Business Statistics Online MCQ Set 6

QN01. The measures used to calculate the variation present among the observations relative to their average is called:

  1. Coefficient of kurtosis
  2. Absolute measures of dispersion
  3. Quartile deviation
  4. Relative measures of dispersion
Answer

(D)Relative measures of dispersion

QN02. If there are many extreme scores on all examination, the dispersion is:

  1. Large
  2. Small
  3. Normal
  4. Symmetric
Answer

(A)Large

QN03. In quality control of manufactured items, the most common measure of dispersion is:

  1. Range
  2. Average deviation
  3. Standard deviation
  4. Quartile deviation
Answer

(A)Range

QN04. If Y = aX ± b, where a and b are any two numbers and a ∦ 0, then the range of Y values will be:

  1. Range(X)
  2. a range(X) + b
  3. a range(X) - b
  4. ∣a∣ range(X)
Answer

(D)∣a∣ range(X)

QN05. Which measure of dispersion can be computed in case of open-end classes?

  1. Standard deviation
  2. Range
  3. Quartile deviation
  4. Coefficient of variation
Answer

(C)Quartile deviation

QN06. If Y = aX ± b, where a and b are any two numbers but a ∦ 0, then M.D(Y) is equal to:

  1. M.D(X)
  2. M.D(X) ± b
  3. ∣a∣ M.D(X)
  4. M.D(Y) + M.D(X)
Answer

(C)∣a∣ M.D(X)

QN07. If the dispersion is small, the standard deviation is:

  1. Large
  2. Zero
  3. Small
  4. Negative
Answer

(C)Small

QN08. The standard deviation one distribution dividedly the mean of the distribution and expressing in percentage is called:

  1. Coefficient of Standard deviation
  2. Coefficient of skewness
  3. Coefficient of quartile deviation
  4. Coefficient of variation
Answer

(D)Coefficient of variation

QN09. If Y = aX + b, where a and b are any two numbers but a ∦ 0, then S.D(Y) is equal to:

  1. S.D(X)
  2. a S.D(X)
  3. ∣a∣ S.D(X)
  4. a S.D(X) + b
Answer

(C)∣a∣ S.D(X)

QN10. Standard deviation is always calculated from:

  1. Mean
  2. Median
  3. Mode
  4. Lower quartile
Answer

(A)Mean

QN11. The variance of 19, 21, 23, 25 and 27 is 8. The variance of 14, 16, 18, 20 and 22 is:

  1. Greater than 8
  2. 8
  3. Less than 8
  4. 8 - 5 = 3
Answer

(B)8

QN12. Var(X) = 4 and Var(Y) =9. If X and Y are independent random variable then Var(2X + Y) is:

  1. 13
  2. 17
  3. 25
  4. -1
Answer

(C)25

QN13. The moments about origin are called:

  1. Moments about zero
  2. Raw moments
  3. Both (a) and (b)
  4. (d)Neither (a) nor (b)
Answer

(C)Both (a) and (b)

QN14. The first moment about X = 0 of a distribution is 12.08. The mean is:

  1. 10.80
  2. 10.08
  3. 12.08
  4. 12.88
Answer

(C)12.08

QN15. In a symmetrical distribution, the coefficient of skewness will be:

  1. 0
  2. Q1
  3. Q3
  4. 1
Answer

(A)0

QN16. If mean=20, median=16 and standard deviation=2, then coefficient of skewness is:

  1. 1
  2. 2
  3. 4
  4. -2
Answer

(B)2

QN17. If the sum of deviations from median is not zero, then a distribution will be:

  1. Symmetrical
  2. Skewed
  3. Normal
  4. All of the above
Answer

(B)Skewed

QN18. The lower and upper quartiles of a distribution are 80 and 120 respectively, while median is 100. The shape of the distribution is:

  1. Positively skewed
  2. Negatively skewed
  3. Symmetrical
  4. Normal
Answer

(C)Symmetrical

QN19. The value of β2 can be:

  1. Less than 3
  2. Greater than 3
  3. Equal to 3
  4. All of the above
Answer

(D)All of the above

QN20. The degree to which numerical data tend to spread about an average value called:

  1. Constant
  2. Flatness
  3. Variation
  4. Skewness
Answer

(C)Variation

QN21. Given below the four sets of observations. Which set has the minimum variation?

  1. 46, 48, 50, 52, 54
  2. 30, 40, 50, 60, 70
  3. 40, 50, 60, 70, 80
  4. 48, 49, 50, 51, 52
Answer

(D)48, 49, 50, 51, 52

QN22. The range of the values -5, -8, -10, 0, 6, 10 is:

  1. 0
  2. 10
  3. -10
  4. 20
Answer

(D)20

QN23. The mean deviation is minimum when deviations are taken from:

  1. Mean
  2. Mode
  3. Median
  4. Zero
Answer

(C)Median

QN24. The sum of squares of the deviations is minimum, when deviations are taken from:

  1. Mean
  2. Mode
  3. Median
  4. Zero
Answer

(A)Mean

QN25. The value of standard deviation changes by a change of:

  1. Origin
  2. Scale
  3. Algebraic signs
  4. None
Answer

(B)Scale

QN26. For two independent variables X and Y if S.D(X) = 1 and S.D(Y) = 3, then Var(3X - Y) is equal to:

  1. 0
  2. 6
  3. 18
  4. 12
Answer

(C)18

QN27. Which of the following statements is false?

