وَأَحْصَىٰ كُلَّ شَيْءٍ عَدَدًا
"And He has enumerated everything in numbers." (Allah perfectly counts and knows the exact measure of all creations).
Q1. Any measure indicating the centre of the data is
called a measure of:
A. Central tendency ✓ Correct Answer
B. Dispersion
C. Skewness
D. Kurtosis
Explanation: A value that indicates the centre/middle of a data set is
called a measure of central tendency (e.g. mean, median, mode).
Q2. An average is a measure of:
A. Central tendency /
location ✓ Correct Answer
B. Dispersion
C. Skewness
D. None of these
Explanation: An average locates the centre of the data, so it is a
measure of central tendency (also called a measure of location).
Q3. The single value that represents the whole data
is called:
A. Range
B. Average ✓ Correct Answer
C. Variance
D. Standard deviation
Explanation: A single representative value of the whole data set is
called an average.
Q4. An average should be based on:
A. All observations ✓ Correct Answer
B. Some observations
C. Half observations
D. None
Explanation: A good average must be based on all observations, not
just a part of the data.
Q5. A good average should be:
A. Well defined only
B. Easy to understand only
C. Based on all observations only
D. All of the above ✓ Correct Answer
Explanation: A good average must be well defined, easy to
understand/compute, and based on all observations — all of these together.
Q6. A measure of central tendency is not independent
of:
A. Origin only
B. Scale only
C. Both origin and
scale ✓ Correct Answer
D. Neither
Explanation: Measures like the mean change when data is shifted
(origin) or multiplied (scale), so it depends on both.
Q7. If y1, y2, ..., yn are each multiplied by 10, the
resulting average would be:
A. Increased by 10
B. Increased 10 times ✓ Correct Answer
C. Decreased by 10
D. Unchanged
Explanation: Multiplying every value by 10 multiplies the mean by 10
as well, i.e. the average increases 10 times.
Q8. If 5 is added to each observation y1, y2, ...,
yn, the average is increased by:
A. 5 ✓ Correct Answer
B. 10
C. 10 times
D. 5 times
Explanation: Adding a constant to every observation adds that same
constant to the mean, so the average increases by 5.
Q9. Sum of values divided by the number of values is
called:
A. Arithmetic mean ✓ Correct Answer
B. Median
C. Mode
D. Geometric mean
Explanation: By definition, Arithmetic Mean = (sum of all values) /
(number of values).
Q10. The arithmetic mean has the same unit as:
A. The original
observations ✓ Correct Answer
B. The square of the observations
C. The cube of the observations
D. It is unit-less
Explanation: Since AM is a sum of values divided by a count, it
retains the same unit as the original data.
Q11. Arithmetic mean can:
A. Only be positive
B. Only be zero
C. Only be negative
D. Be negative, positive or
zero ✓ Correct Answer
Explanation: Depending on the data, the arithmetic mean can be
negative, positive, or zero — there's no restriction.
Q12. The mean of the first n positive integers
(1,2,...,n) is:
A. 0
B. (n+1)/2 ✓ Correct Answer
C. n(n+1)/2
D. None
Explanation: Sum of first n integers = n(n+1)/2, dividing by n gives
mean = (n+1)/2.
Q13. The sum of the deviations of values from their
arithmetic mean is always:
A. Zero ✓ Correct Answer
B. Positive
C. Negative
D. Undefined
Explanation: This is a fundamental property of AM: Σ(x - x̄) = 0
always.
Q14. The sum of squared deviations of values is least
(minimum) when taken from the:
A. Arithmetic mean ✓ Correct Answer
B. Median
C. Mode
D. Geometric mean
Explanation: This is the least squares property: Σ(x-x̄)² is smaller
than Σ(x-a)² for any other value a.
Q15. The mean of a constant 'a' (repeated n times) is
equal to:
A. Zero
B. a ✓ Correct Answer
C. na
D. a/n
Explanation: If every value equals a, the mean of those n identical
values is simply a.
Q16. If y = a + bx, then ȳ =
A. a + b·x̄ ✓ Correct Answer
B. b·x̄
C. a
D. x̄
Explanation: Applying the linear transformation to the mean itself: ȳ
= a + b·x̄.
