QUESTION BANK BASIC STATISTICS AND …

1 QUESTION BANKBASIC STATISTICS AND PROBABILITYC omplementary course of B Sc Mathematics Semester 1(CUCBCSS 2014 adm) totality of all objects under a study is called_____a)Sample b) GroupC)Population d) of the following is notan example for a primary data?a)Mailed questionnaireb)Localcorrespondents c)Indirect oral investigationd)Survey reports in newspapers, statisticalpopulation may consists ofa)Infinite number of items b)Finite number of items c)either (a) or (b)d)Neither (a) nor (b) study based on complete enumeration of data is known asa)Sample survey b)Pilot survey c)Census survey d)None of the observations in a group has a tendency to be very near to aparticular valuecalled_____a)Central tendency b)measures of central tendencyc)Measures of deviationd) calculated in which all the items are not equally important iscalled_____a)simple average b)weighted average c)combined arithmetic mean d)None among the following is a measure of positional average?

2 A)Arithmetic mean b) median c)harmonic mean d)Geometric is the simple arithmetic mean of 15,0,36,0 and 9?a)20 b)15 c)10 d) is the arithmetic mean of the following data?Marks20-2930-3940-4950-5960-6970-79 Frequency5111822168a) b) c) d) the combined arithmetic mean of two samples of sizes 6 and 4respectively whose means are 15 and )20 b)19 c)40 d) w1,w2,..,wnare the weights attached to the items x1,x2,..,xn, then theweighted arithmetic mean is given bya)( wi xi)/( xi)b)( wixi)/( xi) c) ( wixi)/( wi) d) ( xi)/( wi) measure of central tendency defined as the middle most value ofthevariable,when the values are arranged in order of magnitude isa) median b)Mode c)Arithmetic Mean d)Harmonic is the median of the following set of scores 13,25,70,19,37,42?a) b)25 c)31 d) is the median of the followingungrouped data?Salary(in Rs) workers2470401510a)150 b)100 c)80 d) + c(N/2 m)/f where m isa)Cumulativefrequency of the median class b)frequency of the median classc)Cumulativefrequency of the classpreceding the median class d) frequency ofthe class preceding the median the median wage of the following personsWage(in Rs)20-3030-4040-5050-6060-70No.

3 Of persons3520105a) b)50 c) d) value in a distribution which occurs most frequently is___a)Arithmetic Mean b)Geometric Mean c) median d) of the following measures of central tendencies need not be possessedby all distributions?a)Geometric Mean b)Harmonic Mean c) median d) of these gives the empirical relationship between Mean, median andMode of a set of observations?a)Mode=2 Mean-3 median b) median -Mode=2/3(Mode-Mean) C)Mode-Mean=3(Mean- median ) d)Mode= is thegeometric mean of 2,4and 8?a)4 b)6 c)5 d) of the following relations always hold true?a)For equal observations AM=GM b)For equal observations GM AM c) Forunequal observations AM GMd) For unequal observations AM= of a state increased by 9%,16%respectively from year 2012 is the average increase over these years?a) b)9% c)12% d)14% cyclist travels from place A to B at a speed of 10 km/hr and back at 15 is the average speed of his whole journey?a) )12km/hr c)14km/hr d)None of of the following is true?

4 A)GM AM HM b)AM GM HM c)GM AM HM d)HM AM marks of 150 students were found to be it was found that ascore of 87 was misread as is the correct mean?a) )59 c) d)None of among the following is not a commonly used measure of dispersion?a)Range b) median c)Standard Deviation d)Mean Deviation27. What is the range of the following data?Class40-4545-5050-5555-6060-6565-70 Frequency413141252a)20 b)30 c)25 d)3528. _____is used when only a rough measure of dispersion is )Mean Deviation b)Standard Deviation c)Quartile Deviation d)Range29. Which among the following is equal to the measure at the (N+1)/2thposition of an ordered data?a) median b)2ndQuartile c)Both (a) and (b) d)Neither (a) nor (b)30. Quartile Deviation or Semi-interquartile range is given bya)(Q2-Q1)/2 b)(Q3-Q2)/2 c)(Q3-Q1)/2 d)(Q3-Q1)/Q231. Calculate the standard deviation forthe following data5,8,7,11,9,10,8,2,4,6a)2 b) 5 c) 6 d) 732. ____ is used to compare the consistency of 2 or more sets of )Coefficient of Variation b)Coefficient of Correlation c)Coefficient ofKurtosis d)Coefficient are theCoefficient of Variation(CV)of fourseparate sets of of Set A is , CV of Set B is ,CV of Set C is and CV of Set D Set is more consistent?

5 A)Set B b)Set D c) Set C d)Set A34. Which of the following is not a positional measure?a) median b)Quartile c)Percentile d)None of these35. ____is the best measure of )Standard Deviation b)Quartile Deviation c)Mean Deviation d)Range36. If the minimum value in a set is 12 and its range is 8,what isits maximumvalue?a)4 b)20 c)12 d)837. If all values of a sample are same,then its variance isa)1 b)0 c)2 d)Cannot be determined38. ____ analysis deals with the intensity of relationship among variablesa)Regression b)Correlation c)Both (a)and (b) d)None of these39. ____ is a coefficient to measure the degree of relationshipbetween two setsof databy using ranks of observationsa)Pearson s Correlation Coefficient b)Rank Correlation Coefficient c)PartialCorrelation D)Multiple Correlation40. Rank Correlation was obtained by ____ to measure degree of relationshipbetween qualitative )KarlPearson b)Galton c)Spearman d)None of them41. Which among the following is the possible value of Coefficient ofCorrelation between 2 sets of values?

