SSC CGL 2016 Tier II — Statistics — 2 December 2016

Statistics

1. 3. In the construction of cost of living index, commodities are selected by :

   • (a) simple random sampling
   • (b) stratified random sampling
   • (c) systematic sampling
   • (d) judgement/ purposive sampling.
   उत्तर देखें

   उत्तर: (d)

2. 4. x और y असहसंबद्ध चर हैं तो इसका यह अर्थ हुआ कि -

   • (a) उनके बीच कोई रेखीय संबंध नहीं है
   • (b) उनके बीच कोई द्विघाती संबंध नहीं है
   • (c) उनके बीच कोई लघुगणकीय संबंध नहीं है
   • (d) उनके बीच कोई त्रिकोणमीतीय संबंध नहीं है
   उत्तर देखें

   उत्तर: (a)

3. 5. In simple random sampling of n units from a population of N units the quantity [1 - (n/N)] is called the

   • (a) sampling fraction
   • (b) expansion factor
   • (c) finite population correction factor
   • (d) degrees of freedom
   उत्तर देखें

   उत्तर: (c)

4. 6. The coefficient of range of the weights of 10 students from the following data: 41,20,15,65,73,84,53,35,71,55 is

   • (a) 1.433
   • (b) 0.696
   • (c) 0.675
   • (d) 1
   उत्तर देखें

   उत्तर: (b)

5. 7. Consider simple random sampling with replacement from a population of size N. The number of samples of size n is

   • (a) NPn
   • (b) NCn
   • (c) Nn
   • (d) None of the options
   उत्तर देखें

   उत्तर: (c)

6. 9. If a population consists of 10 units and SRSWOR is adopted, the probability of selecting a specified sample of 2 units is :

   • (a) 1/10
   • (b) 1/45
   • (c) 1/90
   • (d) 1/100
   उत्तर देखें

   उत्तर: (b)

7. 11. Suppose a person would earn Rs. 10,000 in base period. Suppose the cost of living index increases by 20% over base period. Then the employers of that person increase his salary by Rs. 1500. Which of the following option is TRUE?

   • (a) He is just able to maintain the same standard of living as in base period.
   • (b) He should claim Rs 500/- as Dearness Allowance.
   • (c) He can improve his standard of living as compared to base period.
   • (d) He should claim Rs 2,000 as Dearness Allowance.
   उत्तर देखें

   उत्तर: (b)

8. 12. The correlation coefficient between two variables X and Y is 0.4. The correlation coefficient between 2X and (-Y) will be :

   • (a) 0.4
   • (b) -0.8
   • (c) -0.4
   • (d) 0.8
   उत्तर देखें

   उत्तर: (c)

9. 13. निम्नलिखित में से गलत विकल्प मालूम करे: (CLI - जीवन निर्वाह सूचकांक)

   • (a) यदि ग्रुप का सूचकांक K गुणा बढ़ता है तो निर्वाह सूचकांक भी बढ़ता है।
   • (b) यदि ग्रुप के सभी सूचकांक एक स्थिर राशि में बढ़ते हैं तो निर्वाह सूचकांक में कोई परिवर्तन नहीं होता है।
   • (c) निर्वाह सूचकांक मुद्रा की क्रय शक्ति के निर्धारण में सहायक होता है।
   • (d) निर्वाह सूचकांक पर विचार करके महंगाई भत्ता नियत किया जाता है।
   उत्तर देखें

   उत्तर: (b)

10. 16. यदि संग्रहित आंकड़ों को समय के संदर्भ में समूह में रखा जाता है तो उसे

    • (a) मात्रात्मक वर्गीकरण कहते है ?
    • (b) गुणात्मक वर्गीकरण
    • (c) भौगोलिक वर्गिकरण
    • (d) कालानुक्रमी वर्गीकरण
    उत्तर देखें

    उत्तर: (d)

11. 19. Which type of sampling is one where only the first sample unit is selected at random and the remaining units are automatically selected in a definite sequence at equal spacing from one another. It is :

    • (a) Multi stage sampling
    • (b) Quota sampling
    • (c) Systematic sampling
    • (d) Area sampling
    उत्तर देखें

