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I B.Com PA , CA EVEN SEM 2016 UNIT I SECTION A 1 The word statistics have been derived from the Latin word (1) Statistik (2) Status (3) Statista 2 Modern statistical devices have been made business forecasting more (1) precise and accurate (2) difficult (3)misunderstanding 3 Statistics does not study (1) Individual cases (2) Group (3)Average 4 Statistics does not deals with (1) Qualitative (2) Quantitative (3) Both 5 Statistics is an art as well as (1) Science (2) Average (3) Theory 6 -----is a measure of central tendancy (1) Mean (2) Median (3) all these 7 ----- is the most commonly used measure of central tendancy (1) mean (2) median (3) mode 8 What is the Mean for the following observation ; 3,4,6,7,10 (1) 4 (2) 5 (3) 6 9 Which divides the value of a variable into two equal parts? (1) Median (2) Mean (3) Mode ----- is the value of item of a series which occurs most 10 frequently (1) mean (2) median (3) mode 11 ----- is not affected by extreme items (1) mean (2) median (3) mode 12 Find mode of the following series 2 3 4 3 4 3 5 3 7 (1) 3 (2) 4 (3) 5 In olden days statistics also called ……………… 13 (1) science of soldiers (2) science of kings(3) science of business man The values which varies with maximum frequency is 14 called (1) mean (2) median (3) mode 15 ----- is a positional average (1) Mean (2) median (3) mode 16 -----is not a patrician value (1) Mean (2) median (3) quartiles ----- is the difference between highest and lowest values 17 in a series (1) Range (2) Mean (3) Dispersion 18 ---- are the eyes of Govt. administration (1) Statistics (2) Economics (3) Politics 19 -----is a figure that represents the whole group (1) Average (2) Value (3) Data 20 Measures of dispersion are called averages of ----- order (1) First (2) second (3) Third 21 Standard Deviation was First used by (1) Karl Pearson (2) Horas Secrist (3)Lorance 22 The most important measure of dispersion (1) Range (2) Mean deviation (3) Standard deviation SECTION B a) What are the limitations of Statistics b) Write down the Collection of data and explain. 2. a) Write down the objectives of Classification b) What are the advantages of diagrammatic representation of data? 3. Find arithmetic mean , mode and median from X: 8 10 12 14 16 18 F: 8 12 18 10 4 16 4. Calculate Mode for CI: 20-30 30-40 40-50 50-60 60-70 70-80 80-90 F : 15 14 17 22 10 18 14 1. 5. Distinguish between classification and tabulation 6. Find out Harmonic mean from given data 15, 16.9,11, 113.5,14.4,75.5,35,315 7.Find Mean, Median ,Mode 24,32,28,26,30,32 8. Find Harmonic Mean , Geometric Mean 10, 5, 8, 12, 15 9. Find Mean, Median ,Mode X : 10 20 30 40 50 F : 5 10 7 8 3 10. Find Harmonic Mean , Geometric Mean X: 10 20 30 40 50 F: 5 10 7 8 3 SECTION C 1. Calculate Mean, Median ,Mode CI: 20-30 30-40 40-50 50-60 60-70 70-80 80-90 F : 15 14 17 22 10 18 14 2 Find Harmonic Mean , Geometric Mean Matks : 10-20 20-30 30-40 40-50 50-60 Students: 12 6 15 9 8 3.Find the diference between Classification and Tabulation 4. Find Harmonic Mean , Geometric Mean Matks : 10-20 20-30 30-40 40-50 50-60 Students: 12 6 15 9 8 5. a. Describe Diagrammatic representation of data b. Describe Graphical representation of data UNIT II 1 ---- is the half distance between the third and first quartiles (1) Q.D (2) M.D (3) S.D 2 The formula of Q.D (1) (Q3-Q1)/2 (2) (Q2-Q3)/2 (3) (Q2-Q1)/2 3 The most important measure of dispersion (1) Range (2) Mean deviation (3) Standard deviation 4 Squre of Standard Deviation is known as (1) Range (2) Variance (3) Quartile 5 For comparing variability in scores of 2 Batsman we can use (1) Standard Deviation (2) Mean (3)Co.efficient of variation 6 Variance = ----(1) (S.D)2 (2) 1/S.D (3) S.D)3 7 In Standard deviation , deviations are taken only from --- values of series (1) Mean (2) Median (3) Mode 8 Co. Efficient of variation is equal to (1) (S.D/Mean)*100 (2) (S.D/Range )*100(3) (Mean/ S.D)* 100 9 ----- means lack of symmetry (1) Skewness (2) Kurtosis (3) Range 10 A distribution is skewed if Mean , Median , Mode are (1) Equal (2) Not equal (3) Symetric 11 ----- is a measure of peakedness (1) Skewness (2) Kurtosis (3) Range 12 Skewness may be ---(1) + or – (2) Zero (3) Both Statistical methods are most dangerous tools in the 13 hands of (1) Expert (2) Inexpert (3) Business man 14 ------ is capable of more algebraic treatment (1) Direct method (2) arithmetic mean(3) Median 15 Median is a ----- average (1) Mathematical (2) Positional (3) Both 16 ---- is not a mathematical average (1) A.M (2) mode (3) H.M 17 ----- is ill-defined (1) arithmetic mean (2) Median (3) Mode 18 ----- divides the data into 4 equal parts (1) Quartiles (2) Mean (3) Median 19 Simplest possible measure of dispersion is (1) Range (2) Q.D (3) M.D ---- cannot be computed in the case of open ended 20 distribution (1) Range (2) Mean (3) Both Standard deviation of a series can have minimum value 21 of ----(1) Zero (2) One (3) Two 22 In ---- signs are ignored (1) S.D (2) Mean (3) Both ----- is defined as the reciprocal of the mean of the 23 reciprocal of these values (1) H.M (2) G.M (3) A.M 24 ------ is used in averaging rates , times etc (1) H.M (2) G.M (3) A.M 25 Measures of dispersion are statistical devices to measure the ----- in a series (1) Variability (2) Convertibility (3)Flexibility SECTION B 1.Calculate Quartile deviation and its co-efficient from the following data: Weight(in kg) : 60 61 62 63 65 70 75 80 No. of Workers : 1 3 5 7 10 3 1 1 2. Explain mean deviation and standard deviation. 3. Calculate the mean deviation about mean for the following data : Marks : 40 50 54 60 68 80 No. of Students: 10 18 20 39 15 8 4. Compute: mean deviation about median for the following data S.No : 1 2 3 4 f : 3 6 24 28 5. Compute karlpearson co efficient of skewness 25,15,23,40,27,25,23,25,20 6. Calculate Bowleys coefficient skewness x: 0 1 2 3 4 5 6 y:7 10 16 25 18 11 8 7 If the sum of Q1 and Q3 is 78.2; the difference between Q3 and Q1 is 14.3 and the median is 35.7, find thecoefficient of skewness. 8. Calculate Karl Pearson’s coefficient of skewness Class Interval: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency: 6 12 22 48 56 32 18 6 SECTION C 1.. Find out the mean deviation about the mean from the following data: X : 10 11 12 13 14 F : 3 12 18 12 3 2. Find Quartile Deviation X : 35 40 45 50 55 60 f : 12 18 24 16 6 4 3. Calculate the median age for the following: Age (less than) : 10 20 30 40 50 60 No. of persons : 4 16 40 76 96 112 4.. Distinguish between primary data and secondary data. 5. Calculate range and coefficient of range for CI: F: 0-9 15 70 120 80 125 10-19 20-29 30-39 40-49 50-59 18 14 15 8 12 6. Calculate Standard Deviation CI: 0-10 F: 7 10-20 20-30 30-40 40-50 50-60 60-70 18 34 50 35 20 6 7. a)Calculate S. D for Expenditure :50-100 No. of families: 20 100-150 10 150-200 30 200-250 5 250-300 10 8) Calculate Coefficient of variation for Marks : No. of Students: 0-10 10-20 20-30 30-40 40-50 12 13 21 19 15 9. . Compute Quartile deviation Marks :1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 Students: 2 11 30 66 76 58 37 16 4 10) Find out Karl pearson’s coefficient of skewness Wage : 12 15 20 25 30 40 50 Worker: 10 25 40 70 32 13 10 UNIT III 1 By………. We mean adjusting them making allowance for changes in the price levels. (1) changing of index numbers (2)deflating of index numbers (3) none 2 An index number is a specialized type of (1) deviation (2) Average (3) variance Laspeyre’s and ……………… index number formula do not 3 satisfy time reversal test. (1) Paashe’s (2) Fishers (3) Kelly’s Cost of living index is known as 4 (1) consumer price index (2) cost price index (3) both Consumer price index is used for 5 (1) formulation of price policy (2)product evaluation (3) both WPI means 6 (1) wholesale price index (2) world price index (3) none 7 ……………may satisfy time reversal test (1) Fishers formula (2) Walsche’ (3) All of these The industrial development of a country is reflected by 8 (1) index of cost of living (2) index of industrial production (3) weighted price index 9 …………….. index possess upward