  1. The standard deviation is independent of change of origin
  2. If the moment coefficient of kurtosis β2 = 3, the distribution is mesokurtic or normal.
  3. If the frequency curve has the same shape on both sides of the centre line which divides the curve into
    two equal parts, is called a symmetrical distribution.
  4. Variance of the sum or difference of any two variables is equal to the sum of their respective variances
Answer

(D)Variance of the sum or difference of any two variables is equal to the sum of their respective variances

QN28. The mean of an examination is 69, the median is 68, the mode is 67, and the standard deviation is 3. The measures of variation for this examination is:

  1. 67
  2. 68
  3. 69
  4. 3
Answer

(D)3

QN29. If X̄ = Rs.20, S= Rs.10, then coefficient of variation is:

  1. 45%
  2. 50%
  3. 60%
  4. 65%
Answer

(B)50%

QN30. The second moment about arithmetic mean is 16, the standard deviation will be:

  1. 16
  2. 4
  3. 2
  4. 0
Answer

(B)4

QN31. First two moments about the value 2 of a variable are 1 and 16. The variance will be:

  1. 13
  2. 15
  3. 16
  4. Difficult to tell
Answer

(B)15

QN32. Departure from symmetry is called:

  1. Second moment
  2. Kurtosis
  3. Skewness
  4. Variation
Answer

(C)Skewness

QN33. If mean=50, mode=40 and standard deviation=5, the distribution is:

  1. Positively skewed
  2. Negatively skewed
  3. Symmetrical
  4. Difficult to tell
Answer

(A)Positively skewed

QN34. In case of positively skewed distribution, the extreme values lie in the:

  1. Middle
  2. Left tail
  3. Right tail
  4. Anywhere
Answer

(C)Right tail

QN35. Which of the following is correct in a negatively skewed distribution?

  1. The arithmetic mean is greater than the mode
  2. The arithmetic mean is greater than the median
  3. (Q3 - Median) = (Median - Q1)
  4. (Q3 - Median) < (Median - Q1)
Answer

(D)(Q3 - Median) < (Median - Q1)

QN36. The measure of dispersion which uses only two observations is called:

  1. Range
  2. Quartile deviation
  3. Mean deviation
  4. Standard deviation
Answer

(A)Range

QN37. If Q3=20 and Q1=10, the coefficient of quartile deviation is:

  1. 3
  2. 1/3
  3. 2/3
  4. 1
Answer

(B)1/3

QN38. The average of squared deviations from mean is called:

  1. Mean deviation
  2. Variance
  3. Standard deviation
  4. Coefficient of variation
Answer

(B)Variance

QN39. Which of the following is a unit free quantity:

  1. Range
  2. Standard deviation
  3. Coefficient of variation
  4. Arithmetic mean
Answer

(C)Coefficient of variation

QN40. Three factories A, B, C have 100, 200 and 300 workers respectively. The mean of the wages is the same in the three factories. Which of the following statements is true?

  1. There is greater variation in factory C.
  2. Standard deviation in. factory A is the smallest.
  3. Standard deviation in all the three factories are equal
  4. None of the above
Answer

(D)None of the above

QN41. Which of the following measures of dispersion is independent of the units employed?

  1. Coefficient of variation
  2. Quartile deviation
  3. Standard deviation
  4. Range
Answer

(A)Coefficient of variation

QN42. The first and second moments about arbitrary constant are -2 and 13 respectively, The standard deviation will be:

  1. -2
  2. 3
  3. 9
  4. 13
Answer

(B)3

QN43. If the third central is negative, the distribution will be:

  1. Symmetrical
  2. Positively skewed
  3. Negatively skewed
  4. Normal
Answer

(C)Negatively skewed

QN44. The lack of uniformity or symmetry is called:

  1. Skewness
  2. Dispersion
  3. Kurtosis
  4. Standard deviation
Answer

(A)Skewness

QN45. If mean=10, median=8 and standard deviation=6, then coefficient of skewness is:

  1. 1
  2. -1
  3. 2/6
  4. 2
Answer

(A)1

QN46. In a symmetrical distribution Q1 = 20 and median= 30. The value of Q3 is:

  1. 50
  2. 35
  3. 40
  4. 25
Answer

(C)40

QN47. If there are ten values each equal to 10, then standard deviation of these values is:

  1. 100
  2. 20
  3. 10
  4. 0
Answer

(D)0

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