    उत्तर: (c)

12. 21. A random sample of size n is drawn from a population of size N by SRSWOR method. Then the standard error of sample mean will be zero if n is

    • (a) N - 1
    • (b) N
    • (c) tending to infinity
    • (d) none of the options
    उत्तर देखें

    उत्तर: (b)

13. 22. The coefficient of correlation between two variables X and Y is 0.48. The covariance is 36. The variance of X is 16. The standard deviation of Y is :

    • (a) 10.15
    • (b) 13.32
    • (c) 16.5
    • (d) 18.75
    उत्तर देखें

    उत्तर: (d)

14. 23. If 4,5,6,6,6,6,6,6,6,7 be a random sample from a Poisson population with parameter λ, then an unbiased estimate of λ is :

    • (a) 4.2
    • (b) 5
    • (c) 5.8
    • (d) 6
    उत्तर देखें

    उत्तर: (c)

15. 24. There are 35 students in a hostel. If the number of students increases by 7, the expenses of the hostel increases by Rs. 42 per day while the average expenditure per head diminishes by Re. 1. The original expenditure of the hostel is:

    • (a) Rs. 380
    • (b) Rs. 420
    • (c) Rs. 490
    • (d) Rs. 510
    उत्तर देखें

    उत्तर: (b)

16. 28. Which of the following is a method of collection of primary data?

    • (a) Direct personal interview
    • (b) Indirect personal interview
    • (c) Schedules through enumerators
    • (d) All of the options
    उत्तर देखें

    उत्तर: (d)

17. 30. If the regression line of Y on X is Y =30 - 0.9X and the standard deviations are Sx = 2 and Sy = 9, then the value of the correlation coefficient rxy is :

    • (a) -0.3
    • (b) -0.2
    • (c) 0.2
    • (d) 0.3
    उत्तर देखें

    उत्तर: (b)

18. 31. A coin is tossed repeatedly until a head appears. If 'p' be the probability of getting a head in any toss and x be the number of tosses required to get the first head then which of the following statement is true:

    • (a) x is an unbiased estimator of p
    • (b) 1/x is an unbiased estimator of 1/p
    • (c) x is an unbiased estimator of 1/p
    • (d) 1/x is an unbiased estimator of p
    उत्तर देखें

    उत्तर: (c)

19. 34. For a trivariate distribution, if the correlation coefficients are r12 = r13 = r23 = r, -1 < r < 1, then r12.3 is:

    • (a) (1-r)/r
    • (b) (1+ r)/r
    • (c) r / (1+r)
    • (d) r / (1-r)
    उत्तर देखें

    उत्तर: (c)

20. 35. An observation is drawn from an experimental distribution with mean θ, if the observation is found to be 2, and we test H0: θ>1 against H1: θ>1 with level e-3 then

    • (a) H0 will be rejected
    • (b) H0 will be accepted H0
    • (c) test will be of power 0.5
    • (d) test will be of power 0.9
    उत्तर देखें

    उत्तर: (b)

21. 36. The average of 25 numbers is 36. If the average of first 13 numbers is 32 and that of the last 13 numbers is 39, then the 13th number is

    • (a) 27
    • (b) 33
    • (c) 23
    • (d) 21
    उत्तर देखें

    उत्तर: (c)

22. 37. In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE= 399.6 The MSE for the analysis would be :

    • (a) 14.8
    • (b) 133.2
    • (c) 44.4
    • (d) 39.9
    उत्तर देखें

    उत्तर: (a)

23. 39. In an ANOVA problem for one-way classified data, with three classes and three observations per class, if the F- value is 1.5 and the total sum of squares is 18, then the mean square between classes is :

    • (a) 2
    • (b) 3
    • (c) 4
    • (d) 5
    उत्तर देखें

    उत्तर: (b)

24. 42. If a data set contains n paired values on two variables x(independent) and y(dependent), then their plot is called :

    • (a) Dendogram
    • (b) Point diagram
    • (c) Scatter diagram
    • (d) Correlogram
    उत्तर देखें

    उत्तर: (c)

