Download QUESTION BANK BASIC STATISTICS AND PROBABILITY

QUESTION BANK
BASIC STATISTICS AND PROBABILITY
Complementary course of B Sc Mathematics Semester 1(CUCBCSS 2014 adm)
1.The totality of all objects under a study is called _______
a) Sample b) Group C)Population d)Specimen
2.Which of the following is not an example for a primary data?
a) Mailed questionnaire b)Local correspondents c)Indirect oral investigation
d)Survey reports in newspapers, journals
3.A statistical population may consists of
a)Infinite number of items b)Finite number of items c)either (a) or (b)
d)Neither (a) nor (b)
4.A study based on complete enumeration of data is known as
a)Sample survey b)Pilot survey c)Census survey d)None of the above
5.Individual observations in a group has a tendency to be very near to a
particular value called_____
a)Central tendency b)measures of central tendency c)Measures of deviation
d)deviation
6.Average calculated in which all the items are not equally important is
called_____
a)simple average b)weighted average c)combined arithmetic mean d)None of
these
7.Which among the following is a measure of positional average?
a)Arithmetic mean b)median c)harmonic mean d)Geometric mean
8.What is the simple arithmetic mean of 15,0,36,0 and 9?
a)20 b)15 c)10 d)60
9.What is the arithmetic mean of the following data?
Marks
20-29 30-39 40-49 50-59 60-69 70-79
Frequency
5
11
18
22
16
8
a)16.5 b)51.6 c)54.5 d)16.6
10.Find the combined arithmetic mean of two samples of sizes 6 and 4
respectively whose means are 15 and 25.
a)20 b)19 c)40 d)21
11.If w1,w2,…,wn are the weights attached to the items x1,x2,…,xn, then the
weighted arithmetic mean is given by
a)(∑wi∑xi)/(∑xi) b)(∑wixi)/(∑xi) c) (∑wixi)/(∑wi) d) (∑xi)/(∑wi)
12.The measure of central tendency defined as the middle most value of the
variable,when the values are arranged in order of magnitude is
a)Median b)Mode c)Arithmetic Mean d)Harmonic Mean
13.What is the median of the following set of scores 13,25,70,19,37,42?
a)44.5 b)25 c)31 d)37
14.What is the median of the following ungrouped data?
Salary(in Rs)
150
100
80
200
130
No.of workers
24
70
40
15
10
a)150 b)100 c)80 d)130
15.Median= l+ c(N/2 – m)/f where ‘m’ is
a)Cumulative frequency of the median class b)frequency of the median class
c)Cumulative frequency of the class preceding the median class d) frequency of
the class preceding the median class
16.Find the median wage of the following persons
Wage(in Rs)
No. of persons
20-30 30-40 40-50 50-60 60-70
3
5
20
10
5
a)45.75 b)50 c)46.75 d)45
17.That value in a distribution which occurs most frequently is___
a)Arithmetic Mean b)Geometric Mean c)Median d)Mode
18.Which of the following measures of central tendencies need not be possessed
by all distributions?
a)Geometric Mean b)Harmonic Mean c)Median d)Mode
19.Which of these gives the empirical relationship between Mean, Median and
Mode of a set of observations?
a)Mode=2Mean-3Median b)Median-Mode=2/3(Mode-Mean) C)ModeMean=3(Mean-Median) d)Mode=3Median-2Mean
20.What is the geometric mean of 2,4and 8?
a)4 b)6 c)5 d)7
21.Which of the following relations always hold true?
a)For equal observations AM=GM b) For equal observations GM≤ AM c) For
unequal observations AM≤GM
d) For unequal observations AM=GM
22.Population of a state increased by 9%,16% respectively from year 2012 to
2013.What is the average increase over these years?
a)12.5% b)9% c)12% d)14%
23.A cyclist travels from place A to B at a speed of 10 km/hr and back at 15
km/hr. What is the average speed of his whole journey?
