{"id":17253,"date":"2020-01-02T15:52:54","date_gmt":"2020-01-02T10:22:54","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=17253"},"modified":"2021-07-02T15:32:56","modified_gmt":"2021-07-02T10:02:56","slug":"1st-puc-statistics-model-question-paper-4","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/1st-puc-statistics-model-question-paper-4\/","title":{"rendered":"1st PUC Statistics Model Question Paper 4 with Answers"},"content":{"rendered":"

Students can Download 1st PUC Statistics Model Question Paper 4 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 4 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.
    \nState \u2018Croxton and Cowdon’s\u2019 definition of statistics.
    \nAnswer:
    \nStatistics is a science of collection, presentation, analysis and interpolation of numerical data.<\/p>\n

    Question 2.
    \nWho is an investigator?
    \nAnswer:
    \nThe person who conducts statistical investigation is a investigator.<\/p>\n

    Question 3.
    \nWhat is tabulation of the data?
    \nAnswer:
    \nTabulation is the process of systematic arrangement of statistical data in vertical columns and horizontal rows, in the form of a table.<\/p>\n

    \"KSEEB<\/p>\n

    Question 4.
    \nWrite the formula of mid-points of a class.
    \nAnswer:
    \n\"1st<\/p>\n

    Question 5.
    \nWhich graph is used to locate a median?
    \nAnswer:
    \nOgives (less than Ogive) are used to locate the value of median.<\/p>\n

    Question 6.
    \nWhat is class frequency?
    \nAnswer:
    \nThe number of observations corresponding to a particular class is known as the class frequency.<\/p>\n

    Question 7.
    \nFind geometric mean of 2 and 8.
    \nAnswer:
    \nWe know that GM = \\(\\sqrt{a \\times b}=\\sqrt{2 \\times 8}=\\sqrt{16}\\) = 4<\/p>\n

    Question 8.
    \nFor a data if D5<\/sub> = 50, then what is the value of P50<\/sub>.
    \nAnswer:
    \nHere D5<\/sub> = 50, which divides into two equal parts. \u2234 P50<\/sub> also divides into two equal parts i.e. P5o<\/sub> = 50.<\/p>\n

    Question 9.
    \nMention the type of correlation between \u2018speed of a vehicle and distance covered by it.
    \nAnswer:
    \nIt is a positive correlation.<\/p>\n

    Question 10.
    \nWhat is interpolation?
    \nAnswer:
    \nInterpolation is the technique of estimating the unknown value of dependent variable (y) for a given value of independant variable (x) which is within the limits or range of the independent variable.<\/p>\n

    Question 11.
    \nIf P(A) = \\(\\frac { 2 }{ 5 }\\) , then find P(A’)
    \n2 2 3
    \nAnswer:
    \nGiven P(A) = \\(\\frac { 2 }{ 5 }\\), then P(A’) = 1 – P(A) = 1 – \\(\\frac { 2 }{ 5 }\\) = \\(\\frac { 3 }{ 5 }\\)<\/p>\n

    Question 12.
    \nDefine a random variable.
    \nAnswer:
    \nRandom variable is a function which assigns a real number-to every sample point in the sample space.<\/p>\n

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

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

    Question 13.
    \nWhat is a continuous variable? Give an example.
    \nAnswer:
    \nA random variable which assumes all the possible values in its range is a continuous random variable.
    \nEx: Height or weight of children.<\/p>\n

    Question 14.
    \nMention two methods of sampling.
    \nAnswer:<\/p>\n

      \n
    1. Simple random sampling.<\/li>\n
    2. Systematic sampling<\/li>\n
    3. Stratified sampling.<\/li>\n<\/ol>\n

      Question 15.
      \nWhat do you mean by inclusive class interval? Give an example.
      \nAnswer:
      \nIn a class if lower limit as well as upper limits are included in the same class, such a class is called inclusive class interval.
      \nEx.C.I. = (0 – 9), (10 – 19)…. (40 – 49).<\/p>\n

      \"KSEEB<\/p>\n

      Question 16.
      \nWhat are stubs and captions of a table?
      \nAnswer:
      \nRow headings are called stubs and column headings are called captions of a table.<\/p>\n

      Question 17.
      \nMention two objectives of diagrams and graphs.
      \nAnswer:<\/p>\n

        \n
      1. They can be remembered for longer period of time.<\/li>\n
      2. They facilitates comparison.<\/li>\n<\/ol>\n

        Question 18.
        \nWhat is histogram?
        \nAnswer:
        \nHistogram is a pictorial representation of graphs of frequency distribution by means of adjacent rectangles, whose areas are proportional to the frequencies represented.<\/p>\n

        Question 19.
        \nFind the harmonic mean of 1, \\(\\frac{1}{2}, \\frac{1}{3}, \\frac{1}{4}\\)
        \nAnswer:
        \n\"1st<\/p>\n