Q17. If y = x/a, then x̄ =
A. x̄ (unchanged)
B. x̄ / a ✓ Correct Answer
C. a·x̄
D. Zero
Explanation: Dividing every x value by a divides the mean by a as
well: mean of y = x̄ / a.
Q18. The sum of squared deviations from mean, Σ(x -
x̄)², is always:
A. Greater than Σ(x-a)² for any a
≠ x̄
B. Less than or equal to
Σ(x-a)² for any a ✓ Correct Answer
C. Equal to Σ(x-a)² for any a
D. Undefined
Explanation: This restates the least-squares property: deviations
squared from the mean are minimal compared to any other reference point a.
Q19. If Σ(x - 5) = 0, then x̄ =
A. 0
B. 5 ✓ Correct Answer
C. -5
D. Cannot be determined
Explanation: Σ(x - a) = 0 only when a equals the mean, so x̄ = 5.
Q20. If y1, y2, ..., yn are each multiplied by 10,
the resulting mean would be:
A. x̄
B. 10x̄ ✓ Correct Answer
C. x̄/10
D. x̄ + 10
Explanation: Multiplying all values by 10 multiplies their mean by 10
too.
Q21. Σ(x - x̄) is equal to:
A. 0 ✓ Correct Answer
B. x̄
C. Undefined
D. None
Explanation: This is the basic property that deviations from the mean
always sum to zero.
Q22. If Σ(x - a) = 0, then x̄ =
A. a ✓ Correct Answer
B. x
C. Undefined
D. Zero
Explanation: Since only the mean makes the sum of deviations zero, a
must equal x̄.
Q23. If the arithmetic mean of n observations is 'a',
then the sum of the observations is:
A. na ✓ Correct Answer
B. a/n
C. n/2
D. a
Explanation: Mean = Sum/n, so Sum = Mean × n = na.
Q24. For a certain distribution, Σ(x-21) = 18 and
Σ(x-28) = 0. Then x̄ =
A. 21
B. -21
C. 18
D. 28 ✓ Correct Answer
Explanation: Σ(x - a) = 0 only when a = x̄, and here Σ(x-28) = 0, so
x̄ = 28.
Q25. If x̄ = 9 and y = 3x + 4, then ȳ =
A. 30
B. 31 ✓ Correct Answer
C. 9
D. 24
Explanation: ȳ = 3x̄ + 4 = 3(9) + 4 = 31.
Q26. The sum of deviations from the mean of a set of
'n' values is:
A. 0 ✓ Correct Answer
B. Negative
C. 5
D. Depends on n
Explanation: By definition of the arithmetic mean, this sum is always
exactly zero.
Q27. Mean is a suitable average for:
A. A symmetrical
distribution ✓ Correct Answer
B. An extremely skewed
distribution
C. Qualitative data
D. Open-end classes
Explanation: The mean works best for symmetrical distributions since
extreme values distort it in skewed data.
Q28. Mean is affected by the change of:
A. Origin only
B. Scale only
C. Both origin and
scale ✓ Correct Answer
D. Neither
Explanation: Shifting (origin) or scaling the data both change the
value of the mean.
Q29. If a distribution consists of 10 values, each
equal to 4, then the mean is:
A. 4 ✓ Correct Answer
B. 10
C. 40
D. 0.4
Explanation: When all values in the data are the same (4), the mean of
that data is also 4.
Q30. The nth root of the product of n positive
observations is called the:
A. Arithmetic mean
B. Median
C. Geometric mean ✓ Correct Answer
D. Mode
Explanation: This is the definition of the geometric mean: GM =
(x1·x2·...·xn)^(1/n).
Q31. The antilog of the arithmetic mean of the
logarithms of the values is the:
A. Arithmetic mean
B. Median
C. Geometric mean ✓ Correct Answer
D. Mode
Explanation: GM can also be computed as the antilog of the mean of the
logarithms of the values.
Q32. Geometric mean of y1, y2, ..., y5 is:
A.
(y1×y2×y3×y4×y5)^(1/5) ✓ Correct Answer
B. (y1+y2+y3+y4+y5)^(1/5)
C. (y1÷y2÷y3÷y4÷y5)^(1/5)
D. (y1×y2×y3×y4×y5)^(1/4)
Explanation: GM is the 5th root of the product of the five values.
