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Objective Questions

Latest SSC CGL AAO Exam Question (Objective Questions), MCQ in English

Subjects : Statistics

Question Bank SSC CGL AAO TIER II Exam Paper II - English

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Statistics

Question 1Single Answer

If x and y are related by x – y – 10 = 0 and mode of x is known to be 23, then the mode of y is :

A
20
B
13
C
3
D
23

Question 2Single Answer

A man travels at a speed of 20 km/hr and then returns at a speed of 30 km/hr. His average speed of the whole journey is

A
25 km/hr
B
24.5 km/hr
C
24 km/hr
D
None

Question 3Single Answer

A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is

Question 4Single Answer

For a moderately skewed distribution, quartile deviation and the standard deviation are related by

Question 5Single Answer

The median of the data 13, 8, 11, 6, 4, 15, 2, 18 is

A
5
B
8
C
11
D
9.5

Question 6Single Answer

The sum of the squares of deviations of a set of observations has the smallest value; when the deviations are taken from their

A
A.M.
B
H. M.
C
G. M.
D
None

Question 7Single Answer

If two samples of sizes 30 and 20 have means as 55 and 60 and variances as 16 and 25 respectively, then what would be the S.D. of the combined sample size 50 ?

A
5.33
B
5.17
C
5.06
D
5

Question 8Single Answer

If two variables x & y are related by 2x + 3y –7 = 0 and the mean and mean deviation about mean of x are 1 and 0.3 respectively, then the coefficient of mean deviation of y about mean is

A
–5
B
4
C
12
D
50

Question 9Single Answer

Which of the following result hold for a set of distinct positive observations ?

A
A.M > G.M > H.M
B
G.M. > A.M. > H.M
C
G.M > A.M > H.M
D
A.M > G.M > H.M

Question 10Single Answer

Measures of dispersion are called averages of the ____ order .

A
1st
B
2nd
C
3rd
D
None

Question 11Single Answer

For a set of 100 observations, taking assumed mean as 4, the sum of the deviations is –11 cm and the sum of the squares of these deviations is 257 cm. The coefficient of variation is :

A
41.13%
B
42.13%
C
0.13%
D
None

Question 12Single Answer

If the AM and HM for two numbers are 5 and 3.2 respectively, then the GM will be

A
4.05
B
16
C
4
D
4.10

Question 13Single Answer

________ are used for measuring central tendency, dispersion and skewness

A
Median
B
Deciles
C
Percentiles
D
Quartiles

Question 14Single Answer

Which of the following companies A or B is more consistent so far as the payment of dividend is concerned ?
Dividend paid by A : 5 9 6 12 15 10 8 10
Dividend paid by B : 4 8 7 15 18 9 6 6

A
A
B
B
C
Both A & B
D
Neither A nor B

Question 15Single Answer

What is the coefficient of range for the following distribution ?
Class Interval : 10-19 20-29 30-39 40-49 50-59
Frequency : 11 25 16 7 3

A
22
B
50
C
75.82
D
72.46

Question 16Single Answer

An aeroplane flies from A to B at the rate of 500 km/hr and comes back from B to A at the rate of 700 km/hr. The average speed of the aeroplane is

A
600 km/hr
B
583.33 km/hr
C
D
620 km/hr

Question 17Single Answer

For a moderately skewed distribution, which of the following relationship holds ?

A
Mean – Median = 3 (Median – Mode)
B
Median – Mode = 3 (Mean – Median)
C
Mean – Mode = 3 (Mean – Median)
D
Mean – Median = 3 (Mean – Mode)

Question 18Single Answer

___ & ___ are called ratio averages :

A
HM & GM
B
HM & AM
C
AM & GM
D
None

Question 19Single Answer

A sample of 35 observations has the mean 80 and S.D. as 4. A second sample of 65 observations from the same population has mean 70 and S.D. 3. The S.D. of the combined sample is :

A
5.85
B
5.58
C
10.23
D
None of these

Question 20Single Answer

If x and y are related as 3x – 4y = 20 and the quartile deviation of x is 12, then the quartile deviation of y is

A
14
B
15
C
16
D
9

Question 21Single Answer

Extreme values have ____ effect on mode .

A
High
B
low
C
No
D
None of these

Question 22Single Answer

The mean salary for a group of 40 female workers is Rs. 5,200 per month and that for a group of 60 male workers is Rs. 6,800 per month. What is the combined salary ?

A
Rs. 6,160
B
Rs. 6,280
C
Rs. 6,890
D
Rs. 6,920

Question 23Single Answer

The best measure of dispersion is

A
Q.D.
B
M.D.
C
Range
D
S.D.