a)12.5km/hr b)12km/hr c)14km/hr d)None of these
24.Which of the following is true?
a)GM≤AM≤HM b)AM≥GM≥HM c)GM≥AM≥HM d)HM≤AM≤GM
25.Mean marks of 150 students were found to be 50.Later it was found that a
score of 87 was misread as 78.What is the correct mean?
a)49.9 b)59 c)50.09 d)None of these
26.Which among the following is not a commonly used measure of dispersion?
a)Range b)Median c)Standard Deviation d)Mean Deviation
27. What is the range of the following data?
Class
40-45 45-50 50-55 55-60 60-65 65-70
Frequency 4
13
14
12
5
2
a)20 b)30 c)25 d)35
28. _____is used when only a rough measure of dispersion is required.
a)Mean Deviation b)Standard Deviation c)Quartile Deviation d)Range
29. Which among the following is equal to the measure at the (N+1)/2 th
position of an ordered data?
a)Median b)2nd Quartile c)Both (a) and (b) d)Neither (a) nor (b)
30. Quartile Deviation or Semi-inter quartile range is given by
a)(Q2-Q1)/2 b)(Q3-Q2)/2 c)(Q3-Q1)/2 d)(Q3-Q1)/Q2
31. Calculate the standard deviation for the following data
5, 8,7,11, 9,10,8,2,4,6
a)2 b)√5 c)√6 d)√7
32. ____ is used to compare the consistency of 2 or more sets of data.
a)Coefficient of Variation b)Coefficient of Correlation c)Coefficient of
Kurtosis d)Coefficient of Skewness
33. Given are the Coefficient of Variation (CV) of four separate sets of data.
CV of Set A is 5.4, CV of Set B is 2.3, CV of Set C is 3.2 and CV of Set D is
1.9.Which Set is more consistent?
a)Set B b)Set D c) Set C d)Set A
34. Which of the following is not a positional measure?
a)Median b)Quartile c)Percentile d)None of these
35. ____is the best measure of dispersion.
a)Standard Deviation b)Quartile Deviation c)Mean Deviation d)Range
36. If the minimum value in a set is 12 and its range is 8, what is its maximum
value?
a)4 b)20 c)12 d)8
37. If all values of a sample are same, then its variance is
a)1 b)0 c)2 d)Cannot be determined
38. ____ analysis deals with the intensity of relationship among variables
a)Regression b)Correlation c)Both (a) and (b) d)None of these
39. ____ is a coefficient to measure the degree of relationship between two sets
of data by using ranks of observations
a)Pearson’s Correlation Coefficient b)Rank Correlation Coefficient c)Partial
Correlation D)Multiple Correlation
40. Rank Correlation was obtained by ____ to measure degree of relationship
between qualitative characteristics.
a)Karl Pearson b)Galton c)Spearman d)None of them
41. Which among the following is the possible value of Coefficient of
Correlation between 2 sets of values?
a)-3 b)-1.9 c)-0.5 d)2
42. Find the rank correlation of the given sets of ranks of preference to
difference by two different persons.
Item
1
2
3
4
5
6
7
8
9
10
Person 1
2
9
8
7
4
10
1
3
6
5
Person 2
3
7
6
4
5
9
2
1
10
8
a)0.2 b)0.3 c)-0.5 d)0.7
43. _____ is the study of functional relationship between the variables, making
it possible to predict /estimate the unknown value of one of the variables from
the known value of the other.
a) Correlational Analysis b)Regression Analysis c)Mean Difference Analysis
d)None of these
44. Fit a straight line for the following data
X
1
2
3
4
6
8
Y
2.4
3
3.6
4
5
6
a)y=0.605x+1.796 b)y=0.506x+1.976 c)y=0.506x+1.796 d)y=0.506 x+1.976
45. Which among the following gives the value of byxin the regression equation
of y on x?