        Question 20.
        \nFor a data, if median is 50 and mean deviation from median is 12, then find the coefficient.
        \nAnswer:
        \n\"1st<\/p>\n

        Question 21.
        \nWhat are regression lines? Where they intersect?
        \nAnswer:
        \nThe graphs of regression equations are called regression lines.
        \nThey intersect at (x\u0304, y\u0304)<\/p>\n

        \"KSEEB<\/p>\n

        Question 22.
        \nIn case of two attributes, if N = 250, (AB) = 30, (A) = 100 and (B) = 50, then find the remaining classes and their frequencies.
        \nAnswer:
        \nIn a 2 \u00d7 2 contingency table of two attributes :
        \n\"1st<\/p>\n

        Question 23.
        \nTwo cards are drawn from a pack of 52 playing cards, what is the probability that they are king?
        \nAnswer:
        \n\"1st<\/p>\n

        Question 24.
        \nIf E(X) = 3 and E(X2<\/sup>) = 25, then find SD (X).
        \nAnswer:
        \n\"1st<\/p>\n

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

        III. Answer any EIGHT of the following questions. 8 \u00d7 5 = 40<\/span><\/p>\n

        Question 25.
        \nWrite the functions of statistics.
        \nAnswer:
        \nThe functions of statistics are :<\/p>\n

          \n
        • It simplifies complexity of the data.<\/li>\n
        • It reduces the bulk of the data.<\/li>\n
        • It adds precision to thinking.<\/li>\n
        • It helps in comparing different sets of figures.<\/li>\n
        • \u00a0It guides in the formulation of policies and helps in planning. \\<\/li>\n
        • It indicates trends and tendencies.<\/li>\n<\/ul>\n

          Question 26.
          \nWhat are the guidelines for the construction of a questionnaire?
          \nAnswer:
          \nThe following points are considered while framing a schedule\/questionnaire.<\/p>\n

            \n
          • Questions should be simple and easy to understand to get spontaneous answers.<\/li>\n
          • Questions should not confuse the reader and they should give one and only one meaning<\/li>\n
          • The number of questions should be kept minimum<\/li>\n
          • If possible the questions should be capable of getting a definite answers, with either yes or no, a number , a place or a date etc.,<\/li>\n
          • Questions should be capable of tabulating<\/li>\n
          • The questions should be such that the least intelligent and a educated can answer them with least trouble<\/li>\n
          • The questions should be arranged in logical order<\/li>\n
          • The questions which hurt the feelings of the informant and which are of personal and confidential nature should be avoided<\/li>\n
          • A far as possible the questions put should be corroborator at least on the point of importance 0 The questions should pre-tested in a small group of individuals before it is used<\/li>\n
          • Questionnaire should look attractive<\/li>\n
          • If possible a covering letter is attached along with the questionnaire.<\/li>\n<\/ul>\n

            \"KSEEB<\/p>\n

            Question 27.
            \nPrepare a blank table showing the particulars relating to the students of a college classified according to :
            \n(a) Faculty : Arts, Commerce, Science.
            \n(b) Caste : SC\/ST, Group I to III, others
            \n(c) Sex : Male and female
            \nAnswer:
            \nStudents strength of a college according to faculty, caste and sex.
            \n\"1st<\/p>\n

            Question 28.
            \nFollowing is the data regarding strength of a college. Draw percentage bar diagram for this data.
            \n\"1st
            \nAnswer:
            \n\"1st
            \nSimilarly others can be calculated.
            \nPercentage bar diagram shows the students strength of a college according to sex for the year 2009-10.<\/p>\n

            \"1st<\/p>\n

            Question 29.
            \nFor the following observations, Find mean, median and mode : 12, 42, 25, 35, 67, 25, 56, 5, 75
            \nAnswer:
            \nArrange in ascending order : 5, 12, 25, 25, 35,42, 56, 67, 75
            \nn = 9
            \n\"1st
            \nmode (z) = size of most repeated item = 25<\/p>\n

            \"KSEEB<\/p>\n

            Question 30.
            \nExplain types of correlation with examples.
            \nAnswer:
            \nThe correlation may be
            \n1. positive
            \n2. negative
            \n3. zero<\/p>\n

            1. Positive correlation : The two variables are said to be positively correlated if they vary \u2022 in the same direction.
            \nExample<\/p>\n

              \n
            • Demand and supply<\/li>\n
            • Income and expenditure<\/li>\n<\/ul>\n

              2. Negative correlation : The two variables are said to be negatively correlated, if they vary in opposite direction.
              \nExample<\/p>\n

                \n
              • Price and Demand\/Sales<\/li>\n
              • Production and price of vegetables<\/li>\n<\/ul>\n

                3. Zero\/non-correlation : The two variables does not show any related variation, they are said to be zero\/non-correlated.
                \nExample 1. Sales of pig iron and sale of pig iron.<\/p>\n

