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School of Distance Education

APPLIED STATISTICS

UNIVERSITY OF CALICUT

SCHOOL OF DISTANCE EDUCATION

COMPLEMENTARY COURSE

B.Sc. MATHEMATICS

IV SEMESTER

(2011 Admission onwards)

APPLIED STATISTICS

QUESTION BANK

1. In case of a positive skewed distribution, the relation between mean,

median and mode that hold is:

a) Median > Mean > Mode b) Mean > Median > Mode

c) Mean = Median = Mode d) None of the above

2. For a Symmetric distribution, the coefficient of skewness:

a) J = 1 b) J = 0

c) J = -3 d) J = -1

3. First and third quartiles of a frequency distribution are 30 and 75. Also

its coefficient of skewness is 0.6. The median of the frequency

distribution is

a) 40 b) 39

c) 38 d) 41

4. If the mean, standard deviation and coefficient of skewness of a

frequency distribution are 60, 45 and -0.4 respectively, the mode of the

frequency distribution is

a) 80 b) 82

c) 78 d) 68

5. For a moderately skew distribution, the empirical relation between

mean (M), Median (Md) and Mode (Mo) is


APPLIED STATISTICS

a) 3 (M – Mo) = M – Md b) 3 (Md – M) = Mo - M

c) 3 (M – Md) = M – Mo d) 2 (Mo – M) = 3 (Md – M)

6. First four moments about the value 5 of a distribution are 2, 20, 40 and

50. Then the mean is

a) 4 b) 5

c) 6 d) 7

7. If the coefficient of Kurtosis of a distribution is zero, the frequency

curve is

a) Leptokurtic b) Platykurtic

c) Mesokurtic d) Any of the above

8. For a platykurtic curve

a) β2 < 3 b) β2 > 3

c) β2 = 0 d) β2 = 3

9. The first four moments about the mean are 0, 2, 0, 11. Then the

Coefficient of Kurtosis is

a)2.25 b) 2.75

c) 3.25 d) 3.75

10 The extreame values in a negatively skewed distribution lie in the

a) Middle b) right tale

c) left tail d) Whole curve

11. If the two lines of regression are perpendicular to each other, the

relation between the regression coefficient is

a) bxy = byx b) bxy .byx = 1

c) bxy + byx = 1 d) bxy + byx = 0

12. If x and y are independent random variables with zero mean and unit

variance, then correlation coefficient (cc) between X + Y and X – Y is

a) b) 0

c) √ d) √13. On the basis of 3 pairs of observations (-1, 1), (0, 0) (1, 1) a statistician

obtains the linear regression of Y on X by the method of least squares.

Which of the following best decribes the line of regression.


APPLIED STATISTICS

a) A straight line parallel to but not identical with the horizontal axis

b) A straight line identical with the vertical axis

c) A straight line identical with the horizontal axis

d) A straight line parallel to but not identical with the horizontal axis

14. First 5 students get to marks for English and 20 marks for Maths. The

remaining 20 students has get 5 marks for English and 25 marks for

Maths. Then the coefficient of correlation between their marks in

English and Maths will be.

a) 0 b) +1

c) -1 d) < 0

15. If we get a straight line parallel to the x-axis when the bivariate data

were plotted on a scatter diagram, the correlation between the variable

is

a) 0 b) +1

c) -1 d) none of these

16. Let ‘n’ pairs of observations are collected from a bivariate distribution

(X, Y) with Correlation Coefficient 0.75. Suppose that each x values be

increased by 5 and each Y values decreased by 5. Then the new

correlation will be

a) > 0.75 b) < 0.75

c) 0.75 d) None of these

17. Suppose Correlation Coefficient between X and Y is 0.65. Suppose that

each Y values are divided by -5 then the new correlation will be.

a) > 0.65 b) 0.65

c) – 0.65 d) 0

18. (X, Y) is a bivariate distribution connected by relation 2x – 3y + 5 = 0.

