{"id":17173,"date":"2020-01-02T12:35:44","date_gmt":"2020-01-02T07:05:44","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=17173"},"modified":"2021-07-02T15:32:58","modified_gmt":"2021-07-02T10:02:58","slug":"1st-puc-statistics-model-question-paper-3","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/1st-puc-statistics-model-question-paper-3\/","title":{"rendered":"1st PUC Statistics Model Question Paper 3 with Answers"},"content":{"rendered":"

Students can Download 1st PUC Statistics Model Question Paper 3 with Answers, Karnataka 1st PUC Statistics Model Question Papers with Answers<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 1st PUC Statistics Model Question Paper 3 with Answers<\/h2>\n

Time: 3 Hrs 15 Min
\nMax. Marks: 100<\/p>\n

Note :<\/p>\n

    \n
  1. Graph sheets and statistical tables will be supplied on request.<\/li>\n
  2. Scientific calculators may be used.<\/li>\n
  3. All working steps should be clearly shown.<\/li>\n<\/ol>\n

    Section-A<\/span><\/p>\n

    I. Answer any TEN of the following questions. (10 \u00d7 1 = 10)<\/span><\/p>\n

    Question 1.
    \nGive any one definition of statistics in singular sense.
    \nAnswer:
    \nCroxton and Cowden defines \u2018statistics is the science of collection, presentation, analysis and interpolation of numerical data.\u2019<\/p>\n

    Question 2.
    \nGive an example for ordinal data.
    \nAnswer:
    \nRanks are given to students according to their marks scored in examination.<\/p>\n

    Question 3.
    \nDefine qualitative classification?
    \nAnswer:
    \nIf the data is classified on the basis of qualitative characteristics or attributes is called qualitative classification.<\/p>\n

    Question 4.
    \nDefine the relative frequency.
    \nAnswer:
    \nIt is the ratio of frequency of the value of a variable to the total frequency.<\/p>\n

    Question 5.
    \nFind the mode for the following data. 4, 1, 0, 2, 3, 2, 0, 2, 1, 2, 5, 0, 1, 2.
    \nAnswer:
    \nMode (z) = 2 (which is repeated more times).<\/p>\n

    \"KSEEB<\/p>\n

    Question 6.
    \nWhat is the false base line used in the graph?
    \nAnswer:
    \nIn order to use the space on the graph effectively a line, shown by vertical wavy line between zero and the first scale or the axes can be broken by kinked line.<\/p>\n

    Question 7.
    \nWrite down a formula to find Bowley’s coefficient of skewness.
    \nAnswer:
    \n\"1st<\/p>\n

    Question 8.
    \nGive an example for a negative correlation.
    \nAnswer:
    \nRise in prices of vegetables and sales.<\/p>\n

    Question 9.
    \nWrite the relation between the coefficient of correlation and the standard deviations in regression coefficient of x on y.
    \nAnswer:
    \nThe regression coefficient of x on y = bxy = \u03b3 \\(\\frac{\\delta x}{\\delta y}\\)<\/p>\n

    Question 10.
    \nWrite any one assumption in Binomial method of interpretation.
    \nAnswer:
    \nThe rate of change figures from one period to another is uniform.<\/p>\n

    Question 11.
    \nDefine random experiment.
    \nAnswer:
    \nAn experiment in which the outcome of that experiment cannot be predictable is called random experiment.<\/p>\n

    Question 12.
    \nWrite the formula of variance of a random variable.
    \nAnswer:
    \nVar(X) = E(x2<\/sup>) – [E(X)]2<\/sup><\/p>\n

    Section-B<\/span><\/p>\n

    II. Answer any TEN of the following questions. (10 \u00d7 2 = 20)<\/span><\/p>\n

    Question 13.
    \nMention the divisions of statistics.
    \nAnswer:
    \nThe main branches\/divisions of statistics are<\/p>\n

      \n
    • statistical methods and<\/li>\n
    • applied statistics.<\/li>\n<\/ul>\n

      Question 14.
      \nDefine discrete and continuous variables.
      \nAnswer:<\/p>\n

        \n
      • A variable which assumes only specified values in the given range is a discrete variable.<\/li>\n
      • A variable which assumes all the possible values within the given range of the data is a continuous variable.<\/li>\n<\/ul>\n

        Question 15.
        \nWrite down the frequency density and relative frequency formulae.
        \nAnswer:
        \n\"1st<\/p>\n

        Question 16.
        \nWhat are source and foot note are meant for in the table?
        \nAnswer:
        \nSource and foot note are written just below the table. The data obtained from publications, offices, journals can be mentioned under source and to explain omissions, abbreviations, remarks about numerical entries of the table can be given under the footnote.<\/p>\n