                Question 31.
                \nMarks obtained by five students in two subjects are as follows : Find Spearman’s rank correlation coefficient for the data.
                \n\"1st
                \nAnswer:
                \nHere the data is non-repeated so,
                \n\"1st
                \nR1<\/sub>, R2<\/sub> be the ranks in accountancy. (X) and Statistics (Y)
                \n\"1st
                \nThere exists a high degree positive correlation between marks in Accountancy and statistics<\/p>\n

                \"KSEEB<\/p>\n

                Question 32.
                \n200 candidates appeared for II PUC examination in a college and 60 of them succeeded. 35 received a special coaching or tutorial class and out of them 20 candidates succeeded. Using Yule’s coefficient, discuss whether the special coaching is effective or not.
                \nAnswer:
                \nLet A and B be \u2018Attending coaching class\u2019 and success in examination.
                \nLet \u03b1 not attending coaching class and \u03b2 – failure in the examination.
                \nthen contingency table can be prepared as below.
                \n\"1st
                \nThe Yule’s coefficient of association :
                \n\"1st<\/p>\n

                Conclusion : Here Q > 0.5, there exists a positive association i.e. special coaching is effective in success in examination.<\/p>\n

                Question 33.
                \nInterpolate the index for 2008 from the following data.
                \n\"1st
                \nAnswer:
                \nLet X and Y be the year and index no.
                \nFrom the data there are 4 known values of y are given,
                \nso expand the Binomial (y -1)4<\/sup> = 0
                \ni.e. y4<\/sub> – 4y3<\/sub> + 6y2<\/sub> – 4y1<\/sub> + y0<\/sub> =0
                \n322 – 4 \u00d7 313 + 6y2<\/sub> = 4 \u00d7 281 +278 = 0
                \n322 – 1252 + 6y2<\/sub> – 1124 + 278 = 0
                \n600 – 2376 + 6y2<\/sub> = 0
                \n-1776 + 6y2<\/sub> = 0
                \n\u2234 y2<\/sub> = \\(\\frac { 1776 }{ 6 }\\) = 296<\/p>\n

                Question 34.
                \nState and prove addition theorem of probability for two non-mutually exclusive events.
                \nAnswer:
                \nStatement: Let A and B be two events with respective probabilities P(A) and P(B). Then the probability of occurrence of at least one of these two events is
                \nP(A \u222aB) = P(A) + P(B) – P(A \u2229B)
                \nProof: A random experiment results \u2018n\u2019 exhaustive events m and m, events are favourable to events A and B respectively. And P out comes are common to A \u00d7 B.
                \nThe probabilities are
                \n\"1st
                \nEvent (A \u222aB) i.e. occurrence of at least one of the events is (m1<\/sub>, + m2<\/sub> -D) favourable events.
                \n\"1st
                \nP(A \u222aB)= P(A) + P(B) – P(A \u2229B): from result (1).
                \nHence the proof.<\/p>\n

                \"KSEEB<\/p>\n

                Question 35.
                \nA bag contains 6 red balls and 4 white balls. What is the probability that two balls drawn are
                \n(i) of the same colour
                \n(ii) of different colours.
                \nAnswer:
                \n(i) P (2 balls drawn are of same colour) = P(2 red balls) OR P(2 white balls)
                \n\"1st<\/p>\n

                (ii) P(drawing different coloured balls) = 1 – P(drawing 2 same coloured balls)
                \n= 1 – \\(\\frac { 21 }{ 45 }\\) = 1 – 0.47 = 0.53
                \n\u2235 P(A’) = 1 – P(A)<\/p>\n

                Question 36.
                \nIf X is a random variable and ‘a’ is any constant, then prove that E(ax) = aE(X) and var(ax) = a2<\/sup>var(x)
                \nAnswer:
                \nProof : (i) E(ax) = \u03a3ax(px)
                \nBy definition E(X) = \u03a3xP(X) = a\u03a3xP(X)
                \n\u2234 E(ax) = aE(x)<\/p>\n

                (ii) var(ax) = E[ax – aE(x)]2<\/sup>
                \nby definition of var (x) = E [x – E(x)]2<\/sup> = E [ax – aE(x)]2<\/sup> = a2<\/sup>E [x – E(x)]2<\/sup>
                \nvar(ax)=a2<\/sup> var(x)<\/p>\n

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

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

                Question 37.
                \nWhich series is better? and which is more consistent?
                \n\"1st
                \nAnswer:
                \nBetterness will be decided on the basis of means of X and Y.
                \nConsistency will be decided on the basis of C.V’s. (coefficient variations)
                \n\"1st
                \n\"1st
                \n\"1st
                \n\"1st
                \nHere X\u0304 > Y\u0304 ; X series is better and
                \nCV(Y) < (V(X); Y series is more consistent.<\/p>\n