Then Correlation Coefficient is

a) +1 b) -1

c) d)

19. X1 and X2 are independent random variables with means 5 and 10 and

Standard Deviation 2 and 3 respectively. Then Correlation Coefficient

between 3x1+4x2 and 3x1 – x2 is


APPLIED STATISTICS

a) b)

c) 0 d) 1

20. Let β be the Regression Coefficient and r be the Correlation Coefficient

then

a) β > r b) β < r

c) -1 ≤ βr ≤ +1 d) βr ≥ 0

21. If X and Y are two variables, there can be at most

a) One regression line b) Two regression lines

c) Three regression lines d) An infinite no. of regression lines

22. In a regression line of Y on X, the variable X is known as

a) Independent variable

b) Dependent variable

c) Sometimes independent and some times dependent variable

d) None of these

23. In the regression line Y = a + bx, b is called the

a) Slope of the line b) Intercept of the line

c) Neither (a) nor (b) d) both (a) and (b)

24. If byx and bxy are two regression coefficients, they have

a) Same sign b) Opposite sign

c) Either same or opposite signs d) Nothing can be said

25. If byx>1 then bxy is

a) Less than 1 b) Greater than 1

c) Equal to 1 d) Equal to 0

26. If x and y are independent, the value of regression coefficient byx is

equal to

a) 1 b) 0

c) ∞ d) Any positive value

27. The lines of regression intersect at the point

a) (X, Y) b) ( , )c) (0, 0) d) (1, 1)

28. The co-ordinates ( , ) satisfy the line of regression of


APPLIED STATISTICS

a) X on Y b) Y on X

c) Both X on Y and Y on X d) None of the two regression lines

29. If r = ± 1, the two lines of regression are:

a) Coincident b) Parallel

c) Perpendicular to each other d) None of the above

30. If r = 0 the lines of regression are

a) Coincident b) Parallel

c) Perpendicular to each other d) None of the above

31. Regression coefficient is independent of:

a) Origin b) Scale

c) Both origin and scale d) Neither origin nor scale

32. If a constant 50 is subtracted from each of the value of X and Y, the

regression coefficient is:

a) reduced by 50 b) th of the original regression coefficient

c) increased by 50 d) not changed

33. If each observation in the set of values (X, Y) is divided by 100, the

regression coefficient of Y on X is:

a) Increased by 100 b) decreased by 100

c) th of byx d) None of the above

34. If each of X values is divided by 5 and of Y by 10, then new byx is:

a) Same as byx b) half of byx

c) twice of byx d) none of the above

35. If each value of X is divided by 2 and of Y is multiplied by 2. Then the

new byx is

a) Same as byx b) twice of byx

c) four time of byx d) eight times of byx

36. If from each value of X and Y, constant 25 is subtracted and then each

value is divided by 10, then new byx is

a) Same as byx b) 2 ½ times of byx

c) 25 times of byx d) 10 times of byx

37. If each value of X is multiplied by 10 and of Y by 20, then new bxy is


APPLIED STATISTICS

a) Same as bxy b) half of bxy

c) four times of bxy d) one fourth of bxy

38. If Correlation Coefficient between X and Y is r, the Correlation

Coefficient between X2 and Y2 is

a) r b) r2

c) 0 d) 1

39. Given two regression lines as 3X – 4Y + 8 = 0 and 4X – 3Y = 1, the

means of X and Y are

a) = 4, = 5 b) = 3, = 4

c) = = d) none of the above

40. The formula for simple correlation coefficient between the variables X

and Y with usual notations is:

a) ( )( ). ( ) b) ∑ ∑ ∑. ∑ (∑ ) ∑ (∑ )c)

∑ ( ) ( )∑ ( ̅ ) . ∑ ( ) d) All the above

41. The unit of Correlation Coefficient is

a) kg/cc b) per cent

c) non-existing d) none of the above

42. The range of simple correlation coefficient is

a) 0 to ∞ b) - ∞ to +∞

c) 0 to 1 d) -1 to 1

43. If rxy = 1, the relation between X and Y is

a) Y is proportional to X b) Y is inversely proportional to X

c) Y is equal to X d) none of the above

44. If rxy = 0, the variables X and Y are

a) linearly related b) independent

c) not linearly related d) none of the above

45. If rxy = -1, the relation between X and Y is of the type:

a) when Y increases X also increasesb) When Y decreases X also decreasesc) X is equal to –Yd) When Y increases, X proportionally decreases

46. Significance of a Simple Correlation Coefficient can be tested by


APPLIED STATISTICS

a) t - test b) z - test

c) Ψ2 test d) F - test

47. The test statistic for testing the significance of rxy = 0 with usual

notations is:

a) t = √ b) t = √c) t = √ d) t = ( )