6 A)-3 b) c) d)242. Find the rank correlation of the given sets of ranks of preference todifference by two different 129874101365 Person 237645921108a) b) c) d) _____ is the study of functional relationship between the variables,makingit possible to predict /estimate the unknown value of one of the variables fromthe known value of the )Correlational Analysis b)Regression Analysisc)MeanDifference Analysisd)None of these44. Fit a straight line for the following )y= + b)y= + c)y= + d)y= x+ Which among the followinggives the value of byxin theregression equationof y on x?a)Pxy/ y2b)Pxy/ x2c)Pxy/ x. yd) y/ regression lines pass through a point which is the point of intersectionof the 2 regression is that point?a)(o, ) b)( ,0) c)( , ) d)( /2, /2) of the statements do not hold true?a)Both regression coefficients cannot be greater than 1b)Regression coefficients are unaffected by origin shift and scale shiftc)Both correlation and regression coefficients are of same signd)Two regression lines coincide iff r= 148.

7 Predict the value of y when x=10 using regression line of y on x of thefollowing data x=140, y=70, x2=2038, y2=1103, xy=1035,n=10a) ) ) ) Which of the following can be regression coefficients byxand bxya)(2,1) b)(3,2/3) c)(6,1/7) d)(1/2,5/2)50. If is the correlation coefficient between x and y,then correlationcoefficient between 2x and 3y+2 isa) b)2 c)3 +2 d)6 + of the following is not a characteristic of a random experiment?a)Number of outcomes is 2 ormoreb)All outcomes are not known in advancec)Outcome obtained in a particular trial is not known in advanced)Experiment can be repeated under identical conditions52. Which of the given sets are not an event ofthe sample space S={a,1,2,3,z}a){a,z} b){1,2,3} c){} d){a,b}53. Which among the following is a sample space obtained while tossing a cointhrice?a){(H,T),(T,H),(T,T),(H,H)} b){(H,H,H),(H,T,T),(T,T,T)}c){(H,H),(T,T )}d){(H,H,H),(H,H,T),(H,T,T),(T,H,T),(H, T,H),(T,T,H),(T,H,H),(T,T,T)}54. Pick out the elementary events from belowi){a,b,c},ii){1,2},iii){1},iv){3,4, 5},v){a,b},vi){c}a)i,iv,vi b)ii,iii,iv c)i,iv d)iii,vi55.

8 In a random experiment of rolling a die and observing the number shownup,let A be the event odd number showing up .Then Ac=a){1,2,3,6} b){1} c){1,3,5} d){2,6}56. If A={1} and B={2,3} in S={1,2,3,5,6},which is the event representing theoccurrence of exactly one of events A,B?a){1,2,3} b){ } c){2,3} d)S57. Classical definition of probability gives that if the elementary events of arandom experiment are mutually exclusive,exhaustive and equally likely,thena)P(A)=Number of outcomes of A/ Total number of outcomesb)P(A)=Number of elements in Ac)P(A)=Number of elements in S/ Number of outcomes of Ad)None of the above58. In a random experiment of selecting a red bead from a bag with five beadsof colours red,white,blue,green and yellow,probability of getting a red bead isa)1/6b)1/5c)3/5d)1/359. Classical definition of probability is applicable only when the followingholds truei)Sample space is finite, ii)Events are mutually exclusive, iii)Events areequally likely, iv)Events are exhaustivea)i,ii b)ii,iii,iv c)i,ii,iii,iv d)i60.

9 Phenomenon of Statistical Regularity is observed whena)Number of trials of a random experiment increasesb)Number of trials of a random experiment is kept minimalc)Relative frequencies approach divergent valuesd)None of of the following is not an axiom in the axiomatic definition ofprobability?a)P(A) 0, A be any event b)P(S)=1 c)A1,A2,.. be disjoint events ,thenP( )=P(A1)+P(A2)+.. d)None of of these definitions of probability defines probability as a functionwhose domain is the class of events taking values on the real line?a)Classical definition b)Axiomatic definition c)Frequency definition d)Noneof these63. For any 2 events A and B, P(AUB)=a)P(A)+P(B) b)P(A)+P(B)-P(A B)c)P(A)-P(A B)d)P(A)-P(B)-P(A B)64. Let A,B and C be events in the same random experiment which of theseexpresses the event A and B but not C occursa)AUBUC b)A B C c)A B Ccd)AUB Cc65. Suppose sample space S has 4 elementsS={a1,a2,a3,a4},which ofthesefunctions defines a probability in S?

10 A)P(a1)=1/2,P(a2)=1/3,P(a3)=1/4,P(a4)=1/ 5b)P(a1)=1/2,P(a2)=1/4,P(a3)=-1/4,P(a4)= 1/2c)P(a1)=1/2,P(a2)=1/4,P(a3)=1/4,P(a4) =0d)None of these66. If P(A)= ,P(B)= ,P(A B)= ,what is the probability thatexactly oneof the events occurs?a) b) c) d) P(A)= ,P(B)= ,P(A B))= ,what is the probability that neither A norB occurs?a) b) c) d) Which of these is the same as (A Bc) U (A B)?a)A\Bb)AUBc)Ad)A B69. Three horses A, B and C are in a race .A is twice likely to win as B and B isthrice as likely to win as is the probability of C winning if probabilityof A winning is p ?A1/7b)1/10c)2/7d)2/1070. Two items arechosen at random from a 12 items of which 4 are defective .Abe the event that both items chosen are defective . What is P(A)?a)1/11 b)14/33 c)10/11 d)1/3371. What is the probability of the event that an even number appears whentossing a fair dice?a) b)1/6c)1/4d)2/372. A speaks truth in 50% cases and B in 60% what % of cases arethey likely to contradict each other in stating the same fact?