bias (1) laspeyre’s (2) fishers (3) Kelly’s Most frequently used index number formula are 10 (1) fixed weighted formula (2) weighted formula (3) un weighted formula Statistical data arranged with respect to time are said to 11 constitute (1) index number (2) time series (3) S.D the fluctuations or variations in the value of a time series exhibited over a period of one year or less are termed as 12 (1) seasonal fluctuations (2) cyclical variation (3) operational fluctuations 13 Time series is a set of data recorded (1) periodically (2) At time or space intervals (3) All of these 14 If the shop of the trend line is positive, it shows (1) declining (2) rising (3) stagnation The gross national product value is deflated through 15 (1) price index numbers (2) weighted index numbers (3) consumer price index numbers A ………. Consists of long term changes, short term 16 variation, irregular variation etc. (1) time series (2) index numbers (3)either A or B The base year for index numbers should be………….. 17 (1) normal period (2) a year only (3) a period at distant part In plural sense, statistics means…………… 18 (1) statistical methods (2) numerical set of data (3) science of collection, presentation etc. 19 The sum of deviations taken from mean is …………….. (1) 0 (2) 1 (3) 2 When an observation in the sata is ……………., then its 20 geometric mean is zero. (1) 0 (2) 1 (3) 2 Which of the following is an absolute measure of dispersion 21 (1) co-efficient of variation (2) standard deviation (3) Co. efficient of quartiles Standard deviation is always …………….. than mean 22 deviation. (1) smaller (2) greater (3) lower 23 A time reversal test is satisfied if we use…………….. (1) Mean (2) mode (3) Geometric mean 24 Which of the following is an economic barometer (1) skewness (2) median (3) index numbers ……………. Is an extension of time reversal test (1) circular test (2) unit test (3) both 25 SECTION B 1. Find the coefficient of correlation for Height of Father: 160 162 163 164 Height of son : 150 152 148 149 2. Compute Rank correlation X:15 20 28 12 40 60 20 Y:40 30 50 30 20 10 30 3. Calculte Pearson’s correlation coefficient Rainfall: 32 35 31 38 27 Production: 52 67 52 47 41 4 Calculate the coefficient of correlation for 165 154 167 160 168 165 57 63 21 72 80 60 42 55 X: 200 500 400 700 600 300 Y: 10 16 14 20 17 13 5 Find byx and bxy from the data given below ∑ 𝑥 = 24; ∑ 𝑦 = 214; ∑ 𝑥 𝑦 = 306; ∑ 𝑥 2 = 164; 𝑁=4 ∑ 𝑦 2 = 576; SECTION C 1. Compute the co efficient of correlation by concurrent deviation method Demand:52 63 45 36 72 65 45 25 Supply:62 53 51 25 79 43 60 33 2 .Calculate the Regression of X on Y x:10 12 13 12 16 y:40 38 43 45 37 3 Calculate 5 yearly moving average Year:1991 1992 1993 1994 1995 Prod :87 61 92 86 112 4 15 43 1996 1997 1998 1999 101 114 107 121 Find the rank correlation: X: 1 2 3 4 5 8 10 Y: 9 8 10 12 14 16 15 5 . Calculate rank correlation coefficient for X: 21 36 42 37 25 Y: 47 40 37 42 43 6. Calculate the two regression equations for the following X: 10 12 13 12 16 15 Y: 40 38 43 45 37 43 UNIT IV 1)Laspeyre’s and ……………… index number formula do not satisfy time reversal test. (1) Paashe’s (2) Fishers (3) Kelly’s 2……………may satisfy time reversal test (1) Fishers formula (2) Walsche’ (3) All of these] 3Cost of living index is known as (1) consumer price index (2) cost price index (3) both 4Consumer price index is used for (1) formulation of price policy (2)product evaluation (3) both 5WPI means…………….. (1) wholesale price index (2) world price index (3) weighted price index 6By………. We mean adjusting them making allowance for changes in the price levels. (1) changing of index numbers (2)deflating of index numbers (3)deflationary index numbers 7An index number is a specialized type of …………… (1) deviation (2) Average (3) variance 8The industrial development of a country is reflected by (1) index of cost of living (2) index of industrial production (3) weighted price index 9…………….. index possess upward bias (1) laspeyre’s (2) fishers (3) Kelly’s 10Most frequently used index number formula are (1) fixed