25. 43. An ANOVA procedure is used for data obtained from five populations. Five samples were taken from the 5 populations each comprising of 20 observations. The degree of freedom associated with F is :

    • (a) 5, 95
    • (b) 5, 99
    • (c) 4, 99
    • (d) 4, 95
    उत्तर देखें

    उत्तर: (d)

26. 44. 'सांख्य' प्रकाशन से लिए गए आंकड़ों को

    • (a) प्राथमिक आंकड़े माना जाएगा ?
    • (b) गौण आंकड़े
    • (c) या (A) या (B)
    • (d) विकल्पों में से कोई नहीं
    उत्तर देखें

    उत्तर: (b)

27. 46. विचरण के संबंध में निम्नलिखित में से कौन सा कथन गलत है ?

    • (a) विचरण के संयोग हेतुओं से बचा जा सकता है
    • (b) संयोग हेतु मानव के नियंत्रण से बाहर है
    • (c) विचरण के निर्देश्य कारणों से बचा जा सकता है
    • (d) निर्देश्य कारणों को मालूम किया जा सकता है और आंका जा सकता है
    उत्तर देखें

    उत्तर: (a)

28. 47. In the one-way analysis of variance model with k factors, let MSE denote the mean sum of squares due to error, MST denote the mean sum of squares due to factors, MTS denote the mean total sum of squares. For testing and homogeneity of the factor means, the test statistic is

    • (a) MSE / MST
    • (b) MSE / MTS
    • (c) MST / MTS
    • (d) MST / MSE
    उत्तर देखें

    उत्तर: (d)

29. 48. Suppose two distributions have the same mean, same standard deviation and are equally skewed, but the first distribution is more peaked than the other. This feature of the frequency distributions in which they are different are called :

    • (a) Central Tendency
    • (b) Dispersion
    • (c) Symmetry
    • (d) Kurtosis
    उत्तर देखें

    उत्तर: (d)

30. 49. समुह- माध्यो की समानता के परीक्षण के लिए किसी ANOVA में, कौन सा परीक्षण करना होता है ?

    • (a) मानक सामान्य परीक्षण
    • (b) काई- वर्ग परिक्षण
    • (c) टी- परिक्षण
    • (d) एफ- परिक्षण
    उत्तर देखें

    उत्तर: (d)

31. 50. If P(A ∩ B) = 1/2, P(Ac ∩ Bc) = 1/2 and 2P(A) = P(B) = p, then the value of p is :

    • (a) 1/4
    • (b) 1/2
    • (c) 1/3
    • (d) 2/3
    उत्तर देखें

    उत्तर: (d)

32. 51. मौसमी सूचकांक के लिए उपनति से अनुपात विधि से अच्छे परिणाम प्राप्त

    • (a) अवधि छमाही दी जाए होते है, यदि :
    • (b) अवधि अल्प कालिक हो
    • (c) अवधि दिर्घकालिक हो
    • (d) सभी विकल्प
    उत्तर देखें

    उत्तर: (b)

33. 52. In a class, there are 25 students whose average age decreases by 3 months when one student aged 22 years is replaced by a new student. The age of the new student is :

    • (a) 16 Yrs 2 months
    • (b) 20 Yrs 5 months
    • (c) 15 Yrs 9 months
    • (d) 18 Yrs 3 months
    उत्तर देखें

    उत्तर: (c)

34. 53. Based on results of 2 way ANOVA, the SSE was computed to be 139.4. If we ignore one of the factors and perform one way ANOVA using the same data, SSE will :

    • (a) increase
    • (b) decrease
    • (c) remain same
    • (d) Either (A) or (B)
    उत्तर देखें

    उत्तर: (a)

35. 54. If the annual trend of production (Y) of a certain commodity in a factory with origin 2,000 and X unit = one year is Y= 148.8 + 7.2X Then the monthly trend equation is :

    • (a) Y = 12.4 + 0.05X
    • (b) Y = 12.4 + 0.6X
    • (c) Y = 148.8 + 0.6X
    • (d) None of the options
    उत्तर देखें

    उत्तर: (a)