Question 24Single Answer

If the mean and S.D. of x are a and b respectively, then the S.D. of

is :

A
a/b
B
–1
C
1
D
ab

Question 25Single Answer

Suppose a population A has 100 observations 101, 102, 103, ...., 200 and another population B has 100 observations 151, 152, 153, ....., 250. If V_A and V_B represents the variance of the two populations respectively, then V_A/ V_B =

A
9/4
B
1
C
4/9
D
2/3

Question 26Single Answer

If there are two groups with 75 and 65 as harmonic means and containing 15 and 13 observations then the combined H.M. is given by :

A
70
B
80
C
70.35
D
69.48

Question 27Single Answer

The G.M. of 4, 6 and 8 is

A
4.17
B
5.32
C
6.14
D
5.77

Question 28Single Answer

The Mean and S.D. for group of 100 observations are 65 and 7.03 respectively. If 60 of these observations have mean and S.D. as 70 and 3 respectively, what is the S.D. for the group comprising 40 observations ?

A
2.03
B
4.03
C
8.03
D
9.33

Question 29Single Answer

The Quartile deviation for the date is
x : 2 3 4 5 6
y : 3 4 8 4 1

A
1/4
B
1/2
C
1
D
0

Question 30Single Answer

If X and Y are two random variables then v(x + y) is

A
v(x) + v(y)
B
v(x) + v(y) – 2v(x, y)
C
v(x) + v(y) + 2v(x, y)
D
v(x) – v(y)

Question 31Single Answer

G.M is a better measure than others when,

A
ratios and percentages are given
B
interval of scale is given
C
Both (a) and (b)
D
Either (a) or (b)

Question 32Single Answer

Mean and S.D. of x is 50 and 5 respectively. Find mean and S.D. of

A
(1, 0)
B
(0, 1)
C
(1, 1)
D
(0, –1)

Question 33Single Answer

Mean and S.D. of a given set of observations is 1,500 and 400 respectively. If there is an increment of 100 in the first year and each observation is hiked by 20% in 2nd years, then find new mean and S.D.

A
1920, 480
B
1920, 580
C
1600, 480
D
1600, 400

Question 34Single Answer

If 5 is subtracted from each observation of some certain item then its coefficient of variation is 10% and if 5 is added to each item then its, coefficient of variation is 6%. Find original coefficient of variation

A
8 %
B
7.5 %
C
4 %
D
None of these

Question 35Single Answer

The median of x,

is 10. Find x where x > 0 .

A
24
B
32
C
8
D
16

Question 36Single Answer

The average salary of 50 men was Rs. 80 but it was found that salary of 2 of them were Rs. 46 and Rs. 28 which was wrongly taken as Rs. 64 and Rs. 82. The revised average salary is :

A
Rs. 80
B
Rs. 78.56
C
Rs. 85.26
D
Rs. 82.92

Question 37Single Answer

Inter Quartile Range is _____ of Quartile Deviation .

A
Half
B
Double
C
Triple
D
Equal

Question 38Single Answer

The sum of squares of deviation from mean of 10 observations is 250. Mean of the data is 10. Find the coefficient of variation .

A
10 %
B
25 %
C
50 %
D
0 %

Question 39Single Answer

If A be the A.M. of two positive unequal quantities X and Y and G be their G.M., then ;

A
A < G
B
A > G
C
A < G
D
A > G

Question 40Single Answer

When mean is 3.57 and mode is 2.13 then the value of median is

A
3.09
B
5.01
C
4.01
D
None of these

Question 41Single Answer

If L₁ = highest observation and L₂ = smallest observation, then Coefficient of Range =

Question 42Single Answer

The equation of a line is 5x + 2y = 17, Mean deviation of y about mean is 5. Calculate mean deviation of x about mean .

A
–2
B
2
C
–4
D
None

Question 43Single Answer

If variance of x is 5, then find the variance of (2 – 3x)

A
10
B
15
C
5
D
– 13

Question 44Single Answer

The harmonic mean of 1, 1/2, 1/3 ... 1/n is

A
1 / (n + 1)
B
2 / (n + 1)
C
(n + 1) / 2
D
1 / (n – 1)

Question 45Single Answer

The mean weight of 15 students is 110 kg. The mean weight of 5 of them is 100 kg. and of another five students is 125 kg. then the mean weight of the remaining students is

A
120
B
105
C
115
D
None of these

Question 46Single Answer

In a class of 11 students, 3 students were failed in a test. 8 students who passed secured 10, 11, 20, 15, 12, 14, 26 and 24 marks respectively. What will be the median marks of the students

A
12
B
15
C
13
D
13.5

Question 47Single Answer

The variance of data : 3, 4, 5, 8 is

A
4.5
B
3.5
C
5.5
D
6.5

Question 48Single Answer

A lady travel at a speed of 20 km/h and returned at quicker speed. If her average speed of the whole journey is 24 km/h, find the speed of return journey (in km/h)