weighted formula (2) weighted formula (3) un weighted formula 11Statistical data arranged with respect to time are said to constitute (1) ndex number (2) time series (3) S.D 12the fluctuations or variations in the value of a time series exhibited over a period of one year or less are termed as (1) seasonal fluctuations (2) cyclical variation (3) operational fluctuations 13Time series is a set of data recorded (1) periodically (2) At time or space intervals (3) All of these 14If the shop of the trend line is positive, it shaws (1) declining (2) rising (3) stagnation 15The gross national product value is deflated through (1) price index numbers (2) weighted index numbers (3) consumer price index numbers 16A ………. Consists of long term changes, short term variation, irregular variation etc. (1) time series (2) index numbers (3)either A or B 17The base year for index numbers should be………….. (1) normal period (2) a year only (3) a period at distant part 18In plural sense, statistics means…………… (1) statistical methods (2) numerical set of data (3) science of collection, presentation etc. 19The sum of deviations taken from mean is …………….. (1) 0 (2) 1 (3) 2 20When an observation in the sata is ……………., then its geometric mean is zero. (1) 0 (2) 1 (3) 2 21Which of the following is an absolute measure of dispersion (1) co-efficient of variation (2) standard deviation (3) Co. efficient of quartiles 22Standard deviation is always …………….. than mean deviation. (1) smaller (2) greater (3) lower 23A time reversal test is satisfied if we use…………….. (1) Mean (2) mode (3) Geometric mean 24Which of the following is an economic barometer (1) skewness (2) median (3) index numbers 25……………. Is an extension of time reversal test (1) circular test (2) unit test (3) both SECTION B and C 1. Using Geometric mean , calculate the cost of living index number for the year 1990 Commodity Price 1980 price 1990 weight Food 60 108 40 Clothing 50 94 17 Fuel 40 65 13 House 125 225 27 Extra 120 240 3 15. a) Explain probability 2. a. Fit a Straight line trend Year: 1997 1998 1999 2000 2001 2002 2003 Production: 48 50 58 52 45 41 49 3. Show that Fisher’s ideal satisfies both Time and Factor reversal tests, Commodity A B C D E Price(1990) 6 2 4 10 8 Qty(1990) 50 100 60 30 40 Price(1992) 10 2 6 12 12 Qty(1992) 56 120 60 24 36 4. Using the method of least squares fit a trend for the following data Year: 1979 1980 1981 1982 1983 Sales: 100 120 140 160 180 5Compute Cost of living index Items : Food Index Number 352 Fuel 10 Clothing 8 Rent Others 12 15 6. Show that time Reversal and Factor Reversal Test Commodity A B C D Price(1980) 10 7 5 16 Qty(1980) 60 70 80 90 Price(1982) 8 9 11 12 Qty(1982) 20 120 60 24 E 12 20 15 36 UNIT V ……… is the geometric mean of Laspeyre’s and Paashe’s 1 Index number. (1) Walsche’s Index Number (2) Kelly’s (3)Fishers From the following which is not a problem in the construction of Index numbers? 2 (1) understanding of the purpose (2)selection of price] (3) selection of base In index number current year quantity is denoted by 3 …………… (1) p1 (2) p0 (3) q1 ndex numbers may be constructed to reflect percentage 4 changes in (1) prices (2) wages (3) All of these 5 Mode – 3 median (1) 2 mean (2) 3 mean (3) mean 6 ---- means asymmetry of a distribution (1) skewness (2) Kurtosis (3) Moments 7 Squares of ---- is known as variance (1) S.D (2) Q.D (3) M.D Find range from the following values 23 32 85 32 42 10 8 20 18 28 (1) 70 (2) 75 (3) 85 9 ----- is a geometric method of measuring variability (1) Lorenz Curve (2) Geometric curve (3)Both Standard deviation of a series can have minimum value 10 of ----(1) 0 (2) 2 (3) 1 11 ----- is ill-defined (1) arithmetic mean (2) Median (3) Mode Statistical methods are most dangerous tools in the 12 hands of (1) Expert (2) Inexpert (3) Business man 13 Cyclic variation Occur at intervals of more than ---- year (1) 1 (2) 2 (3) 3 14 Pie chart is always ……………………… (1) circular (2) freehand (3) both ……………….. percentage of values of a series are less than 15 Q1 (1) 75 (2) 50 (3) 25 16 From