        \"KSEEB<\/p>\n

        Question 17.
        \nMention the purpose of drawing histogram and ogives for a frequency distribution.
        \nAnswer:
        \nFrom the histogram the pattern of distribution of frequencies in the frequency distribution can be studied and from the ogives number of frequencies\/a variable like above or below the given variable\/frequency can be studied.<\/p>\n

        Question 18.
        \nWhat do you mean by measures of position or positional averages? Mention different measures.
        \nAnswer:
        \nMeasures which divides the data into equal parts are called positional averages.
        \nThe different measures are :<\/p>\n

          \n
        • Quartiles (with median)<\/li>\n
        • Deciles<\/li>\n
        • Percentiles<\/li>\n<\/ul>\n

          Question 19.
          \nMention the type of skewness from the following frequency distribution.
          \n\"1st
          \nAnswer:
          \nIn table, there is more concentration of the frequencies at the end of the distribution, compared to the beginning, so the distribution is negatively skewed.<\/p>\n

          In table 2, there is more concentration of the frequencies at the beginning of the distribution, compared to the end, so the distribution is positively skewed.<\/p>\n

          Question 20.
          \nMention values of coefficient of kurtosis for a Platykurtic distribution and leptokurtic distribution.
          \nAnswer:
          \nFor a platykurtic distribution the coefficient of kurtosis \u03b22<\/sub> < 3 and for a Leptokurtic distribution \u03b22<\/sub> > 3.<\/p>\n

          Question 21.
          \nDefine positive and negative correlation with one example each.
          \nAnswer:
          \nIf the variables vary in the same direction is called positive correlation:
          \nEx : Demand and supply.
          \nIf the variables vary in the opposite direction is called negative correlation
          \nEx : price and demand<\/p>\n

          Question 22.
          \nWhen the two regression lines intersect and coincide ?
          \nAnswer:
          \nThe two regression lines intersect at (x\u0304,y\u0304) and they coincide where there is a perfect correlation.<\/p>\n

          Question 23.
          \nHow do you interpret in the Yales’ coefficient of association Q = -ve and Q = +ve
          \nAnswer:
          \nIf Q = -ve there is negative association or dissociation and if Q = +ve there is a positive association between the attributes.<\/p>\n

          Question 24.
          \nShow that 0 \u2264 P(A) \u2264 1.
          \nAnswer:
          \nBy the definition of probability P(A) = \\(\\frac { m }{ n }\\)
          \nHere m the favourable event can take the least value 0 and the highest value n.
          \ni.e. 0 \u2264 m \u2264 n (by mathematical law)
          \n\\(\\text { i.e. } \\frac{0}{n} \\leq \\frac{m}{n} \\leq \\frac{n}{n}\\)
          \n0 \u2264 P(A) \u22641.
          \nHence the proof.<\/p>\n

          Question 25.
          \nDefine p.m.f. (probability mass function)?
          \nAnswer:
          \nLet X is a discrete random variable with respective probability P(X): P(X=x), then P(X) is called p.m.f. if :<\/p>\n

            \n
          • P(x) \u2265 0 for all value of x.<\/li>\n
          • \u03a3P(X) = l<\/li>\n<\/ul>\n

            \"KSEEB<\/p>\n

            Section-C<\/span><\/p>\n

            III. Answer any EIGHT of the following questions. (8 x 5 = 40)<\/span><\/p>\n

            Question 26.
            \nWhat are the causes of distrust of statistics?
            \nAnswer:
            \nFollowing are the causes of distrust of statistics :<\/p>\n

              \n
            • Figures can easily be believed.<\/li>\n
            • Quoting only figures for reference.<\/li>\n
            • Ignoring the limitations of statistics.<\/li>\n
            • Inadequate and improper samples for verification.<\/li>\n
            • Untrained and lack of knowledge in statistics.<\/li>\n<\/ul>\n

              Question 27.
              \nDefine secondary data and in short explain different sources of secondary data.
              \nAnswer:
              \nSecondaty data are those which are collated already by some other persons and which are published in Journals, magazines, news papers etc.<\/p>\n

                \n
              • Secondary data mas be published unpublished.<\/li>\n
              • Publisheds official publications of the state and Central Govt.<\/li>\n
              • Foreign or international bodies sockets UNO, INF, etc.<\/li>\n
              • Unpublished sources: Govt records, municipal offices, research records etc.<\/li>\n<\/ul>\n