a) Pxy/σy2 b) Pxy/σx2 c) Pxy/σx.σy d) σy/σx
46. Both regression lines pass through a point which is the point of intersection
of the 2 regression lines. Which is that point?
a)(o, ȳ) b)(ẍ,0) c)(ẍ, ȳ) d)(ẍ/2,ȳ/2)
47. Which of the statements do not hold true?
a)Both regression coefficients cannot be greater than 1
b)Regression coefficients are unaffected by origin shift and scale shift
c) Both correlation and regression coefficients are of same sign
d) Two regression lines coincide iff r=±1
48. Predict the value of y when x=10 using regression line of y on x of the
following data
∑x=140, ∑y=70,∑x2=2038,∑y2=1103,∑xy=1035,n=10
a) 4.18 b) 5.71 c) 7.05 d) 2.87
49. Which of the following can be regression coefficients byx and bxy
a)(2,1) b)(3,2/3) c)(6,1/7) d)(1/2,5/2)
50. If γ is the correlation coefficient between x and y, then correlation
coefficient between 2x and 3y+2 is
a)γ b)2γ c)3γ+2 d)6γ+2
51. Which of the following is not a characteristic of a random experiment?
a) Number of outcomes is 2 or more
b) All outcomes are not known in advance
c) Outcome obtained in a particular trial is not known in advance
d) Experiment can be repeated under identical conditions
52. Which of the given sets are not an event of the 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 coin
thrice?
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 below
i){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, vi
55. In a random experiment of rolling a die and observing the number shown
up, 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 the
occurrence of exactly one of events A,B?
a){1,2,3} b){ } c){2,3} d)S
57. Classical definition of probability gives that if the elementary events of a
random experiment are mutually exclusive, exhaustive and equally likely, then
a)P(A)=Number of outcomes of A/ Total number of outcomes
b)P(A)=Number of elements in A
c)P(A)=Number of elements in S/ Number of outcomes of A
d) None of the above
58. In a random experiment of selecting a red bead from a bag with five beads
of colours red, white, blue, green and yellow, probability of “getting a red bead”
is
a) 1/6 b) 1/5 c) 3/5 d) 1/3
59. Classical definition of probability is applicable only when the following
holds true
i) Sample space is finite, ii) Events are mutually exclusive, iii) Events are
equally likely, iv) Events are exhaustive
a) i, ii b)ii, iii, iv c)i, ii, iii, iv d) i
60. Phenomenon of Statistical Regularity is observed when
a) Number of trials of a random experiment increases
b) Number of trials of a random experiment is kept minimal
c) Relative frequencies approach divergent values
d) None of these
61. Which of the following is not an axiom in the axiomatic definition of
probability?
a)P(A)≥0, A be any event b)P(S)=1 c)A1,A2,… be disjoint events ,then
P(A1UA2U….)=P(A1)+P(A2)+…. d)None of these
62. Which of these definitions of probability defines probability as a function
whose domain is the class of events taking values on the real line?
a)Classical definition b)Axiomatic definition c)Frequency definition d)None
of these
63. 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 these
expresses the event “A and B but not C” occurs
a)AUBUC b)A∩B∩C c)A∩B∩Cc d)AUB∩Cc
65. Suppose sample space S has 4 elements S= {a1,a2,a3,a4},which of these
functions defines a probability in S?
a)P(a1)=1/2,P(a2)=1/3,P(a3)=1/4,P(a4)=1/5
b)P(a1)=1/2,P(a2)=1/4,P(a3)=-1/4,P(a4)=1/2
c)P(a1)=1/2,P(a2)=1/4,P(a3)=1/4,P(a4)=0
d) None of these
66. If P (A)=0.3,P(B)=0.2,P(A∩B)=0.1,what is the probability that exactly one
of the events occurs?
a) 0.3 b) 0.4 c) 0.6 d) 1
67.If P(A)=0.7,P(B)=0.2,P(A∩B))=0.2,what is the probability that neither A nor
B occurs?
a) 0.3 b) 0.2 c) 0.8 d) 0.7
68. Which of these is the same as (A∩Bc) U (A∩B)?
a) A\B b) AUB c) A d) A∩B
69. Three horses A, B and C are in a race .A is twice likely to win as B and B is
thrice as likely to win as C. What is the probability of C winning if probability
of A winning is ‘p’?