the following which is not a kind of index number (1) price (2) quality (3) value 17 Mean - Mode = 3 (mean – Median) (1) median (2) mean (3) mode 18 Quartiles can be determined graphically using (1) ogive (2) Histogram (3) frequency polygon 19 A time series is a set of values arranged in ……………… order. (1) spatial (2) chronological (3)descending Which of the following statement is true (1) Mean is not affected due to sampling 20 fluctuations (2) mean is not affected by extreme values. (3) Arithmetic mean is not stable Variation in a time series that occurs due to chance is 21 (1) regular component (2) irregular component (3) stagnant ……………. Moves like a pendulum of clock and it is never ending process. [a. 22 (1) free hand curve (2) moving average(3) cyclical fluctuation The algebraic sum of deviations of values of a variable 23 from its arithmetic mean is ………………………. (1) -1 (2) 1 (3) 0 24 When mean = 5, median = 10, mode = ……….. (1) 10 (2) 20 (3) 25 25 2 is a relative measure of ……………………. (1) Skewness (2) variance (3) Kurtosis UNIT V 1 ……… is the geometric mean of Laspeyre’s and Paashe’s Index number. (1) Walsche’s Index Number (2) Kelly’s (3)Fishers 2 From the following which is not a problem in the construction of Index numbers? (1) understanding of the purpose (2)selection of price] (3) selection of base 3 In index number current year quantity is denoted by …………… (1) p1 (2) p0 (3) q1 4 ndex numbers may be constructed to reflect percentage changes in (1) prices (2) wages (3) All of these 5 Mode – 3 median (1) 2 mean (2) 3 mean (3) mean 6 ---- means asymmetry of a distribution (1) skewness (2) Kurtosis (3) Moments 7 Squares of ---- is known as variance (1) S.D (2) Q.D (3) M.D 8 Find range from the following values 23 32 85 32 42 10 20 18 28 (1) 70 (2) 75 (3) 85 9 ----- is a geometric method of measuring variability (1) Lorenz Curve (2) Geometric curve (3)Both Standard deviation of a series can have minimum value 10 of ----(1) 0 (2) 2 (3) 1 11 ----- is ill-defined (1) arithmetic mean (2) Median (3) Mode Statistical methods are most dangerous tools in the 12 hands of (1) Expert (2) Inexpert (3) Business man 13 Cyclic variation Occur at intervals of more than ---- year (1) 1 (2) 2 (3) 3 14 Pie chart is always ……………………… (1) circular (2) freehand (3) both ……………….. percentage of values of a series are less 15 than Q1 (1) 75 (2) 50 (3) 25 16 From the following which is not a kind of index number (1) price (2) quality (3) value 17 Mean - Mode = 3 (mean – Median) (1) median (2) mean (3) mode 18 Quartiles can be determined graphically using (1) ogive (2) Histogram (3) frequency polygon A time series is a set of values arranged in ……………… 19 order. (1) spatial (2) chronological (3)descending Which of the following statement is true (1) Mean is not affected due to sampling 20 fluctuations (2) mean is not affected by extreme values. (3) Arithmetic mean is not stable Variation in a time series that occurs due to chance is 21 (1) regular component (2) irregular component (3) stagnant ……………. Moves like a pendulum of clock and it is never ending process. [a. 22 (1) free hand curve (2) moving average(3) cyclical fluctuation 23 The algebraic sum of deviations of values of a variable from its arithmetic mean is ………………………. (1) -1 (2) 1 (3) 0 24 When mean = 5, median = 10, mode = ……….. (1) 10 (2) 20 (3) 25 25 2 is a relative measure of ……………………. (1) Skewness (2) variance (3) Kurtosis ……… is the geometric mean of Laspeyre’s and Paashe’s Index number. (1) Walsche’s Index Number (2) Kelly’s (3)Fishers SECTION B 1 State the addition and multiplication theorem of probability 2.From the following data, interpolate the missing value Year: 1983 1984 1985 1986 1987 Sales: 72 57 ? 81 103 3 What is the chance that a Leap year, selected at random will contain 53 Sundays? 4.Two Unbaised coins are tossed together .Find the Probability of getting tail in both the coins 5.From a pack of well shuffled playing cards, one card is drawn at random.Find the probability that it is a. an ace b. A spade c. A clubs d. An ace or spade