36. 55. If A1, A2 and A3 are three independent events with P(A1) = 1/3, P(A2) = 1/4 and P(A3) = 2/5, then the probability that exactly one of the events occurs is :

    • (a) 3/20
    • (b) 1/10
    • (c) 9/20
    • (d) 3/10
    उत्तर देखें

    उत्तर: (c)

37. 56. If the trend line with 2008 as origin is Y= 20.6 + 1.68X, then the trend line with 2004 as origin is :

    • (a) Y = 34.61 + 1.68X
    • (b) Y = 20.6 + 6.72X
    • (c) Y = 13.88 + 1.68X
    • (d) None of the options
    उत्तर देखें

    उत्तर: (c)

38. 57. Moments are statistical constants from which we can find the different features of a distribution. Which one of the following is INCORRECT ?

    • (a) First Central Moment is the mean.
    • (b) Second Central moment is the variance.
    • (c) Second and Central Moments are needed to find skewness.
    • (d) Second and fourth central moments are needed to find the kurtosis.
    उत्तर देखें

    उत्तर: (a)

39. 58. If the equation of exponential trend with 2004 as origin is Y= 20(1.5)x , Then equation of the exponential trend with 2006 as origin is :

    • (a) Y = 20(1.5)x
    • (b) Y = 45(1.5)x
    • (c) Y = 8.89(1.5)x
    • (d) Y = 20/(1.5)x
    उत्तर देखें

    उत्तर: (b)

40. 59. A closet contains 8 pairs of shoes. If 4 shoes are chosen at random, then the probability that all the four shoes are of the same type (left or right) is :

    • (a) 1/13
    • (b) 2/13
    • (c) 3/13
    • (d) 4/13
    उत्तर देखें

    उत्तर: (a)

41. 60. Demand for seats in a university is at its highest in the fall; demand also trends to grow and fall off in 25 year waves. In time service forecasting, the former demand characteristic would be called_______ and the latter would be called ___________.

    • (a) seasonality; cyclicality
    • (b) cyclicality; seasonality
    • (c) randomality; seasonality
    • (d) seasonality; variability
    उत्तर देखें

    उत्तर: (a)

42. 61. Fill up the blank: The secular trend is the part of time points where more or less regular and _______ is observed showing either the tendency of growth or decline.

    • (a) long-term movement
    • (b) short-term movement
    • (c) oscillatory movement
    • (d) None of the options
    उत्तर देखें

    उत्तर: (a)

43. 63. In a multiplicative time series model, the seasonal indices computed by the ratio-to-trend method

    • (a) are alternate in sign
    • (b) add to 0
    • (c) add to 1
    • (d) multiply to 1
    उत्तर देखें

    उत्तर: (d)

44. 64. For two equally likely, exhaustive and independent events A and B, P(A ∩ B) is :

    • (a) 0
    • (b) 1
    • (c) 0.5
    • (d) 0.25
    उत्तर देखें

    उत्तर: (d)

45. 65. किसी योज्य काल श्रेणी से द्विधाती उपनति टूर करने के लिए डिफरेंसिंग का :

    • (a) प्रयोग नहीं किया जा सकता
    • (b) एक बार प्रयोग करना चाहिए
    • (c) दो बार प्रयोग करना चाहिए
    • (d) कम से कम तीन बार प्रयोग करना चाहिए
    उत्तर देखें

    उत्तर: (c)

46. 66. For four observations -1, 0, 1, 4, the measure of kurtosis equals

    • (a) 1
    • (b) 2
    • (c) 3
    • (d) 4
    उत्तर देखें

    उत्तर: (b)

47. 67. In multiplicative model of time series: Xt= Tt x St x Ct x It, where Tt , St , Ct , It are trend, seasonal, cyclical and irregular components, what can be said about the values of It?

    • (a) It is a random positive quantity
    • (b) It is a random negative quantity
    • (c) It is non-random positive real quantity
    • (d) It is a non-random negative quantity
    उत्तर देखें

    उत्तर: (a)

48. 68. Let A and B be the two possible outcomes of an experiment and suppose P(A) = 0.4, P(A U B) = 0.7 and P(B) = p, for what choice of p, A and B independent?