A 1/7 b) 1/10 c) 2/7 d) 2/10
70. Two items are chosen at random from a 12 items of which 4 are defective .A
be the event that ‘both items chosen are defective’. What is P(A)?
a)1/11 b)14/33 c)10/11 d)1/33
71. What is the probability of the event that an even number appears when
tossing a fair dice?
a) ½ b) 1/6 c) 1/4 d) 2/3
72. ‘A’ speaks truth in 50% cases and ‘B’ in 60% cases. In what % of cases are
they likely to contradict each other in stating the same fact?
a) 1/3 b) ½ c) 3/10 d) 1/5
73. What is the probability that there should be 53 Sundays in a non-leap year?
a) 2/7 b) 1/7 c) 53/365 d) 312/365
74. One card is selected at random from 50 cards numbered 1 to 50.What is the
probability that the drawn card ends in digit 2?
a) 1/10 b) 1/5 c) 3/10 d) None of these
75. In a rowing race, the odds that A will win is 2 to 3 and the odds that B will
win is 1 to 4.What is the probability that A or B wins the race?
a )3/5 b) 1/5 c) 2/5 d) 4/5
76. Given P (A) › 0, P(B) › 0, then P(B/A)=_____
a)P(A∩B)/P(A) b)P(B∩A)/P(B) c)P(AUB)/P(A) d)P(BUA)/P(B)
77. What is the probability that a single toss of a fair dice results in a number
greater than 3 if it is given that toss resulted in an odd number?
a) 1/6 b) 1/2 c) 1/3 d) 5/6
78. Which of the following variables are discrete?
a) Speed of a car b) The amount of water in a tank c) Number of trees in a
plot d) The time one has to wait for a bus to arrive
79. Multiplication theorem states that ‘if A and B be events in a sample space
P(A) › 0,P(B) › 0,then P(A∩B)=_______
a)P(A/B).P(A) b)P(B/A).P(B) c)P(A/B).P(B) d )None of these
80. P (A1∩A2∩A3) = P (A1). P (A2/A1). P (A3/__ )
a) A2 b) A1∩A2 c) A1 d) A1UA2
81. Two cards are drawn from a well shuffled pack of 52 cards. Find the
probability that they are both aces if the first card is replaced.
a)1/144 b)1/169 c)4/169 d)1/36
82. A box X contains 2 white and 3 red balls. Another box Y contains 4 white
and 5 red balls. One ball is drawn from one of the boxes and is found to be red.
What is the probability that it was drawn from box Y?
a) 3/52 b) 21/52 c) 25/52 d) 9/52
83. If 2 events A and B are independent, then P (A/B) =_____
a)P(A) b)P(B) c)P(A∩B) d)None of these
84. Two events are not independent if
a) Events are not mutually exclusive b) Events are mutually exclusive c)
Outcome of one trial does not depend on the outcome of the other trial d) None
of these
85. Probability that A hits a target is 1/4 and that B hits is 2/5.What is the
probability that the target will be hit if A and B each shoot at the target?
a)13/20 b)15/20 c)11/20 d)None of these
86. Let A and B be events with P (A) =3/8, P (B) =5/8 and P (AUB) = 3/4.Find
P(A/B).
a) ¼ b) 2/3 c) 2/4 d)2/5
87. A coin is tossed until a tail turns up. Let Z be the function representing the
required number of tosses. Here sample space
S={T,HT,HHT,HHHT,HHHHT,…..}. Z(T)=1, Z(HT)=2,….What is the range
set of Z?