                \"KSEEB<\/p>\n

                Question 38.
                \nFind Karl Pearson’s coefficient of skewness for the following data.
                \n\"1st
                \nAnswer:
                \n\"1st
                \nX = Midpoints or C.l.
                \nModal class = size of highest frequency
                \n\"1st
                \nAfter converting into exclusive CI = 19.5 – 24.5
                \n\"1st
                \nThe distribution is negatively skewed<\/p>\n

                Question 39.
                \nFor the following bivariate data, find Karl Pearson’s coefficient of correlation
                \n\"1st
                \nAnswer:
                \n\"1st
                \n\"1st
                \nThere exists a high degree positive correlation between x and y.<\/p>\n

                \"KSEEB<\/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 probability that a boy will pass an examination is \\(\\frac { 3 }{ 5 }\\) and that of a girl is \\(\\frac { 2 }{ 5 }\\). Find the probability that
                \n(i) both of them passes the examination
                \n(ii) at least one of them passes the examination.
                \nAnswer:
                \n(i) P(Boy and Girl passes examination)
                \n= P(B \u2229G) = P(B).P(G) = \\(\\frac { 3 }{ 5 }\\) \u00d7 \\(\\frac { 2 }{ 5 }\\) = \\(\\frac { 6 }{ 25 }\\)<\/p>\n

                (ii)
                \nP (at lest one of them passes the examination)
                \n= P(A \u222aB) = P(A) + P(B) – P(A \u2229B)
                \nP(B \u222aG) = P(B) + P(G) – P(B \u2229G)
                \n\\(=\\frac{3}{5}+\\frac{2}{5}-\\frac{6}{25}=\\frac{3 \\times 5+2 \\times 5-6}{25}=\\frac{19}{25}=0.76\\)<\/p>\n

                Question 40.
                \n(b) Find the mathematical expectations of number of beads obtained when two fair coins are tossed.
                \nAnswer:
                \nLet’X denote the number of heads obtained which take the values of X : 0 (No heads), 1 (one head) and 2 (2 heads) with respective probabilities \\(\\frac { 1 }{ 4 }\\), \\(\\frac { 2 }{ 4 }\\), \\(\\frac { 1 }{ 4 }\\) .
                \n\"1st<\/p>\n

                Question 41.
                \nFollowing are the weights in (kgs) of 40 students of a college. Prepare a continuous frequency distribution table with suitable class interval.
                \nWeight in (kgs) :
                \n45 56 50 41 55 51 46 50 45 57 64 48 53 43 63 45 57 44 54 59 49 52 42 61 51 63 48 56 45 50 55 50
                \nAnswer:
                \nHighest value = 64, Lowest value = 41
                \nRange = HV – LV = 64 – 41 = 23
                \n\"1st<\/p>\n

                \"KSEEB<\/p>\n

                Question 42.
                \nDraw a histogram. Hence find the value of mode(Z) through the graph.
                \n\"1st
                \nAnswer:
                \n\"1st<\/p>\n

                Question 43.
                \nFor the following data find the second Quartile. (Q2<\/sub>).
                \n\"1st
                \nAnswer:
                \nConvert the less than cumulative frequency distribution in to simple (i.e. upper limits and L.C.F.are given)
                \n\"1st
                \n\"1st<\/p>\n

                \"KSEEB<\/p>\n

                Question 44.
                \nThere are 10 tickets in a bag which are numbered 1, 2, 3…10. Two tickets are drawn randomly one after the other with replacement. Find the expectation of the sum of the numbers drawn.
                \nAnswer:
                \nLet X and Y be the numbers on the first and second tickets drawn.
                \nThen the numbers on the 1st ticket drawn is a discrete random variable which takes the values : X – 1, 2, 3 …….. 10 with each probability \\(\\frac { 1 }{ 10 }\\) each.
                \nTo
                \nE(X) = \u03a3X.P(X)
                \n= 1 \u00d7 \\(\\frac { 1 }{ 10 }\\) + 2 \u00d7 \\(\\frac { 1 }{ 10 }\\) + 3 \u00d7 \\(\\frac { 1 }{ 10 }\\) + …. +10 \u00d7 \\(\\frac { 1 }{ 10 }\\)
                \n= \\(\\frac { 1 }{ 10 }\\) [1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10] = \\(\\frac { 55 }{ 10 }\\) = 5.5 10L J 10
                \nSince X and Y are independent takes same values with respective probabilities.
                \n\u2234 E(X + Y) = E(X).E(Y) = 5.5 + 5.5 = 11<\/p>\n","protected":false},"excerpt":{"rendered":"

                Students can Download 1st PUC Statistics Model Question Paper 4 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 4 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\/17253"}],"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=17253"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/17253\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=17253"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=17253"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=17253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}