وَأَحْصَىٰ كُلَّ شَيْءٍ عَدَدًا
"And He has enumerated everything in numbers." (Allah perfectly counts and knows the exact measure of all creations).
Q1. Scatter of observations around their centre is
called:
A. Dispersion
B. Spread
C. Variability
D. All of these ✓ Correct Answer
Explanation: Dispersion, spread, and variability are all synonyms used
for the same concept — the scattering of data around its centre.
Q2. A measure indicating the amount of scatter about
the centre is called a measure of:
A. Average
B. Dispersion ✓ Correct Answer
C. Skewness
D. Kurtosis
Explanation: A measure that quantifies how spread out the data is, is
called a measure of dispersion.
Q3. The highest degree of concentration occurs when
all observations are of:
A. Different magnitude
B. Different size
C. Different signs
D. The same size ✓ Correct Answer
Explanation: If every value is the same, there is no scatter at all —
maximum concentration, zero dispersion.
Q4. If all observations are of the same size, then
scatter is:
A. Zero ✓ Correct Answer
B. Positive
C. Negative
D. None
Explanation: Identical values have no spread between them, so the
scatter (dispersion) is zero.
Q5. The scatter (dispersion) could be zero if all
observations are:
A. Equal to the mean
B. Of the same size
C. Greater than the mean
D. Both (a) and (b) ✓ Correct Answer
Explanation: If every value equals the mean, they must all be equal in
size to each other — both descriptions are correct.
Q6. An average will exactly represent the
distribution if:
A. Scatter is zero ✓ Correct Answer
B. Scatter is positive
C. Scatter is negative
D. (a) and (c)
Explanation: Only when there's no dispersion (scatter = zero) does a
single average perfectly represent every observation.
Q7. An average will be less representative of the
data in case of:
A. Low dispersion
B. High dispersion ✓ Correct Answer
C. High concentration
D. Negative dispersion
Explanation: The more spread out the data (high dispersion), the less
a single average value represents individual observations.
Q8. Which type of measure of dispersion has the same
unit as the original data?
A. Relative
B. Absolute ✓ Correct Answer
C. Both (a) and (b)
D. None
Explanation: Absolute measures of dispersion (range, S.D., etc.) are
expressed in the same unit as the original data.
Q9. Which measure of dispersion has no unit?
A. Relative ✓ Correct Answer
B. Absolute
C. Both (a) and (b)
D. None
Explanation: Relative measures of dispersion are ratios/percentages,
so they are unit-less.
Q10. The relative measure of dispersion measures the
variation relative to:
A. Kurtosis
B. Some other measure of
dispersion
C. Skewness
D. Some average ✓ Correct Answer
Explanation: Relative dispersion expresses an absolute measure of
dispersion as a ratio of some average (e.g. coefficient of variation).
Q11. Which of the following is not a measure of
dispersion?
A. Mean ✓ Correct Answer
B. Range
C. Variance
D. Mean deviation
Explanation: Mean is a measure of central tendency, not of dispersion.
Q12. Measures of dispersion are changed by a change
in:
A. Origin
B. Scale
C. Unit of measurement
D. Both (b) and (c) ✓ Correct Answer
Explanation: Dispersion measures are affected when data is rescaled or
the unit of measurement changes, but not by a simple shift in origin.
Q13. The least possible value of a measure of
dispersion is:
A. Zero ✓ Correct Answer
B. Negative
C. Undefined
D. None
Explanation: Dispersion can never be negative — its smallest possible
value is zero (when there's no spread at all).
Q14. The difference between the largest and smallest
observations is called:
A. Quartile deviation
B. Mean deviation
C. Range ✓ Correct Answer
D. Standard deviation
Explanation: By definition, Range = Largest value − Smallest value.
Q15. Range is a measure of:
A. Location
B. Dispersion ✓ Correct Answer
C. Skewness
D. Kurtosis
Explanation: Range measures how spread out the data is, so it is a
measure of dispersion.
Q16. Range is a ___ measure of dispersion.
A. Absolute ✓ Correct Answer
B. Relative
C. Unit-less
D. None
Explanation: Range is expressed in the same unit as the data, making
it an absolute measure of dispersion.