                Question 28.
                \nIn the year 2010 in Bangalore 1200 accidents occurred. Of all the accidents 918 were fatal deaths. Out of total accidents 450 were bike accidents, 380 ends in death of drivers, 150 accidents occurred due to auto and car ends with 58 deaths. Remaining accidents were hit and run cases of which 80% were end the life of pedestrians. Tabulate the above information.
                \nAnswer:
                \nTable showing vehicle accidents in Bangalore in the year 2010
                \n\"1st
                \nSource : Imaginary
                \nFact Note : 80% of 600 = \\(\\frac { 80 }{ 100 }\\) \u00d7 600 = 480 ,
                \n* Computed Figures<\/p>\n

                Question 29.
                \nCompute mode from the following data :
                \n\"1st
                \nAnswer:
                \nLet x and y be IQ and number of children.
                \nModal class = size of highest frequency
                \n\"1st<\/p>\n

                \"KSEEB<\/p>\n

                Question 30.
                \nFollowing is the data regarding the height and weight of students. Find the coefficient of correlation using Person’s method.<\/p>\n

                \"1st
                \nAnswer:
                \nLet X and Y be the height and weight.
                \n\"1st
                \nHere dx = x – A = x – 165, dy = y – B = -55
                \n\"1st
                \nn = 6
                \n\"1st
                \nThere exists high degree positive correlation between height and weight.<\/p>\n

                Question 31.
                \nThe two regression equations : the regression equation of X on Y is 10x – 2y = 4 and regression equation of Y on X is 2y – 5x = 8. Find x\u0304, y\u0304 and \u03b3xy<\/sub>.
                \nAnswer:
                \nConsider regression equation of x on y:
                \n10x – 2y = 4; 10x = 2y + 4
                \n\"1st
                \nregression equation of y on x : 2y – 5x = 8
                \n2y = 5x + 8
                \n\\(y=\\frac{5}{2} x+\\frac{8}{2}\\)
                \n\u21d2 byx = 2.5
                \n\u2234 gxy = \u00b1\\(\\sqrt{\\mathrm{bxy} \\cdot \\mathrm{byx}}=\\sqrt{0.2 \\times 2.5}\\) = 0.7071 .
                \nSolving the two regression equations
                \n10x – 2y = 4
                \n2y – 5x = 8
                \ni.e. 10x – 2y = 4
                \n2y – 5x = 8
                \ni.e. 10x – 2y =4
                \n(+) -5x + 2y = 8
                \n5x = 12,x = \\(\\frac { 12 }{ 5 }\\) \u21d2 x\u0304 = 2.4
                \nput x\u0304 = 2.4 in 2y – 5x = 8
                \n2y – 5(2.4) = 8
                \n2y = 8 +12.0
                \ny = \\(\\frac { 20 }{ 2 }\\) = 10 \u21d2 y\u0304 = 10<\/p>\n

                \"KSEEB<\/p>\n

                Question 32.
                \nFind Yule’s coefficient of association from the following data.
                \n\"1st
                \nAnswer:
                \nThe given table can be written as below
                \n\"1st
                \nThe Yule’ s coefficient of Association
                \n\"1st
                \n\u2234 Q = 0.6303
                \nThere exsits positoive association between A and B.<\/p>\n

                Question 33.
                \nFind missing premium payable for the age group 35 per thousand of a Insurance Policy from the following data.
                \n\"1st
                \nAnswer:
                \nUsing binomial expression method :
                \nSince 4 known values of y are given so,
                \n\u03940<\/sub>4<\/sup> = (y – 1)4<\/sup> = 0
                \ni.e y4<\/sub> – 4y3<\/sub> + 6y2<\/sub> – 4y1<\/sub> + y0<\/sub> = 0
                \n\"1st
                \n42 – 4 \u00d7 35 + 6y2<\/sub> – 4 \u00d7 26 + 23 = 0
                \n42 – 140 + 6y2<\/sub> – 104 + 23 = 0
                \n6y2<\/sub> – 179 = 0
                \ny2<\/sub> = \\(\\frac { 179 }{ 6 }\\) = 29.83
                \n\u2234 The premium for the age 35 is \u20b9 29.83<\/p>\n

                Question 34.
                \nState and prove addition theorem of probability for two mutually exclusive event
                \nAnswer:
                \nStatement: Let A and B be two mutually exclusive events with respective probabilities P(A) and P(B). Then the probability of occurrence of atleast one of the events is –
                \nP (A \u222a B) = P(A) + P(B)
                \nProof: Arandom experiment results ‘iV exhaustive mutually exclusive out comes, of which m. and m2 outcomes are favorable to events A and B.
                \nThen P(A) = \\(\\frac{m_{1}}{n}\\)
                \nP(B) = \\(\\frac{m_{2}}{n}\\) Results (1)
                \nHere the favourable events to occur either A or B are (m1<\/sub> + m2<\/sub>)
                \n\"1st
                \nP (A \u222a B) = P(A) + P(B)
                \nHence the proof.<\/p>\n