A
25
B
30
C
35
D
38

Question 49Single Answer

Let the mean of the variable 'x' be 50, then the mean of u = 10 + 5x will be

A
250
B
260
C
265
D
273

Question 50Single Answer

Given the observations 4, 9, 11, 14, 37. The Mean deviation about the Median is

A
11
B
8.5
C
7.6
D
7.45

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Statistics

Question 51Single Answer

β₁ represents

A
Skewness
B
Kurtosis
C
Dispersionsx
D
All of the above

Question 52Single Answer

β₂ represents

A
Skewness
B
Kurtosis
C
Dispersions
D
All of the above

Question 53Single Answer

γ₁is =

A
β₂
B
β₁
C
D

Question 54Single Answer

γ₂ is =

A
β₂ – 3
B
β₂ + 3
C
both
D
none

Question 55Single Answer

β coefficients are suggested by

A
Karl Pearson
B
R.A. Fisher
C
Bowle
D
Kellis

Question 56Single Answer

γ coefficients are suggested by

A
Karl Pearson
B
R.A. Fisher
C
Bowle
D
Kellis

Question 57Single Answer

The curve is bell shaped or symmetric then skewness value is

A
zero
B
one
C
any positive value
D
any negative value

Question 58Single Answer

If β₂ = 3 then the Kurtesis is

A
Leptokurtic
B
Platykurtic
C
Mesokurtic
D
Any of the above

Question 59Single Answer

If β₂ < 3 then the Kurtesis is

A
Leptokurtic
B
Platykurtic
C
Mesokurtic
D
Any of the above

Question 60Single Answer

If β₂> 3 then the Kurtesis is

A
Leptokurtic
B
Platykurtic
C
Mesokurtic
D
Any of the above

Question 61Single Answer

If γ₂ = 0 then the Kurtesis is

A
Leptokurtic
B
Platykurtic
C
Mesokurtic
D
Any of the above

Question 62Single Answer

If γ₂ < 0 then the Kurtesis is

A
Leptokurtic
B
Platykurtic
C
Mesokurtic
D
Any of the above

Question 63Single Answer

The limits of the Karl Pearson Coefficient of Skewness .......

A
–1 to +1
B
–2 to +2
C
–3 to +3
D
–4 to +4

Question 64Single Answer

The limits of the Bowle's Coefficient of Skewness ........

A
–1 to +1
B
–2 to +2
C
–3 to +3
D
–4 to +4

Question 65Single Answer

For a positive skewed frequency curve, the inequality that holds is ?

A
Q₁ + Q₃> 2Q₂
B
Q₁ + Q₂ > 2Q₃
C
Q₁ + Q₃ > 2Q₃
D
Q₃ + Q₁ > 2Q₂

Question 66Single Answer

For a negatively skewed frequency distribution curve, the third central moment,

A
µ₃ > 0
B
µ₃ < 0
C
µ₃ = 0
D
µ₃ does not exist

Question 67Single Answer

For a symmetrical distribution, the coefficient of skewness ?

A
α₃ = 1
B
α₃ = 3
C
α₃ = 0
D
α₃ = –1

Question 68Single Answer

For a leptokurtic frequency curve, the measure of Kurtosis ?

A
α₄ = 0
B
α₄= – 3
C
α₄ < 1
D
α₄ > 3

Question 69Single Answer

In case of positive skewed distribution, the extreme values lie in the ?

A
left tail
B
right tail
C
middle
D
anywhere

Question 70Single Answer

The extreme values in a negatively skewed distribution lie in the ?

A
middle
B
right tail
C
left tail
D
whole curve

Question 71Single Answer

Bowley Coefficient of Skewness is based upon ..........

A
Deciles
B
Octibles
C
Percentiles
D
Quartiles

Question 72Single Answer

Kelley's Coefficient of Skewness is based upon ..............

A
Deciles
B
Octibles
C
Percentiles
D
A & C

Question 73Single Answer

Suppose 5 observations on marks are obtained as 78, 77, 79, 39, 29 .

with m_r as the r^th order central moment. Identify the correct statement .

A
b₁ = 0
B
b₂ > 1
C
b₂ = 0.5
D
b₂ = 1

Question 74Single Answer

If in a data set, the first and the third quartiles are close enough, then the frequency distribution is ?