Q17. Range is based on all the observations.
A. True
B. Sometimes true
C. Never ✓ Correct Answer
D. None
Explanation: Range depends only on the maximum and minimum values — it
ignores all the values in between, so this statement is never true.
Q18. Range of a constant is:
A. Negative
B. Positive
C. Zero ✓ Correct Answer
D. None
Explanation: If every value is the same constant, max = min, so the
range is zero.
Q19. Range of 7, 7, 7, 7 is:
A. 7
B. Positive
C. Negative
D. Zero ✓ Correct Answer
Explanation: Since all values are identical (7), max − min = 0.
Q20. Range depends on:
A. Two extreme values ✓ Correct Answer
B. Central half of the data
C. Negative values
D. None
Explanation: Range is calculated using only the two extreme values —
the maximum and minimum.
Q21. Range is independent of:
A. Scale
B. Origin ✓ Correct Answer
C. Unit of measurement
D. None
Explanation: Shifting all values by adding/subtracting a constant
(change of origin) doesn't affect the range, since both max and min shift
equally.
Q22. If a constant is added to all the values of a
variable, then range:
A. Increases
B. Decreases
C. Doesn't change ✓ Correct Answer
D. Is undefined
Explanation: Adding the same constant to every value shifts max and
min equally, so their difference (range) stays the same.
Q23. If all the values of a variable are multiplied
by a constant, then range is:
A. Increased by the constant
B. Multiplied by the
constant ✓ Correct Answer
C. Unchanged
D. Divided by the constant
Explanation: Multiplying every value by a constant multiplies both max
and min by that constant, so the range is also multiplied by it.
Q24. Range is not a stable measure of dispersion.
A. True ✓ Correct Answer
B. Undefined statement
C. False
D. None
Explanation: Since range depends only on two extreme values, it is
highly sensitive to outliers, making it an unstable measure.
Q25. Range is capable of further mathematical
treatment.
A. True
B. Sometimes true
C. False ✓ Correct Answer
D. None
Explanation: Range cannot be combined algebraically across sub-groups
the way variance can, so this statement is false.
Q26. Half the difference between q3 and q1 is called:
A. Quartile deviation ✓ Correct Answer
B. Mean deviation
C. Range
D. None
Explanation: Quartile Deviation = (Q3 − Q1) / 2, by definition.
Q27. Quartile deviation is also called:
A. Relative measure
B. Semi-inter-quartile
range ✓ Correct Answer
C. Average
D. Central tendency
Explanation: Quartile deviation is also known as the
semi-inter-quartile range.
Q28. Semi-inter-quartile range is a measure of:
A. Location
B. Dispersion
C. Scatter
D. Both (b) and (c) ✓ Correct Answer
Explanation: Since dispersion and scatter mean the same thing here,
quartile deviation measures both.
Q29. Quartile deviation of a constant is:
A. Zero ✓ Correct Answer
B. Positive
C. Negative
D. Doesn't exist
Explanation: If all values are the same constant, Q1 = Q3, so quartile
deviation = 0.
Q30. If a variable X contains only one value 'a' in
the domain, then Q.D =
A. Doesn't exist
B. Positive
C. Negative
D. Zero ✓ Correct Answer
Explanation: With only one distinct value, Q1 = Q3 = a, so the
quartile deviation is zero.
Q31. If y = bx + a, then Q.D(y) =
A. b · Q.D(x) ✓ Correct Answer
B. b · Q.D(x) + a
C. Q.D(x)
D. b² · Q.D(x)
Explanation: Quartile deviation depends only on the scale factor b,
and is unaffected by the shift 'a'.
Q32. Quartile deviation of 8, 8, 8 is:
A. Zero ✓ Correct Answer
B. Positive
C. Negative
D. None
Explanation: All values are equal, so Q1 = Q3, making the quartile deviation
zero.
Q33. Quartile deviation can never be:
A. Positive
B. Negative ✓ Correct Answer
C. Zero
D. None
Explanation: Since Q3 ≥ Q1 always, quartile deviation can never be
negative.
Q34. When all values are of the same size, then
quartile deviation is:
A. 1/2
B. 0 ✓ Correct Answer
C. -1/2
D. 3/4
Explanation: With identical values, Q1 equals Q3, so quartile
deviation is 0.