Q33. Geometric mean of a and b is:
A. √(a·b) ✓ Correct Answer
B. √(a+b)
C. √(a/b)
D. Does not exist
Explanation: For two values, GM = √(a×b).
Q34. Geometric mean of 5, 10, 0 is:
A. -5
B. 5
C. 0 ✓ Correct Answer
D. Does not exist
Explanation: Since one of the values is 0, the product is 0, making
the geometric mean 0.
Q35. If any observation in the data is zero, then the
Geometric Mean is:
A. Zero ✓
Correct Answer
B. Less than zero
C. Greater than zero
D. Undefined
Explanation: A zero value makes the product of all values zero, so GM
= 0.
Q36. For an average rate of change, the best average
is the:
A. Geometric mean ✓ Correct Answer
B. Arithmetic mean
C. Median
D. Mode
Explanation: Geometric mean is the correct average for rates of
change/growth since it accounts for compounding.
Q37. Geometric mean becomes imaginary if any value in
the data is:
A. Fractional
B. Positive
C. Negative ✓
Correct Answer
D. Zero
Explanation: Taking roots of negative products can give an imaginary
result, so GM becomes imaginary with negative values.
Q38. Geometric mean is based on:
A. All observations ✓ Correct Answer
B. Extreme values only
C. Positive values only, ignoring
rest
D. None
Explanation: GM, like AM, uses every observation in the data set in
its calculation.
Q39. If Z = Y/X, then g_z =
A. g_y / g_x ✓ Correct Answer
B. g_y × g_x
C. g_y + g_x
D. None
Explanation: Geometric mean of a ratio equals the ratio of the
geometric means: g_z = g_y / g_x.
Q40. Geometric mean of a constant greater than zero
is equal to:
A. Zero
B. That constant ✓ Correct Answer
C. Undefined
D. Does not exist
Explanation: If every value equals the same positive constant, GM of
that data equals the constant itself.
Q41. Geometric mean is meaningless (undefined) if any
value in the data set is:
A. Positive
B. Zero or negative ✓ Correct Answer
C. Fractional
D. A whole number
Explanation: GM cannot be properly computed if a value is zero
(product becomes 0) or negative (root becomes imaginary).
Q42. Geometric mean is a suitable (appropriate)
average for:
A. Rates and ratios
B. Index numbers
C. Percentages
D. All of these ✓ Correct Answer
Explanation: GM is the appropriate average for rates, ratios,
percentages and index numbers alike.
Q43. The suitable average for index numbers is:
A. Arithmetic mean
B. Median
C. Geometric mean ✓ Correct Answer
D. Mode
Explanation: Index numbers are best averaged using the geometric mean.
Q44. Geometric mean is always a:
A. Positive number ✓ Correct Answer
B. Negative number
C. Zero
D. Any of these
Explanation: For positive data, GM is always a positive value.
Q45. Which average is less affected by extreme
values?
A. Arithmetic mean
B. Geometric mean ✓ Correct Answer
C. Both equally
D. Neither
Explanation: Geometric mean gives less weight to extreme values
compared to the arithmetic mean.
Q46. The reciprocal of the arithmetic mean of the
reciprocals of the values is called the:
A. Harmonic mean ✓ Correct Answer
B. Arithmetic mean
C. Geometric mean
D. None
Explanation: This is exactly the definition of the harmonic mean.
Q47. Sum of the reciprocals of the values divided by
number of observations, its reciprocal, is equal to the:
A. Arithmetic mean
B. Harmonic mean ✓ Correct Answer
C. Geometric mean
D. All of these
Explanation: This calculation process defines the harmonic mean.
Q48. Harmonic mean is based on:
A. All observations ✓ Correct Answer
B. Half observations
C. Extreme values only
D. None
Explanation: Like AM and GM, HM also uses every observation in the
data set.
Q49. Harmonic mean is not independent of:
A. Origin only
B. Scale only
C. Both origin and
scale ✓ Correct Answer
D. Neither
Explanation: HM changes when data is shifted or scaled, so it depends
on both origin and scale.