                Question 35.
                \nA bowl contains 8 balls – 5 white and 3 balls. Two balls are drawn at random one after the other. Find the balls drawn are both white
                \n(i) with replacement
                \n(ii) without replacement.
                \nAnswer:
                \nLet P(A) – probability of drawing a white ball in the first draw and
                \nP(B) – probability of drawing a white ball in the second draw.
                \n(i) With replacement the events are independent
                \n= P(2 white balls) = P(A \u2229 B) = P(A) P(B) = \\(\\frac { 5 }{ 8 }\\) \u00d7 \\(\\frac { 5 }{ 8 }\\) = \\(\\frac { 25 }{ 04 }\\)<\/p>\n

                (ii) Without replacement, second event is dependent on the first event
                \nP(2 white balls) =P(A \u2229B) = P(A)P(B\/A) = \\(\\frac { 5 }{ 8 }\\) \u00d7 \\(\\frac { 4 }{ 7 }\\) = \\(\\frac { 20 }{ 56 }\\)<\/p>\n

                \"KSEEB<\/p>\n

                Question 36.
                \nA fair die is thrown once. A person will get \u20b9 5 if the die results in multiplying 3. Otherwise he loses \u20b9 2. Find his expectations.
                \nAnswer:
                \nLet X denote expected amount, which takes the values X : 5 and -2. With respective probabilities as:
                \nP(x = 5) = P(getting muItiple of 3)
                \n= \\(\\frac { 2 }{ 6 }\\) ; {i.e. 3,6}
                \nP(x = 2) = \\(\\frac { 4 }{ 6 }\\) ;{i.e. 1,2,4,5}
                \nThe probability of distribution is
                \n\"1st
                \nExpected amount: E(X) = \u03a3X.P(X)
                \n= 5 \u00d7 \\(\\frac { 2 }{ 6 }\\) – 2 \u00d7 \\(\\frac { 4 }{ 6 }\\) = 1 – 67 – 1.33 = 0.34 i.e. 34 paise gain.<\/p>\n

                Section-D<\/span><\/p>\n

                IV. Answer any TWO of the following questions. (2 \u00d7 10 = 20)<\/span><\/p>\n

                Question 37.
                \nFollowing is the data regarding the prices (\u20b9) of onion in Bangalore and Chitradurga collected in 6 weeks on every Monday of marked day.
                \n\"1st
                \n(i) which town shows more price on average.
                \n(ii) which town shows more consistent and stable in price.
                \nAnswer:
                \n\"1st
                \nLet x and y be the prices in Banglore and chitradurga
                \n\"1st
                \n(i) Here X\u0304 = 61.5 and Y\u0304 = 37.33
                \nBangalore process shows more process than average<\/p>\n

                (ii) C.V(X) = 11.4% ; C.V(Y) = 14.48%
                \nBangalore priles average more consistent and stable in price.<\/p>\n

                Question 38.
                \nCalculate Bowleg’s coefficient of skewness.
                \n\"1st
                \nAnswer:
                \n\"1st
                \nCompute Quartiles using the following procedure.
                \nAfter calculating L.C.f
                \n\"1st
                \n\"1st
                \n\"1st
                \nThe distribution is positively skewed.<\/p>\n

                \"KSEEB<\/p>\n

                Question 39.
                \nFor the following data :
                \n(a) Calculate two regression equations
                \n(b) Estimate the value of x when y = 30
                \n(c) Determine the value of correlation coefficient using regression coefficients.
                \n\"1st
                \nAnswer:
                \nThe two regression equations are :
                \n(x – x\u0304) = bxy<\/sub> (y – y\u0304)
                \n(y – y) = byx<\/sub> (x-x)
                \n\"1st
                \n\"1st
                \n\"1st
                \n(i) The regression equation of x on y:
                \n(x – x\u0304) = bxy<\/sub> (y – y\u0304)
                \nx – 18 = 2 (y – 8)
                \nx = 2y + 2
                \nThe regression equation of y on x:
                \ny – y\u0304 = byx<\/sub> (x – x\u0304)
                \ny – 8 = 0.4348 (x -18)
                \ny = 0.4348x + 0.1736<\/p>\n