Q35. If two distributions have the same quartiles,
then their quartile deviation is:
A. The same ✓ Correct Answer
B. 0
C. Different
D. Negative
Explanation: Since Q.D. depends only on Q1 and Q3, equal quartiles
give the same quartile deviation.
Q36. If a constant is added to or subtracted from
each value of the observations, then quartile deviation is:
A. Increased
B. Unchanged ✓ Correct Answer
C. Zero
D. Undefined
Explanation: Adding/subtracting a constant shifts Q1 and Q3 equally,
so their difference (Q.D.) remains unchanged.
Q37. Quartile deviation is changed by a change of:
A. Origin
B. Scale ✓ Correct Answer
C. Location
D. Both (a) and (c)
Explanation: Q.D. only changes when data is rescaled (multiplied), not
when it's shifted (origin/location).
Q38. Which of these is not based on all the
observations?
A. Range
B. Quartile deviation
C. Both (a) and (b) ✓ Correct Answer
D. Variance
Explanation: Both range (uses only max/min) and quartile deviation
(uses only Q1, Q3) ignore most of the data.
Q39. Mean deviation is a ___ measure of dispersion.
A. Absolute ✓ Correct Answer
B. Relative
C. Both (a) and (b)
D. None
Explanation: Mean deviation is expressed in the same unit as the data,
so it's an absolute measure.
Q40. Mean deviation can't be:
A. Zero
B. Positive
C. Negative ✓ Correct Answer
D. None
Explanation: Since mean deviation uses absolute values of deviations,
it can never be negative.
Q41. Mean deviation can be calculated from:
A. Mean
B. Median
C. Mode
D. All of these ✓ Correct Answer
Explanation: Mean deviation can be computed by taking absolute deviations
from the mean, median, or mode.
Q42. Algebraic signs are ignored while calculating:
A. Quartile deviation
B. Mean deviation ✓ Correct Answer
C. Variance
D. Range
Explanation: Mean deviation uses absolute values of the deviations,
ignoring their positive/negative signs.
Q43. Mean deviation of a constant is:
A. Zero ✓ Correct Answer
B. Greater than zero
C. Negative
D. Undefined
Explanation: If all values are the same constant, every deviation from
the mean is zero, so mean deviation = 0.
Q44. If y = bx + a, then m.d.(y) =
A. |b| · m.d.(x) ✓ Correct Answer
B. |b| · m.d.(x) + a
C. m.d.(x) + a
D. None
Explanation: Mean deviation scales with the absolute value of b and is
unaffected by the shift a.
Q45. If X = a (a constant), then m.d.(x) =
A. Zero ✓ Correct Answer
B. a
C. Undefined
D. None
Explanation: All values equal a means every deviation is zero, giving
a mean deviation of zero.
Q46. Mean deviation of 5, 5, 5, 5, 5 is:
A. 5
B. Positive
C. Negative
D. Zero ✓ Correct Answer
Explanation: All values are identical, so every deviation from the
mean (5) is zero.
Q47. Mean deviation is independent of:
A. Origin
B. Scale
C. Location
D. Both (a) and (c) ✓ Correct Answer
Explanation: Mean deviation, like most dispersion measures, doesn't
change when data is simply shifted (origin/location), only when it's rescaled.
Q48. Mean deviation is based on:
A. All observations ✓ Correct Answer
B. Extreme observations only
C. Half of the observations
D. None
Explanation: Mean deviation uses the deviation of every single
observation from the average.
Q49. Mean deviation gives more information than the:
A. Range
B. Quartile deviation
C. Inter-quartile range
D. All of these ✓ Correct Answer
Explanation: Since mean deviation uses every observation (unlike range
or quartile-based measures), it captures more information than all of them.
Q50. Mean deviation is least when calculated from:
A. Mean
B. Mode
C. Median ✓ Correct Answer
D. Harmonic mean
Explanation: A key property: the sum of absolute deviations is
minimized when taken from the median.
Q51. The variance of a set of observations is defined
as the mean of squared deviations from the:
A. Mean ✓ Correct Answer
B. Median
C. Mode
D. Harmonic mean
Explanation: By definition, Variance = mean of the squared deviations
from the arithmetic mean.