Q50. Harmonic mean of a constant is equal to:
A. Zero
B. That constant ✓ Correct Answer
C. Undefined
D. Does not exist
Explanation: If all values equal the same constant, their harmonic
mean is also that constant.
Q51. Harmonic mean of 2, 5, 0, 6 is:
A. 2.5
B. 3.5
C. 0
D. Does not exist ✓ Correct Answer
Explanation: HM requires the reciprocal of each value; since 1/0 is
undefined, the harmonic mean does not exist.
Q52. Harmonic mean of a and b is:
A. (a+b)/2ab
B. ab/(a+b)
C. 2ab/(a+b) ✓ Correct Answer
D. None
Explanation: For two values, HM = 2ab/(a+b).
Q53. Harmonic Mean can't be calculated if any value
in the data is:
A. Zero ✓ Correct Answer
B. Positive
C. Negative
D. A fraction
Explanation: HM involves dividing by each value (reciprocals), so a
zero value makes it impossible to calculate.
Q54. If x1, x2, ..., xn are n observations with
harmonic mean h, then Σ(1/x) =
A. n/h ✓ Correct Answer
B. h/n
C. nh
D. n+h
Explanation: Since h = n / Σ(1/x), rearranging gives Σ(1/x) = n/h.
Q55. If y = ax, then h_y (harmonic mean of y) =
A. a·h_x ✓ Correct Answer
B. a²·h_x
C. h_x
D. a + h_x
Explanation: Scaling all values by a scales the harmonic mean by a as
well.
Q56. Harmonic Mean gives less weight to:
A. Small values
B. Large values ✓ Correct Answer
C. All values equally
D. Negative values
Explanation: Because HM is based on reciprocals, large values
contribute smaller reciprocal terms, giving them less influence.
Q57. Harmonic Mean gives more weight to:
A. Small values ✓ Correct Answer
B. Large values
C. All values equally
D. Negative values
Explanation: Small values produce large reciprocals, so HM is
influenced more strongly by small values.
Q58. The geometric mean of the arithmetic mean and
harmonic mean of a data set is equal to the:
A. Arithmetic mean
B. Geometric mean of the
original data ✓ Correct Answer
C. Harmonic mean
D. Mode
Explanation: There's a known relation: GM² = AM × HM, so GM of (AM,
HM) equals the data's own geometric mean.
Q59. If data has only one mode, it's called:
A. Unimodal ✓ Correct Answer
B. Bimodal
C. Multimodal
D. None
Explanation: A data set with exactly one mode is called unimodal.
Q60. If data has two modes, it's called:
A. Unimodal
B. Bimodal ✓ Correct Answer
C. Multimodal
D. None
Explanation: A data set with exactly two modes is called bimodal.
Q61. Mode of the data 5, 2, 2, 3, 3 is:
A. 5
B. 2 and 3 (bimodal) ✓ Correct Answer
C. 4
D. Does not exist
Explanation: Both 2 and 3 occur twice (most frequently), so the data
is bimodal with modes 2 and 3.
Q62. If each value in a data set occurs the same
number of times, then the mode:
A. Equals all the values
B. Is 0
C. Is the greatest value
D. Does not exist ✓ Correct Answer
Explanation: When no value occurs more frequently than another, there
is no unique most-frequent value, so mode does not exist.
Q63. If y = a + bx, then mode(y) =
A. a + b
B. b·mode(x)
C. a
D. a + b·mode(x) ✓ Correct Answer
Explanation: Applying the linear transformation directly to the mode:
mode(y) = a + b·mode(x).
Q64. If y = x/a, then mode(y) =
A. mode(x)
B. mode(x)/a ✓ Correct Answer
C. Undefined
D. Zero
Explanation: Dividing all values by a divides the mode by a as well.
Q65. Mode is affected by the change of:
A. Origin only
B. Both origin and
scale ✓ Correct Answer
C. Scale only
D. Neither
Explanation: Mode changes when data is shifted (origin) or multiplied
(scale) — it depends on both.
Q66. If y1, y2, ..., yn are each multiplied by 10,
the resulting mode would be:
A. mode(y)
B. 10·mode(y) ✓ Correct Answer
C. mode(y)/10
D. mode(y) + 10
Explanation: Multiplying all values by 10 multiplies the mode by 10 as
well.