A
leptokurtic
B
platykurtic
C
positively skewed
D
negatively skewed

Question 75Single Answer

Which of the following is true for a symmetric distribution ?
Q₃ = Third quartile
Q₁= First quartile
Q₂ = second quartile or median

A
(Q₃ – Q₂) = (Q₂ – Q₁)
B
(Q₃ – Q₁) = 2Q₂
C
(Q₃ – Q₂) < (Q₂ – Q₁)
D
(Q₃ – Q₂) > (Q₂ – Q₁)

Question 76Single Answer

There are six slips in a box and numbers 1, 1, 2, 2, 3 ,3 are written on these slips. Two slips are taken at random from the box. The expected values of the sum of numbers on the two slips is :

Question 77Single Answer

A letter is taken out at random from the word RANGE and another is taken out from the word PAGE. The probability that they are the same letters is :

A
1/20
B
3/20
C
3/5
D
3/4

Question 78Single Answer

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of same colour is :

A
B
C
D
none

Question 79Single Answer

A card is drawn from a well shuffled pack of 52 cards. Let E₁ "a king or a queen is drawn" & E₂ "a queen or a jack is drawn", then :

A
E₁ and E₂are not independent
B
E₁and E₂ are mutually exclusive
C
E₁and E₂ are independent
D
none of these

Question 80Single Answer

In an non-leap year, the probability of getting 53 sundays or 53 Tuesdays or 53 Thursdays is :

Question 81Single Answer

If A and B are two events and

, then the value of P(A' ∪ B') is :

Question 82Single Answer

The probability that there is at least one error in an account statement prepared by A is 0.3 and for Band C, they are 0.4 and 0.45 respectively. A, Band Cprepared 20, 10 and 40 statements respectively.' The expected number of correct statements in all is :

A
32
B
45
C
42
D
25

Question 83Single Answer

From a pack of cards, two are drawn, the first being replaced before the second is drawn. The chance that the first is a diamond and the second is king is :

Question 84Single Answer

The theory of compound probability states that for any two events A and B :

A
P(A ∩ B) = P(A) x P (B)
B
P(A ∩ B) = P(A) x P(B / A)
C
P(A ∪ B) = P(A) x P(B / A)
D
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

Question 85Single Answer

The probability of getting qualified in IITJEE and AIEEE by a student are respectively

. The probability that the student gets qualified for one of the these tests is :

Question 86Single Answer

Amitabh plays a game of tossing a dice. If the number less than 3 appears, he is getting Rs. a, otherwise he has to pay Rs. 10. If the game is fair, find a :

A
25
B
20
C
22
D
18

Question 87Single Answer

Suppose E and F are two events of a random experiment. If the probability of occurrence of E is 1/5 and the probability of occurrence of F given Eis 1/10, then the probability of nonoccurrence of at least one of the events E and F is :

Question 88Single Answer

A bag contains 8 red and 5 white balls. Two successive draws of 3 balls are made without replacement. The probability that the first draw will produce 3 white balls and second 3 red balls is :

Question 89Single Answer

A box contains 12 electric lamps of which 5 are. defective. A man selects three lamps at random. What is the expected number of defective lamps in his selection ?

A
1.25
B
2.50
C
1.05
D
2.03

Question 90Single Answer

Three identical dice are rolled. The probability that the same number will appear on each of them is :

Question 91Single Answer

Among the examinees in an examination 30%, 35% and 45% failed in Statistics, in Mathematics and in at least one of the subjects respectively. An examinee is selected at random. Find the probability that he failed in Mathematics only :

A
0.245
B
0.25
C
0.254
D
0.55

Question 92Single Answer

An article consists of two parts A and B. The manufacturing process of each part is such that probability of defect in A is 0.08 and that B is 0.05. What is the probability that the assembled product will not have any defect ?

A
0.934
B
0.864
C
0.85
D
0.874

Question 93Single Answer

Daily demand for calculators is having the following probability distribution :
Demand : 1 2 3 4 5 6
Probability : 0.10 0.15 0.20 0.25 0.18 0.12
Determine the variance of the demand .

A
2.54
B
2.93
C
2.22
D
2.19

Question 94Single Answer

If 10 men, among whom are A and B, stand in a row, what is the probability that there will be exactly 3 men between A and B ?

Question 95Single Answer

The probability of an event can assume any value between

A
0 and 1
B
–1 and 0
C
–1 and 1
D
none of these

Question 96Single Answer

The odds are 9 : 5 against a person who is 50 years living till he is 70 and 8 : 6 against a person who is 60 living till he is 80. Find the probability that at least one of them will be alive after 20 years .

Question 97Single Answer

An urn contains 6 white and 4 black balls. 3 balls are drawn without replacement. What is the expected number of black balls that will be obtained ?

Question 98Single Answer

If P(A) = p and P(B) = q, then

A
P(A / B) < q / p
B
P(A / B) > p / q
C
P(A / B) < p / q
D
P(A / B) > P / q

Question 99Single Answer

The probability that a trainee will remain with a company is 0.8. The probability that an employee earns more than Rs. 20,000 per month is 0.4. The probability that an employee, who was a trainee and remained with the company or who earns more than Rs. 20,000 per month is 0.9. What is the probability that an employee earns more than Rs. 20,000 per month given that he is a trainee, who stayed with the company ?