Q52. Variance of 4, 4, 4, 4 is:
A. Zero ✓ Correct Answer
B. Positive
C. Negative
D. 4
Explanation: All values equal 4, so every squared deviation from the
mean is zero.
Q53. Variance can never be:
A. Zero
B. Positive
C. Negative ✓ Correct Answer
D. None
Explanation: Since variance is a mean of squared terms, it can never
be negative.
Q54. The standard deviation is the positive square
root of:
A. Mean
B. Variance ✓ Correct Answer
C. Mean deviation
D. None
Explanation: By definition, Standard Deviation = +√Variance.
Q55. If each of the observations of a variable equals
a constant, then S² is:
A. Zero ✓ Correct Answer
B. Negative
C. S
D. Doesn't exist
Explanation: Identical observations mean every deviation from the mean
is zero, so variance (S²) = 0.
Q56. If y = a + bx, then Sy = Sx when:
A. b = 0
B. b = 1 ✓ Correct Answer
C. b = -2
D. b = 2
Explanation: Since Sy = |b|·Sx, the standard deviations are equal only
when |b| = 1, e.g. b = 1.
Q57. For a normal distribution, x̄ ± 2s includes what
percentage of the observations?
A. 68.27%
B. 88.27%
C. 99.45%
D. 95.45% ✓ Correct Answer
Explanation: In a normal distribution, about 95.45% of observations
fall within 2 standard deviations of the mean.
Q58. For a normal distribution, x̄ ± 3s includes what
percentage of the observations?
A. 68.27%
B. 88.27%
C. 99.73% ✓ Correct Answer
D. 95.45%
Explanation: In a normal distribution, about 99.73% of observations
fall within 3 standard deviations of the mean.
Q59. If V(X) = 4, then V(2X + 4) =
A. 2
B. 4
C. 16 ✓ Correct Answer
D. Zero
Explanation: V(2X+4) = 2² · V(X) = 4 × 4 = 16, since adding a constant
doesn't affect variance.
Q60. If S(X) = 5, then S(2x + 5/5) =
A. 10 ✓ Correct Answer
B. 5
C. 15
D. 2
Explanation: S(2x + 1) = |2| · S(x) = 2 × 5 = 10, since the constant
term doesn't affect standard deviation.
Q61. The standard deviation is used to measure the
extent of:
A. Dispersion ✓ Correct Answer
B. Data location
C. Central tendency
D. None
Explanation: Standard deviation quantifies how spread out (dispersed)
the data is around the mean.
Q62. Standard deviation of 3, 3, 3 is:
A. 3
B. Zero ✓ Correct Answer
C. Negative
D. Positive
Explanation: All values are identical, so there's no deviation from
the mean at all — S.D. = 0.
Q63. If y = -10x, then Sy =
A. 10·Sx ✓ Correct Answer
B. 10²·Sx
C. Sx
D. None
Explanation: Sy = |-10| · Sx = 10·Sx, since standard deviation uses
the absolute value of the scaling constant.
Q64. The square root of variance is:
A. Mean deviation
B. Quartile deviation
C. Range
D. Standard deviation ✓ Correct Answer
Explanation: By definition, Standard Deviation = √Variance.
Q65. The coefficient of variation is used to measure:
A. Consistency ✓ Correct Answer
B. Skewness
C. Average
D. Kurtosis
Explanation: C.V. compares relative variability, so it's commonly used
to judge the consistency/uniformity of data.
Q66. The lack of uniformity or symmetry in a
distribution is called:
A. Skewness
B. Symmetry
C. Asymmetry
D. Both (a) and (c) ✓ Correct Answer
Explanation: Skewness and asymmetry both describe the same lack of
symmetry in a distribution.
Q67. If mean > median > mode, then the
distribution is:
A. Normal
B. Negatively skewed
C. Positively skewed ✓ Correct Answer
D. Symmetrical
Explanation: When the mean is pulled to the right of median and mode,
the distribution is positively skewed.
Q68. If mean = 60 and mode = 50, then the
distribution is:
A. Positively skewed ✓ Correct Answer
B. Negatively skewed
C. Symmetrical
D. Both (a) and (b)
Explanation: Since mean (60) is greater than mode (50), the
distribution is positively skewed.