    • (a) 0.2
    • (b) 0.3
    • (c) 0.4
    • (d) 0.5
    उत्तर देखें

    उत्तर: (d)

49. 70. If the arithmetic mean is 26.8 and the median is 27.9, then the mode is :

    • (a) 27.3
    • (b) 29.3
    • (c) 30.1
    • (d) 27.4
    उत्तर देखें

    उत्तर: (c)

50. 71. In time series analysis which source of variation can be estimated by the ratio-to-trend method:

    • (a) trend
    • (b) seasonal variation
    • (c) seasonal index
    • (d) cyclical fluctuations
    उत्तर देखें

    उत्तर: (c)

51. 72. किसी ठेकेदार को नलकर्म का ठेका मिलेगा, इसकी प्रायिकता 2/3 है और बिजली का ठेका उसे नहीं दिया जाएगा इस बात की प्रायिकता 5/9 है। उसे कम से कम एक ठेका मिलेगा इसकी प्रायिकता यदि 4/5 हो तो उसे दोनों ठैके मिलने की प्रायिकता बताइए ?

    • (a) 13/45
    • (b) 14/45
    • (c) 16/45
    • (d) 17/45
    उत्तर देखें

    उत्तर: (b)

52. 74. If the actual values in time series from 2000 to 2006 are 77, 88, 94, 85, 91, 98 and 90 and the equation of the trend line with 2003 as origin is Y = 89 + 2X , then in case of multiplicative model, the trend eliminated values are :

    • (a) 0.93, 1.04, 1.08, 0.96, 1.0, 1.05, 0.95
    • (b) 1.08, 0.96, 0.92, 1.04, 1.0, 0.95, 1.05
    • (c) 0.93, 0.96, 1.08, 1.04, 1.0, 0.95, 1.05
    • (d) None of the options
    उत्तर देखें

    उत्तर: (a)

53. 75. A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36, then P(A) and P(B), respectively are :

    • (a) 0.6, 0.6
    • (b) 0.8, 0.2
    • (c) 0.4, 0.4
    • (d) 0.9, 0.4
    उत्तर देखें

    उत्तर: (c)

54. 76. काल श्रेणी में श्रंखलित आपेक्षिक निम्नलिखित में से किसका प्रभाव दूर करते हैं ?

    • (a) उपनति
    • (b) चक्रीय विचरण
    • (c) अनियमित विचरण
    • (d) सभी विकल्प
    उत्तर देखें

    उत्तर: (a)

55. 78. Let E and F be two events with P(E ) > 0, P(F|E) = 0.3 and P(E ∩ Fc) = 0.2. Then P(E) equals:

    • (a) 1/7
    • (b) 2/7
    • (c) 4/7
    • (d) 5/7
    उत्तर देखें

    उत्तर: (b)

56. 79. If the trend equation fitted from a data on production (y in kg) of a fertilizer factory is 26y = 5335 + 624t, where time(t) has unit 1 year. Then monthly increase in production of fertilisers (in kg) is:

    • (a) 5335
    • (b) 5335/26
    • (c) 624
    • (d) 2
    उत्तर देखें

    उत्तर: (d)

57. 80. The probability that an urn containing 5 balls contains only white balls if the first two balls drawn from it were found to be white is :

    • (a) 1/20
    • (b) 1/10
    • (c) 1/2
    • (d) 1/4
    उत्तर देखें

    उत्तर: (c)

58. 81. Suppose owing to increased prices, a consumer reduces consumption of all commodities by 10% compared to the previous year. If IL and IP are the Laspeyres' and Paasche's price indices for the current year with the previous year as base, then

    • (a) IP= 0.9 X IL
    • (b) IL= 0.9 X IP
    • (c) IP X IL = 0.9 X (100)2
    • (d) IP = IL
    उत्तर देखें

    उत्तर: (d)

59. 82. The standard deviation of a distribution is 5. The value of the fourth central moment, in order that the distribution be mesokurtic, should be :