Q67. If 5 is added to each observation, the mode is
increased by:
A. 5 ✓ Correct Answer
B. 10
C. 10 times
D. 5 times
Explanation: Adding a constant to every value shifts the mode by that
same constant.
Q68. In case of grouped data, mode can be found by:
A. Inspection only
B. Interpolation ✓ Correct Answer
C. At random
D. None
Explanation: For grouped (continuous) data, the mode is located using
an interpolation formula within the modal class.
Q69. For qualitative (categorical) data, the suitable
average is:
A. Mean
B. Mode ✓ Correct Answer
C. Geometric mean
D. Harmonic mean
Explanation: Since qualitative data can't be numerically averaged, the
mode (most frequent category) is the appropriate measure.
Q70. The central value of arranged (ordered) data is
called:
A. Median ✓ Correct Answer
B. Mean
C. Mode
D. None
Explanation: The median is defined as the middle value of data arranged
in order.
Q71. The sum of absolute deviations is least when
taken from the:
A. Median ✓ Correct Answer
B. Mean
C. Mode
D. Geometric mean
Explanation: A key property of the median: Σ|x - median| is smaller
than Σ|x - a| for any other value a.
Q72. If a constant 'a' is added to each observation,
the median is increased by:
A. a ✓ Correct Answer
B. 10
C. 2a/3
D. a/2
Explanation: Adding a constant to every value shifts the median by
that same amount.
Q73. Median is a value above and below which
observations lie in equal proportion of:
A. 1/3
B. 2/3
C. 1/√2
D. 1/2 ✓ Correct Answer
Explanation: The median splits the ordered data exactly in half — 1/2
of observations lie above and 1/2 below.
Q74. Median is a value at or below which ordered data
lie:
A. 50% ✓ Correct Answer
B. 25%
C. 100%
D. None
Explanation: By definition, 50% of the ordered observations lie at or
below the median.
Q75. If a and b are two values, then their mean and
median are both equal to:
A. √(ab)
B. (a+b)/2 ✓ Correct Answer
C. a - b
D. a
Explanation: For just two values, both the mean and the median equal
(a+b)/2.
Q76. Median is a value that divides ordered data
into:
A. 2 equal parts ✓ Correct Answer
B. 3 equal parts
C. 4 equal parts
D. 5 equal parts
Explanation: The median divides ordered data into two equal halves.
Q77. Median is based on:
A. All observations
B. Extreme values
C. Position of the
item(s) ✓ Correct Answer
D. All of the above
Explanation: Unlike the mean, median depends only on the position of
the middle item(s), not on every value's magnitude.
Q78. Median is a suitable average for:
A. A symmetrical distribution
B. An extremely skewed
distribution ✓ Correct Answer
C. Qualitative data
D. None
Explanation: Since median is not affected by extreme values, it's the
preferred average for skewed distributions.
Q79. Median is affected by the change of:
A. Origin only
B. Scale only
C. Both origin and
scale ✓ Correct Answer
D. Neither
Explanation: Median shifts when data is shifted (origin) and scales
when data is scaled — it depends on both.
Q80. Median of a constant is equal to:
A. Zero
B. That constant ✓ Correct Answer
C. Undefined
D. Does not exist
Explanation: If all values equal the same constant, the median of that
data is also that constant.
Q81. Median is affected by a change in:
A. Origin only
B. Scale only
C. Position of items only
D. All of these ✓ Correct Answer
Explanation: Median depends on origin, scale, and the position of
items in the ordered data — all of these.
Q82. Is the median affected by extreme values?
A. False ✓ Correct Answer
B. True
C. Always true
D. None
Explanation: Median only depends on the middle position, so extreme
values do NOT affect it — the statement is false.
Q83. Is the median not capable of further
mathematical treatment?
A. False
B. Never true
C. True ✓ Correct Answer
D. None
Explanation: Since median is based on position rather than actual
magnitudes, it cannot be combined algebraically like the mean — this is true.
Q84. The mean and median of exactly two values a and
b are:
A. Equal ✓ Correct Answer
B. Unequal
C. Opposite in sign
D. They don't exist
Explanation: For two values, both mean and median equal (a+b)/2, so
they are equal.