Q69. If mean < median < mode, then the
distribution is:
A. Normal
B. Negatively skewed ✓ Correct Answer
C. Positively skewed
D. Symmetrical
Explanation: When the mean is pulled to the left of median and mode,
the distribution is negatively skewed.
Q70. If mean = 50 and mode = 60, then the
distribution is:
A. Positively skewed
B. Negatively skewed ✓ Correct Answer
C. Symmetrical
D. Both (a) and (b)
Explanation: Since mean (50) is less than mode (60), the distribution
is negatively skewed.
Q71. If mean = median = mode, then the distribution
is:
A. Skewed
B. Negatively skewed
C. Positively skewed
D. Symmetrical ✓ Correct Answer
Explanation: Equal mean, median, and mode is the hallmark of a
perfectly symmetrical distribution.
Q72. A symmetrical distribution has mean equal to 4.
Its mode will be:
A. Less than 4
B. 4 ✓ Correct Answer
C. Greater than 4
D. None
Explanation: In a symmetrical distribution, mean = median = mode, so
the mode also equals 4.
Q73. If Q3 − median > median − Q1, the
distribution is:
A. Normal
B. Negatively skewed
C. Positively skewed ✓ Correct Answer
D. Symmetrical
Explanation: A larger gap on the upper side (Q3 side) than the lower
side indicates a longer right tail — positively skewed.
Q74. In a symmetrical distribution:
A. Mean > median > mode
B. Mean < median < mode
C. Mean = median = mode ✓ Correct Answer
D. None
Explanation: The defining property of a symmetrical distribution is
that mean, median, and mode all coincide.
Q75. Which of the following is correct for a
negatively skewed distribution?
A. A.M. is greater than mode
B. A.M. is less than
mode ✓ Correct Answer
C. A.M. is greater than median
D. None
Explanation: In a negatively skewed distribution, the mean is pulled
below the mode by the long left tail.
Q76. The word skewness means a lack of:
A. Symmetry ✓ Correct Answer
B. Skewness
C. Variability
D. None
Explanation: Skewness literally describes an absence of symmetry in a
distribution.
Q77. If a distribution is not symmetrical, it is
called:
A. Asymmetrical
B. Skewed
C. Both (a) and (b) ✓ Correct Answer
D. Normal
Explanation: A non-symmetrical distribution can be described as either
asymmetrical or skewed — both terms apply.
Q78. A positively skewed distribution is one whose
tail extends to the:
A. Right-hand side ✓ Correct Answer
B. Left-hand side
C. Both (a) and (b)
D. Equal at both ends
Explanation: In a positively skewed distribution, the longer tail
extends toward the right (higher values).
Q79. A negatively skewed distribution is one whose
tail extends to the:
A. Right-hand side
B. Left-hand side ✓ Correct Answer
C. Upward
D. Equal at both ends
Explanation: In a negatively skewed distribution, the longer tail
extends toward the left (lower values).
Q80. In a positively skewed distribution:
A. Mean > median >
mode ✓ Correct Answer
B. Mean < median < mode
C. Mean = median = mode
D. None
Explanation: The classic ordering for a positively skewed
(right-tailed) distribution is Mean > Median > Mode.
Q81. In a negatively skewed distribution:
A. Mean > median > mode
B. Mean < median <
mode ✓ Correct Answer
C. Mean = median = mode
D. None
Explanation: The classic ordering for a negatively skewed
(left-tailed) distribution is Mean < Median < Mode.
Q82. In a positively skewed distribution:
A. Q3 - med = med - Q1
B. Q3 - med > med -
Q1 ✓ Correct Answer
C. Q3 - med < med - Q1
D. None
Explanation: A longer right tail means the gap above the median
(Q3−med) exceeds the gap below it (med−Q1).
Q83. In a negatively skewed distribution:
A. Q3 - med = med - Q1
B. Q3 - med > med - Q1
C. Q3 - med < med -
Q1 ✓ Correct Answer
D. None
Explanation: A longer left tail means the gap below the median
(med−Q1) exceeds the gap above it (Q3−med).
