population for the year 2011.
                    \n\"2nd
                    \nAnswer:
                    \nLet x and y be the year and population. The quadratic equation is –
                    \ny = a + bx + c\u03a3x2<\/sup>
                    \nNormal equations are na + blx + clx2 = ly
                    \nalx + b\u03a3x2 + c\u03a3x3 = \u03a3xy a\u03a3x2<\/sup> + b\u03a3x3<\/sup> + c\u03a3x4<\/sup> = \u03a3x2<\/sup>y
                    \n\"2nd
                    \nFrom (1) 5a + b.0 + c.10 = 3550
                    \ni.e. 5a + 10c = 3550 -(4)
                    \nFrom (2) a.0 + 6.10 + c.0 = 1410
                    \n\u2234 b = 141
                    \nFrom (3) a.10 + b.0 + c.34 = 7310
                    \ni.e. 10a + 34c =7310 (5)
                    \nBy solving (4) and (5) we get a and c
                    \n(4) x 2 – (5)
                    \n\"2nd
                    \n\u2234 c = 15
                    \nSubstitute c = 15 in (4)
                    \nwe get 5a +10(15) = 3550 \u2234 a = 680
                    \nThe fitted quadratic trend equation is
                    \n\u0177 = 680 + 141x + 15x2<\/sup>
                    \nEstimation of the population for the year 2011 Here x = 3, 2<\/sup> = 9
                    \n\u01772011<\/sub> = 1238millions.<\/p>\n","protected":false},"excerpt":{"rendered":"

                    You can Download Chapter 3 Time Series 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 3 Time Series 2nd PUC Statistics Time Series 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\/13228"}],"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=13228"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/13228\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=13228"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=13228"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=13228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}