48. The statistic t for testing the hypothesis rxy = 0 based on a sample of

size ‘n’ from a bivariate population has degrees of freedom:

a) n b) n - 1

c) n - 2 d) n - 3

49. If each group consist of one observation only, the value of correlation is

a) 0 b) 1

c) between 0 and 1 d) between -1 and 1

50. The range of multiple correlation coefficient R is

a) 0 to 1 b) 0 to ∞

c) -1 to 1 d) -∞ to ∞

51. The range of partial correlation coefficient is

a) 0 to 1 b) 0 to ∞

c) -1 to 1 d) -∞ to ∞

52. The formula for multiple correlation coefficient R2.13 in terms of simplecorrelation coefficient r12, r13 and r23 is

a) b)

c) d)

53. If X1, X2 and X3 are three variables, the partial correlation between X2

and X3 eliminating the effect of X1 in terms of simple correlation

coefficient is given by the formula:

a) r23.1 = ( ) b) r23.1 = ( )c) r23.1 = ( ) d) All the above


APPLIED STATISTICS

54. If is the correlation coefficient between X and Y, the correlation

coefficient between ax + b and Y is.

a) a b) a + b

c) a2 d)

55. If the two lines of regression are x + 2y – 5 = 0 and 2x + 3y – 8 = 0, the

regression line of Y on X is

a) 2x + 3y – 8 = 0 b) x + 2y – 5 = 0

c) any of the two lines d) none of the two lines

56. Give the two regression lines x + 2y – 5 = 0, 2x + 3y – 8 = 0 and V(x)= 12

the value of V(y) is

a) 16 b) 4

c) d)

57. Let the Regression lines of Y on X and X on Y are respectively Y = aX + b

and X = cY + d, then the correlation coefficient between X and Y is

a) ⁄ b) ⁄c) √ d) √

58. If the correlation coefficient between two variables X and Y is very high,

the two lines of regression are:

a) far apart b) coincident

c) near to each other d) none of the above

59. Which of the following relation is correct

a) . = . b) . = .c) = d) . = .

60. The correlation between the five paired measurements (3, 6), (½, 1),

(2, 4), (1, 2), (4, 8) for the variables X and Y is equal to:

a) 0 b) -1

c) d) 1

61. If the correlation between X and Y is 0.5, then the correlation between

2x-4 and 3-2y is

a) 1 b) 0.5

c) -0.5 d) 0


APPLIED STATISTICS

62. Let the equation of the line of regression are 2X – 3Y = 0 and 4Y – 5X = 8

then the correlation between X and Y is

a) b)

c) d)

63. Given the two regression lines X + 2Y = 5 and 2X + 3Y = 8 and = 4,then the value of is

a) 12 b)

c) 6 d) none of the above

64. Given = 0.6, = 0.5 and = 0.8, the value of . is

a) 0.4 b) 0.72

c) 0.38 d) 0.47

65. If Var(X + Y) = Var(X) + Var(Y), then the value of correlation coefficient

a) 0 b) 1

c) -1 d) 0.5

66. If Var(X + Y) = Var(X – Y) then the correlation coefficient between X and

Y is

a) 1 b) ½

c) ¼ d) 0

67. The sum of first ‘n’ natural numbers is:

a) ( ) b)

c) d) n(n + 1)

68. The formula of rank correlation coefficient is

a) ( ) b) 1 – ∑( )c) ∑( ) d) 1 – ∑

69. In rank correlation, let di = xi – yi then ∑ is

a) 0 b) 1

c) -1 d) none of the above

70. If = 0.7, = 0.6 and = 0.5 then R1.23 is:

a) 0.70 b) 0.50

c) 0.75 d) 0.84


APPLIED STATISTICS

71. A time series data is a set of data recorded at

a) periodically b) time or space intervals

c) successive point of time d) all the above

72. The time series analysis helps:

a) to compare the two or more series b) to make predictions

c) to know the behavior of business d) all the above

73. A time series consists of:

a) two components b) three components

c) four components d) five components

74. The forecasts on the basis of a time series are:

a) cent per cent true b) true to a great extent

c) never true d) none of the above

75. The component of a time series attached to long-term variations is

termed as:

a) cyclic variation b) secular trend

c) irregular variation d) all the above

76. The component of a time series which is attached to short-term

fluctuations is:

a) seasonal variations b) cyclic variations

c) irregular variations d) all the above

77. The sales of a department store on Dushara and Diwali are associated

with the component of a time series:

a) secular trend b) seasonal variation

c) irregular variation d) all the above

78. Secular trend is indicative of long-term variation towards:

a) increase only b) decrease only

c) either increase or decrease d) none of the above

79. Linear trend of a time series indicates towards:

a) constant rate of change b) constant rate of growth

c) change in geometric progression d) all the above

80. Method of least squares to fit in the trend is applicable only if the trend

is:


APPLIED STATISTICS

a) linear b) parabolic

c) both (a) and (b) d) neither (a) nor (b)

81. Irregular variations in a time series are caused by:

a) lockouts and strikes b) epidemics

c) floods d) all the above

82. An additive model of a time series with the components T, S, C and I is

a) Y = T + S + C x I b) Y = T + S x C x I

c) Y = T + S + C + I d) Y = T + S x C + I

83. A multiplicative model of a time series with components T, S, C and I is

a) Y = T x S x C x I b) T = Y / [S x C x I]

c) C x I = Y / [T x S] d) all the above

84. A method full of subjectivity to find out the trend line is:

a) Semi-average method b) moving average method

c) free-hand method d) all the above

85. If the origin in a trend equation is shifted forward by 3 years, X in the

equation Y = a + bx will be replaced by:

a) X - 3 b) X + 3

c) 3X d) None of the above

86. If the origin in the trend equation Y = a + bx is shifted backward by 2

years, the variable X in the trend equation will be replaced by:

a) X - 2 b) X + 2

c) X/2 d) None of the above

87. If the trend line with 1975 as origin is Y = 20.6 + 1.68 X, the trend line

with origin 1971 is

a) Y = 20.6 + 6.72X b) Y = 13.88 + 1.68X

c) Y = 34.61 + 1.68X d) None of the above

88. The equation Y = βx represents

a) Compertz Curve b) Exponential Curve

c) Logarithmic Curve d) None of these

89. Simple average method is used to calculate

a) trend values b) Cyclic variation

c) Seasonal indices d) None of these


APPLIED STATISTICS

90. Irregular variations are

a) regular b) cyclic

c) episodic d) all the above

91. Simple average method for finding out seasonal indices is good when

a) The time series is free from trend

b) The time series has no cycle effect

c) The time series has no trend and cyclic variation

d) The series has all the components of the time series present

92. The moving average in a time series are free from the influences of:

a) seasonal and cyclic variations b) seasonal and irregular variations

c) trend and cyclical variations d) trend and random variations

93. Value of b in the trend line Y = a + bX is

a) always positive b) always negative

c) both positive and negative d) none of these

94. A time series consist of.

a) long-term changes b) short term variations

c) Irregular variations d) all the above

95. For the given five values 15, 24, 18, 33, 42 the three years moving

averages are:

a) 19, 22, 33 b) 19, 25, 31

c) 19, 30, 31 d) none of the above

96. Variation in the items produced in a factory may be due to:

a) chance factors b) assignable causes

c) both (a) and (b) d) none of the above

97. Chance or random variation in the manufactured product is:

a) Controlable b) Not controlable

c) both (a) and (b) d) none of the above

98. Variation due to assignable causes in the product occurs due to:

a) faulty process b) Carelessness of Operators

c) poor quality of raw materials d) all the above

99. The faults due to assignable causes:

a) can be removed b) cannot be removedc) can sometimes be removed d) all the above


APPLIED STATISTICS

100. Control charts in statistical quality control are meant for:

a) Describing the pattern of variation

b) Checking whether the variability in the product is within the

tolerance limits or not

c) Uncovering whether the variability in the product is due to

assignable causes or not

d) all the above.

101. Control charts consists of:

a) three control lines b) upper and lower control limits

c) the level of the process d) all the above

102.To control the quality of a specific resistance of a wire, we use

a) - Chart b) R - chart

c) both (a) and (b) d) none of these

103. The chart that are used to deal with the characteristics which are notpossible to measure, but can observe as absent or present from theproduct:

a) - Chart b) P - Chart

c) R – Chart d) C - Chart

104.The chart which is applicable when the quality of product is a discrete

variable:

a) - Chart b) P - Chart

c) R – Chart d) C - Chart

105.The control limits for chart is

a) LC = μ - 3 √ & UC = μ + 3 √b) LC = μ - 3 √ & UC = μ - 3 √c) LC = μ + 3 √ & UC = μ + 3 √d) LC = μ + 3 √ & UC = μ - 3 √