Q84. In a symmetrical distribution:
A. Q3 - med = med - Q1 ✓ Correct Answer
B. Q3 - med > med - Q1
C. Q3 - med < med - Q1
D. None
Explanation: Perfect symmetry means the median lies exactly midway
between Q1 and Q3.
Q85. In a symmetrical distribution, mean =
A. (Q3 - Q1)/2
B. (Q3 + Q1)/2 ✓ Correct Answer
C. Q3 + Q1
D. None
Explanation: In a symmetrical distribution, the mean coincides with
the median, which equals (Q3+Q1)/2.
Q86. For a symmetrical distribution, the quartiles
are equidistant from the:
A. Mean
B. Median ✓ Correct Answer
C. Mode
D. All of these
Explanation: Since Q3−median = median−Q1 in a symmetrical
distribution, the quartiles are equidistant from the median.
Q87. For a symmetrical distribution, the coefficient
of skewness must be:
A. Zero ✓ Correct Answer
B. Negative
C. Positive
D. None
Explanation: A symmetrical distribution has no skew, so the
coefficient of skewness is zero.
Q88. Pearson's coefficient of skewness is given by:
A. Sk = (x̄ - mode)/S
B. Sk = 3(x̄ - median)/S
C. Sk = (q3+q1-2·med)/(q3-q1)
D. Both (a) and (b) ✓ Correct Answer
Explanation: Pearson gave two equivalent formulas for skewness: one
using mode, another using median when mode is unstable.
Q89. Bowley's coefficient of skewness is given by:
A. Sk = (x̄ - mode)/S
B. Sk = 3(x̄ - median)/S
C. Sk =
(q3+q1-2·med)/(q3-q1) ✓ Correct Answer
D. Both (a) and (b)
Explanation: Bowley's coefficient of skewness is based on quartiles:
Sk = (Q3 + Q1 − 2·Median) / (Q3 − Q1).
Q90. Bowley's coefficient of skewness is based on:
A. Mean, mode and S.D
B. Quartiles ✓ Correct Answer
C. Mean, median and S.D
D. None
Explanation: Bowley's formula uses only the quartiles (Q1, Q2/median,
Q3) of the data.
Q91. Bowley's coefficient of skewness lies between:
A. 0 to 1
B. -1 to 1 ✓ Correct Answer
C. -1 to 0
D. None
Explanation: Bowley's coefficient always falls in the range -1 to +1.
Q92. Which of these is a pure (unit-less) number?
A. Bowley's coefficient
B. Pearson's coefficient
C. Moments coefficient
D. All of these ✓ Correct Answer
Explanation: All the coefficients of skewness (Bowley's, Pearson's,
moment-based) are pure ratios with no units.
Q93. The mean of deviations from the mean after
raising them to integer powers is called a:
A. Measure of dispersion
B. Average
C. Moment ✓ Correct Answer
D. None
Explanation: This process — averaging powered deviations from the mean
— defines a statistical moment.
Q94. m2 =
A. S² ✓ Correct Answer
B. Zero
C. Mean
D. S
Explanation: The second moment about the mean, m2, is by definition
equal to the variance, S².
Q95. If m2 = 4, the standard deviation is:
A. 2 ✓ Correct Answer
B. 16
C. 64
D. 256
Explanation: Standard deviation = √variance = √m2 = √4 = 2.
Q96. The first moment about zero (origin) is equal
to:
A. Mean ✓ Correct Answer
B. Zero
C. Standard deviation
D. None
Explanation: The first raw moment (about the origin) equals the
arithmetic mean by definition.
Q97. The moments about the mean are also called:
A. Moments about zero
B. Raw moments
C. Central moments ✓ Correct Answer
D. None
Explanation: Moments calculated about the mean are known as central
moments.
Q98. Moments are used to study the:
A. Kurtosis
B. Skewness
C. Both (a) and (b) ✓ Correct Answer
D. Probability
Explanation: Moments (specifically the 3rd and 4th) are used to
measure both skewness and kurtosis of a distribution.
Q99. The first moment about the mean is always:
A. Negative
B. Positive
C. Zero ✓ Correct Answer
D. None
Explanation: Since deviations from the mean always sum to zero, the
first central moment (m1) is always zero.