                (ii) Estimation of x when y = 30
                \nx = 2y + 2 = 2(30) + 2 = 62<\/p>\n

                (iii) \u03b3\u00a0 = \u00b1\\(\\sqrt{b_{x y} \\cdot b_{y x}}=\\sqrt{2 \\times 0.4348}\\) = 0.9325<\/p>\n

                Section-E<\/span><\/p>\n

                IV. Answer any TWO of the following questions. (2 \u00d7 5 = 10)<\/span><\/p>\n

                Question 40.
                \n(a) The odds favouring the event of a person A hitting a volley are 2 to 5. The odds against the event of another person B hitting a volley are 1 to 5. If both shoot at a volley, then find the probability that (i) both of them hit (ii) at least one of them hit the volley.
                \nAnswer:
                \nLet P(A) = probability that person A hit a volley = \\(\\frac { 2 }{ 2 + 5 }\\) = \\(\\frac { 2 }{ 7 }\\) \u2234 P(A’) = \\(\\frac { 5 }{ 7 }\\)
                \nand P(B’) = probability that a person B not hitting a target = \\(\\frac { 1 }{ 1 + 5 }\\) = \\(\\frac { 1 }{ 6 }\\)
                \n\u2234 P(B) = \\(\\frac { 5 }{ 6 }\\)<\/p>\n

                (i) P(both of them hit) = P(A \u2229 B) = P(A).P(B)
                \nBoth are independent so,
                \n\\(=\\frac{2}{7} \\times \\frac{5}{6}=\\frac{10}{42}=0.238\\)<\/p>\n

                (ii) P (at least one of them will hit)
                \n= P(A \u222a B) = P(A) + P(B)-P(A \u2229 B)
                \n\\(=\\frac{2}{7}+\\frac{5}{6}-\\frac{2}{7} \\times \\frac{5}{6}=0.88\\)<\/p>\n

                (b) A die is thrown once. Find the expectation of the numbers obtained on the faces of a die.
                \nAnswer:
                \nLet X denote the numbers obtained when a die is thrown which takes the values
                \nx: 1,2,3,4, 5,6 with each having probability \\(\\frac { 1 }{ 6 }\\)
                \nThe probability distribution is
                \n\"1st
                \nExpected number : E(X) = \u03a3X.P(X)
                \n= \\(1 \\times \\frac{1}{6}+2 \\times \\frac{1}{6}+3 \\times \\frac{1}{6} \\times \\ldots .6 \\times \\frac{1}{6}\\)
                \n= \\(\\frac { 1 }{ 6 }\\) [l + 2 + ….6] = \\(\\frac { 1 }{ 6 }\\)(21) = 3.5<\/p>\n

                \"KSEEB<\/p>\n

                Question 41.
                \nFollowing is the data regarding the marks obtained by a certain group of girls in a class in statistics test.
                \n\"1st
                \nPrepare a frequency table.
                \nAnswer:
                \nTable showing the marks obtained by the girls in the statistics test.
                \n\"1st<\/p>\n

                Question 42.
                \nDraw less than and more than ogives from the following frequency distribution. Find the median.
                \n\"1st
                \nAnswer:
                \nOGives of Frequency Distribution
                \n\"1st
                \n\"1st<\/p>\n

                \"KSEEB<\/p>\n

                Question 43.
                \nCompute mean deviation from median for the following data. Also compute its relative measure.
                \n\"1st
                \nAnswer:
                \n\"1st
                \n\"1st<\/p>\n

                Question 44.
                \nTwo dice are rolled. Find the probability of that
                \n(i) the faces of dice are of same number
                \n(ii) the sum is 5.
                \nAnswer:
                \n(i) n = total no. of outcomes when two dice are rolled. = 62<\/sup> = 36
                \nP (A) = P(The faces of dice are of same no.)
                \nm = [(1,1) (2,2) (3,3) (4,4) (5,5) (6, 6)] = 6
                \nP (A) = \\(\\frac { 6 }{ 36 }\\) = \\(\\frac { 1 }{ 6 }\\)<\/p>\n

                (ii) m = sum is 5 = [(1,4) (2,3) (3,2) (4,1)] = 4 4 1
                \np (sum is 5) = \\(\\frac { 4 }{ 36 }\\) = \\(\\frac { 1 }{ 9 }\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

                Students can Download 1st PUC Statistics Model Question Paper 3 with Answers, Karnataka 1st PUC Statistics Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 1st PUC Statistics Model Question Paper 3 with Answers Time: 3 Hrs 15 Min Max. Marks: …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/17173"}],"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=17173"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/17173\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=17173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=17173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=17173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}