106.The control limits for R-Chart is

a) LC = (1 – 3C) & UC = (1 + 3C)

b) LC = (3 – C) & UC = (1 + 3C)

c) LC = (1 – 3C) & UC = (3 + C)

d) LC = (3 – C) & UC = (3 + C)


APPLIED STATISTICS

107.The control limits for P – Chart is:

a) UC = P - 3 ( − )/ and LC = P - 3 ( − )/b) UC = P + 3 ( − )/ and LC = P - 3 ( − )/c) UC = P + 3 ( − ) and LC = P - 3 ( − )/d) UC = P + 3 ( − )/ and LC = P - 3 ( − )

108. The control limits for C-chart is

a) UCL = ^ + 4 ^ and LCL = ^ - 4 ^b) UCL = ^ + 3 ^ and LCL = ^ - 3 ^c) UCL = ^ + 2 ^ and LCL = ^ - 2 ^d) UCL = ^ + ^ and LCL = ^ - ^

109. Statistical quality control methods are extensively used in industrial

production process because of

a) Reduction in cost b) Greater efficiency

c) Timely detection of faults d) all the above

110.For a normal population probability of any point falling outside the

3 – σ control line is

a) 0.5 b) 0.05

c) 0.02 d) 0.0027

111. Analysis of variance is used to test:

a) Means of three or more populations

b) Variance of three or more population

c) Difference between 2 means

d) Difference between 2 variances

112.The assumption used in ANOVA is:

a) The population from which the samples were obtained must be

normally distributed

b) The samples must be independent

c) The variances of the population must be equal

d) all the above


APPLIED STATISTICS

113. In ANOVA we use

a) t - distribution b) Ψ 2 - distribution

c) F – distribution d) none of these

114. Consider K independent samples each containing n1, n2, …………… nk

items such that n1 + n2 + ….. + nk = n. In ANOVA we use F-distribution

with degrees of freedom.

a) K – 1, n - K b) K – 1, n - 1

c) K – n, n - K d) n – K, K - 1

115. In one way ANOVA, with usual notation, the error degrees of freedom is

a) n - 1 b) n - K

c) K - 1 d) K - n

116. In one way ANOVA, given SSB = 2580, SSE = 1656 K = 4, n = 20 then

the value of F is

a) 7.3 b) 8.3

c) 9.3 d) 10.3

117. In two way ANOVA with m rows and n colums, the error degrees of

freedom is

a) m - 1 b) (n – 1) m

c) (m – 1)n d) (m – 1)(n – 1)

118.In one way ANOVA, the calculated F value is less than the table F value

then:

a) Accept the hypothesis that the population means are equal

b) Reject the hypothesis that the population means are equal

c) Sometimes accept and sometimes reject the null hypothesis

d) All the above.

119.In two way ANOVA with m = 5, n = 4. Then total degrees of freedom is

a) 20 b) 21

c) 19 d) 18

120.In one way ANOVA with total number of observation is 15 with 5

treatments then total degrees of freedom is

a) 75 b) 3

c) 10 d) 14


APPLIED STATISTICS

ANSWER KEY

1.b 2.b 3.b 4.c 5.c 6.d

7.c 8.a 9.b 10.c 11.d 12.b

13.a 14.c 15.a 16.c 17.c 18.a

19.c 20.d 21.b 22.a 23.a 24.a

25.a 26.b 27.b 28.c 29.a 30.c

31.a 32.d 33.d 34.b 35.c 36.a

37.b 38.b 39.a 40.d 41.c 42.d

43.a 44.c 45.d 46.a 47.b 48.c

49.b 50.a 51.c 52.d 53.d 54.d

55.b 56.b 57.c 58.c 59.b 60.d

61.c 62.b 63.a 64.c 65.a 66.d

67.a 68.b 69.a 70.c 71.d 72.d

73.c 74.b 75.b 76.d 77.b 78.c

79.a 80.c 81.d 82.c 83.d 84.c

85.b 86.a 87.b 88.b 89.c 90.c

91.c 92.b 93.c 94.d 95.b 96.c

97.b 98.d 99.a 100.d 101.a 102.c

103.b 104.d 105.a 106.a 107.b 108.b

109.d 110.d 111.a 112.d 113.c 114.a

115.b 116.b 117.d 118.a 119.c 120.d

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