Q100. The second moment about the mean is equal to:
A. Variance ✓ Correct Answer
B. Standard deviation
C. Mean
D. Coefficient of variation
Explanation: By definition, the second central moment (m2) equals the
variance.
Q101. The square root of the second moment about the
mean is:
A. Variance
B. Standard deviation ✓ Correct Answer
C. Mean
D. Coefficient of variation
Explanation: √m2 = √variance = standard deviation.
Q102. Shappard's correction is used to reduce:
A. Dispersion
B. Skewness
C. Grouping error ✓ Correct Answer
D. None
Explanation: Shappard's correction adjusts moments to account for the
error introduced by grouping continuous data into classes.
Q103. Shappard's correction is not applicable when:
A. The distribution is highly
skewed
B. The class interval size is not
equal
C. Both (a) and (b) ✓ Correct Answer
D. For third and fourth moments
Explanation: Shappard's correction assumes a roughly symmetrical
distribution with equal class widths, so it fails when either condition is
violated.
Q104. A symmetrical distribution has mean equal to 4.
Its median will be:
A. Less than 4
B. 4 ✓ Correct Answer
C. Greater than 4
D. None
Explanation: In a symmetrical distribution, mean = median = mode, so
median also equals 4.
Q105. All odd-order moments are zero when the
distribution is:
A. Symmetrical ✓ Correct Answer
B. Asymmetrical
C. Skewed
D. None
Explanation: In a perfectly symmetrical distribution, all odd moments
about the mean (1st, 3rd, 5th, ...) vanish to zero.
Q106. The normal distribution is also called:
A. Mesokurtic ✓ Correct Answer
B. Platykurtic
C. Leptokurtic
D. None
Explanation: The normal distribution has kurtosis β2 = 3, which
defines the mesokurtic shape.
Q107. If b1 = 0, the distribution will be:
A. Symmetrical ✓ Correct Answer
B. J-shaped
C. U-shaped
D. None
Explanation: b1 (the skewness coefficient) equal to zero indicates a
symmetrical distribution.
Q108. If m2 = 4 and m4 = 16, then the distribution
is:
A. Platykurtic ✓ Correct Answer
B. Mesokurtic
C. Leptokurtic
D. None
Explanation: β2 = m4/m2² = 16/16 = 1, which is less than 3, indicating
a platykurtic (flatter) distribution.
Q109. If b1 = 0 and b2 = 3, the distribution is
called:
A. Negatively skewed
B. Normal ✓ Correct Answer
C. Positively skewed
D. None
Explanation: Zero skewness (b1=0) combined with kurtosis of exactly 3
(b2=3) describes the normal distribution.
Q110. If β1 = 0 and β2 = 3, the distribution is:
A. Symmetrical
B. Mesokurtic
C. Normal
D. All of these ✓ Correct Answer
Explanation: These conditions together (no skew, kurtosis = 3) exactly
describe a normal distribution, which is symmetrical and mesokurtic.
Q111. If β1 = 0 and β2 = 5, the distribution is:
A. Symmetrical, mesokurtic
B. Symmetrical, platykurtic
C. Symmetrical, leptokurtic ✓ Correct Answer
D. Normal
Explanation: β1=0 means symmetrical, and β2=5 (>3) means more
peaked than normal — leptokurtic.
Q112. If m4 = 243, then m2 in a mesokurtic
distribution is:
A. 9 ✓ Correct Answer
B. -9
C. 729
D. None
Explanation: For a mesokurtic distribution, β2 = m4/m2² = 3, so m2² =
243/3 = 81, giving m2 = 9.
Q113. β1 is called a measure of:
A. Kurtosis
B. Skewness ✓ Correct Answer
C. Both (a) and (b)
D. Dispersion
Explanation: β1 (based on the third moment) is the standard measure of
skewness.
Q114. If β1 = 0, the distribution is:
A. Asymmetrical
B. Skewed
C. Both (a) and (b)
D. Symmetrical ✓ Correct Answer
Explanation: Zero skewness coefficient (β1=0) indicates the
distribution is symmetrical.