a){1,2,3,…} b){0,1,2,3,…} c){1,2,3} d)None of these
88. Let X be the number of tails obtained on tossing 3 coins.
S={HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}.X takes values 0,1,2 and 3.If
F is the distribution function of the random variable X, what is F(2)?
a) 1/8 b) 1/2 c) 7/8 d)1
89. A random variable is said to be discrete if its range set is
a) Finite b) Countably infinite c) Either (a) or (b) d) Neither (a) nor (b)
90. Two dice are rolled .Let X is the maximum of the numbers that turns up. If
P(X) represents the probability mass function, what is P(X=3)?
a) 1/36 b) 5/36 c) 3/36 d) 7/36
91. Which of the following is not a property of probability density function?
a) P(X) ≥0, for all x ԑ R b) ∑P(x) =1,summation taken for all values of x
c) Both (a) and (b) d) Neither (a) nor (b)
92. The probability distribution of a random variable X is given below. Find c.
X
-1
0
1
P(X=x)
1/4
c
1/4
a) 1/4 b) 1/2 c) 1 d) 0
93. Let X be a random variable with the following probability density function.
X
-1
0
1
f (x)
1/4
1/2
¼
What is the value of the probability density function of z=x2 at x=0?
a) 0 b) ½ c) 1/4 d) 1
94. If x is a discrete random variable with pdf f(x),the function F whose domain
is the set of all real numbers defined by F(x)=∑f(u), u≤x is called the ____ of
the random variable.
a)probability mass function b)cumulative probability distribution function
c)distribution function d)Both (b) and (c)
95. If X is the random variable representing the number of tails obtained when a
coin is tossed four times, the maximum value taken by X is
a) 0 b) 3 c) 4 d) 16
96. Let X be a discrete random variable whose distribution function is given by
F(x) =0, x‹1
=1/10, 1≤x‹2
=3/10, 2≤x‹3
=5/10, 3≤x‹4
=8/10, 4≤x‹5
=81/100, 5≤x‹6
=83/100, 6≤x‹7
=1, x≥7
Find P {3‹X≤6}
a )0.83 b) 0.33 c) 0.53 d) 0.73
97. In the previous question (Question no. 96) P{X=3} =____
a) 1/5 b) 3/10 c) 1/100 d) 1/50
98. When a card is drawn from a well shuffled deck of cards, what is the
probability of getting a black king?
a)2/26 b)4/26 c)2/52 d)4/52
99. A class contains 10 men and 20 women of which half men and half
women have brown eyes. Find the probability that a person chosen at
random is a man or has brown eyes.
a) 1/5 b) ½ c) 1/3 d) 2/3
100. A pair of fair dice is tossed. What is the probability that the
maximum of the two numbers is greater than 4?
a) 4/36 b) 20/36 c) 2/36 d) 6/36
Answer key
1)c
2)d
3)c
4)c
5)b
6)b
7)b
8)c
9)b
10)b
11)c
12)a
13)c
14)c
15)c
16)c
17)d
18)c
19)d
20)a
21)a
22)c
23)b
24)b
25)c
26)b
27)c
28)d
29)c
30)c
31)d
32)a
33)b
34)d
35)a
36)b
37)b
38)b
39)b
40)c
41)c
42)d
43)b
44)d
45)b
46)c
47)b
48)a
49)c
50)a
51)b
52)d
53)d
54)d
55)d
56)a
57)a
58)b
59)c
60)a
61)d
62)b
63)a
64)d
Prepared by
Dr.Elizabeth B.John,
Guest Lecturer,
Government College of Teacher Education,
Kozhikode.
65)c
66)a
67)c
68)c
69)b
70)a
71)a
72)b
73)b
74)a
75)a
76)a
77)c
78)c
79)c
80)b
81)b
82)c
83)a
84)b
85)c
86)d
87)a
88)c
89)c
90)b
91)d
92)b
93)b
94)d
95)c
96)b
97)a
98)c
99)d
100)b