Measures of Dispersion Objective Questions Answers for Practice

76. If Y = aX ± b, where a and b are any two constants and a ≠ 0, then Vat (Y) is equal to:

1. a² Var(X) – b
2. a² Var(X)
3. a Var(X)
4. a Var(X) + b

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

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

78. The ratio of the standard deviation to the arithmetic mean expressed as a percentage is called:

1. Coefficient of kurtosis
2. Coefficient of variation
3. Coefficient of standard deviation
4. Coefficient of skewness

79. Which of the following statements is correct?

1. The second moment about origin equals variance
2. The variance is positive quantity and is expressed in square of the units of the observations
3. The standard deviation of a constant is equal to unity
4. The sum of absolute deviations is minimum if these deviations are taken from the mean.

80. Which of the following statements is false?

1. 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.
2. Variance of the sum or difference of any two variables is equal to the sum of their respective variances
3. The standard deviation is independent of change of origin
4. If the moment coefficient of kurtosis β2 = 3, the distribution is mesokurtic or normal.

81. If Var(X) = 25, then is equal to:

1. 25
2. 5
3. 15-Feb
4. 50

82. To compare the variation of two or more than two series, we use

1. Coefficient of variation
2. Coefficient of skewness
3. Combined standard deviation
4. Corrected standard deviation

83. The standard deviation of -5, -5, -5, -5, 5 is:

1. -25
2. -5
3. 5

84. Standard deviation is always calculated from:

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

85. 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. 69
2. 3
3. 67
4. 68

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

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

87. In a set of observations the variance is 50. All the observations are increased by 100 %. The variance of the increased observations will become:

1. 100
2. No change
3. 50
4. 200

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