Q115. If β1 ≠ 0, the distribution is:
A. Asymmetrical
B. Skewed
C. Both (a) and (b) ✓ Correct Answer
D. Symmetrical
Explanation: A non-zero skewness coefficient means the distribution is
skewed / asymmetrical — both terms apply.
Q116. If √β1 < 0, the distribution is:
A. Negatively skewed ✓ Correct Answer
B. Symmetrical
C. Normal
D. None
Explanation: A negative value of √β1 indicates the distribution has a
longer left tail — negatively skewed.
Q117. If √β1 > 0, the distribution is:
A. Symmetrical
B. Positively skewed ✓ Correct Answer
C. Normal
D. Negatively skewed
Explanation: A positive value of √β1 indicates the distribution has a
longer right tail — positively skewed.
Q118. β2 is called a measure of:
A. Kurtosis ✓ Correct Answer
B. Skewness
C. Both (a) and (b)
D. Dispersion
Explanation: β2 (based on the fourth moment) is the standard measure
of kurtosis (peakedness).
Q119. If β2 = 3, the distribution is:
A. Mesokurtic ✓ Correct Answer
B. Leptokurtic
C. Platykurtic
D. None
Explanation: A kurtosis value of exactly 3 defines a mesokurtic
(normal-shaped) distribution.
Q120. If β2 < 3, the distribution is:
A. Mesokurtic
B. Leptokurtic
C. Platykurtic ✓ Correct Answer
D. None
Explanation: A kurtosis value less than 3 indicates a
flatter-than-normal distribution — platykurtic.
Q121. If β2 > 3, the distribution is:
A. Mesokurtic
B. Leptokurtic ✓ Correct Answer
C. Platykurtic
D. None
Explanation: A kurtosis value greater than 3 indicates a more peaked
distribution — leptokurtic.
Q122. A symmetrical distribution may be:
A. Mesokurtic
B. Leptokurtic
C. Platykurtic
D. Any of these ✓ Correct Answer
Explanation: Symmetry (skewness) and peakedness (kurtosis) are
independent properties — a symmetrical distribution can have any kurtosis.
Q123. The most peaked distribution is called:
A. Mesokurtic
B. Leptokurtic ✓ Correct Answer
C. Platykurtic
D. All
Explanation: A leptokurtic distribution has a sharp, high peak — the
most peaked of the three types.
Q124. The least peaked (flattest) distribution is:
A. Mesokurtic
B. Leptokurtic
C. Platykurtic ✓ Correct Answer
D. All
Explanation: A platykurtic distribution is flatter than normal, with
the least peaked shape.
Q125. The word kurtosis is used to indicate:
A. Peakedness ✓ Correct Answer
B. Skewness
C. Symmetry
D. All of these
Explanation: Kurtosis specifically measures how peaked or flat a
distribution's shape is.
Q126. The mesokurtic shape is usually associated with
the:
A. Normal distribution ✓ Correct Answer
B. Skewed distribution
C. Negatively skewed distribution
D. None
Explanation: The mesokurtic (moderately peaked) shape is
characteristic of the standard normal distribution.
Q127. A distribution having exactly one mode is
called:
A. Unimodal ✓ Correct Answer
B. Bimodal
C. Trimodal
D. Multimodal
Explanation: A single mode makes the distribution unimodal.
Q128. A distribution having exactly two modes is
called:
A. Unimodal
B. Bimodal ✓ Correct Answer
C. Trimodal
D. Multimodal
Explanation: Two modes make the distribution bimodal.
Q129. A multimodal distribution has:
A. Only one mode
B. Only two modes
C. More than two modes ✓ Correct Answer
D. None
Explanation: By definition, a multimodal distribution has more than
two modes.
Q130. For a moderately skewed distribution, the
median divides the distance between the mean and mode in the ratio:
A. 1:3
B. 1:2 ✓ Correct Answer
C. 2:3
D. None
Explanation: The empirical relation Mean − Mode = 3(Mean − Median)
implies the median splits the mean-to-mode distance in a 1:2 ratio.
Q131. For a moderately skewed distribution, mode =
A. 3·median - 2·mean ✓ Correct Answer
B. 3·median - 2·mode
C. 3·mean - 2·mode
D. None
Explanation: The well-known empirical relation is: Mode = 3·Median −
2·Mean.
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