    • (a) equal to 3
    • (b) greater than 1875
    • (c) equal to 1875
    • (d) less than 1875
    उत्तर देखें

    उत्तर: (c)

60. 83. If 'I' represents a cost of living index, then the purchasing power of money is proportional to

    • (a) I
    • (b) I2
    • (c) √I
    • (d) 1/ I
    उत्तर देखें

    उत्तर: (d)

61. 84. एकल संतत श्रेणी प्राप्त

    • (a) आधार परिवर्तन करने के लिए सूचकांकों की दो या अधिक अतिव्यापी श्रंखलाओं के संयोजन की प्रणाली को कहते हैं ?
    • (b) समबंधन
    • (c) अपस्फीतन
    • (d) विकल्पों में से कोई नहीं
    उत्तर देखें

    उत्तर: (b)

62. 85. The formula for calculating an index number should be such that it gives the same ratio between one point of comparison and the other, no matter which of the two is taken as the base or putting it another way, the index number reckoned forward should be reciprocal of the one reckoned backwards'- which test of consistency of index number is this ?

    • (a) Unit Test
    • (b) Time Reversal Test
    • (c) Circular Test
    • (d) Factor Reversal Test
    उत्तर देखें

    उत्तर: (b)

63. 86. Event S and T are independent with P(S) < P(T), P(S ∩ T) = 6/25 and P(S|T) + P(T|S) = 1. Then P(S) is :

    • (a) 6/25
    • (b) 3/5
    • (c) 1/5
    • (d) 2/5
    उत्तर देखें

    उत्तर: (d)

64. 87. Initially there are 9 workers, all being paid a uniform wage. Later a 10th worker is added whose wage rate is Rs 20 less than for the others. The average wage gets :

    • (a) decreased by Rs 20 20
    • (b) decreased by Rs 10 10
    • (c) remains unchanged
    • (d) decreased by Rs 2 2
    उत्तर देखें

    उत्तर: (d)

65. 90. For a frequency distribution of a variable x, mean = 32, median = 30. The distribution is :

    • (a) Positively skewed
    • (b) Negatively skewed
    • (c) Mesokurtic
    • (d) Platykurtic
    उत्तर देखें

    उत्तर: (a)

66. 91. It is known from past experience that in a certain plant there are on the average 4 industrial accidents per month. The probability that in a given month there will be less than 4 accidents is : (e-4 = 0.0183)

    • (a) 0.398
    • (b) 0.433
    • (c) 0.442
    • (d) 0.465
    उत्तर देखें

    उत्तर: (b)

67. 94. In a negatively skewed distribution

    • (a) Mean > Mode > Median
    • (b) Mode > Median > Mean
    • (c) Mean > Median > Mode
    • (d) Mode < Median > Mean
    उत्तर देखें

    उत्तर: (b)

68. 95. Let x ~ Binomial (5,0.6) and Y ~ Poisson (2) be independent. Then P(xy = 0) equals :

    • (a) e-2. (0.4)5
    • (b) e-2 + (0.4)5
    • (c) e-2 + (0.4)5- e-2. (0.4)5
    • (d) e-2. (0.6)5 + (1-e-2)(0.4)5
    उत्तर देखें

    उत्तर: (b)

69. 96. The mean and standard deviation of a variable x are 36 and 4 respectively. Then the mean and standard deviation of [50 - (x/4)], respectively are :

    • (a) 41, 1
    • (b) 29, 2
    • (c) 40, 1
    • (d) 39, 4
    उत्तर देखें

    उत्तर: (a)

70. 98. If a variable has three values -k, 0 and 3k with corresponding frequencies as 3k, 2k and k respectively, then the value of coefficient of skewness b1 is :

    • (a) 2K
    • (b) 2
    • (c) 1/2
    • (d) K/2
    उत्तर देखें

    उत्तर: (b)

71. 100. If μr be the rth order central-moment of a population μ0, μ1 and μ2 are : (where, σ = standard deviation)

    • (a) 0, 1, σ2
    • (b) 1, 0, σ2
    • (c) 1, 1, σ
    • (d) 1, 0, σ
    उत्तर देखें

    उत्तर: (b)