Q85. Median may be calculated for open-end classes:
A. False
B. Doesn't exist
C. True ✓ Correct Answer
D. None
Explanation: Since median only needs the class where the middle
observation falls, it can be calculated even for open-end classes.
Q86. Median changes when a constant is added to or
subtracted from the variable:
A. False
B. Never true
C. True ✓ Correct Answer
D. None
Explanation: Adding/subtracting a constant shifts every value, hence
it shifts the median too — this is true.
Q87. Σ|x - m| ≤ Σ|x - a| for any a; here m is the:
A. Mean
B. Mode
C. Median ✓ Correct Answer
D. Geometric mean
Explanation: This inequality describes the least absolute deviation
property, which holds uniquely for the median.
Q88. The median of the data -3, 0, -5 is:
A. -3 ✓ Correct Answer
B. 0
C. -5
D. Does not exist
Explanation: Arranged in order: -5, -3, 0 — the middle value is -3.
Q89. If y1, y2, ..., yn are each multiplied by 10,
the resulting median would be:
A. median(y)
B. 10·median(y) ✓ Correct Answer
C. median(y)/10
D. median(y) + 10
Explanation: Multiplying every value by 10 multiplies the median by 10
as well.
Q90. If 5 is added to each observation y1,...,yn, the
median is increased by:
A. 5 ✓ Correct Answer
B. 10
C. 10 times
D. 5 times
Explanation: Adding a constant to every value shifts the median by the
same constant.
Q91. If y = a + bx, then median(y) =
A. a + b·median(x) ✓ Correct Answer
B. a
C. b·median(x)
D. median(x)
Explanation: Applying the transformation directly to the median:
median(y) = a + b·median(x).
Q92. Quantiles that divide the arrayed data into 4
equal parts are called:
A. Quartiles ✓ Correct Answer
B. Percentiles
C. Deciles
D. Median
Explanation: By definition, quartiles split ordered data into 4 equal
parts.
Q93. Quantiles of a constant are:
A. Equal ✓ Correct Answer
B. Unequal
C. Undefined
D. None
Explanation: If all values are identical, every quantile (Q1, Q2, Q3,
etc.) equals that same constant.
Q94. Quartiles are the values which divide a data set
into:
A. Four equal parts ✓ Correct Answer
B. Five equal parts
C. Six equal parts
D. None
Explanation: Quartiles (Q1, Q2, Q3) split the data into four equal
parts.
Q95. The three values that divide a distribution into
four equal parts are called:
A. Quartiles ✓ Correct Answer
B. Percentiles
C. Deciles
D. Median
Explanation: There are exactly three quartiles (Q1, Q2, Q3) that
create four equal groups.
Q96. Q1 is the value below which the following
percentage of observations lie:
A. 25% ✓ Correct Answer
B. 50%
C. 75%
D. 100%
Explanation: The first quartile Q1 marks the point below which 25% of
the data lies.
Q97. Q3 is the value below which the following
percentage of observations lie:
A. 25%
B. 50%
C. 75% ✓ Correct Answer
D. 100%
Explanation: The third quartile Q3 marks the point below which 75% of
the data lies.
Q98. Median, quartiles, percentiles and deciles are
collectively called:
A. Quantiles ✓ Correct Answer
B. Mean
C. Mode
D. None
Explanation: All position-based measures (median, quartiles, deciles,
percentiles) fall under the general term quantiles.
Q99. Median is equal to:
A. q2
B. P50
C. d5
D. All of these ✓ Correct Answer
Explanation: The median is the same point as the 2nd quartile, the
50th percentile, and the 5th decile — all equivalent.
Q100. The area above Q3 and below Q1 is:
A. 25%
B. 50% ✓ Correct Answer
C. 75%
D. 100%
Explanation: Between Q1 (25%) and Q3 (75%) lies the middle 50% of the
data (the interquartile range).
Q101. q3 is equal to:
A. P30
B. P75 ✓ Correct Answer
C. d3
D. None
Explanation: Q3 corresponds to the 75th percentile, i.e. P75.
Q102. Quantiles that divide the arrayed data into 10
equal parts are called:
A. Quartiles
B. Percentiles
C. Deciles ✓ Correct Answer
D. Median
Explanation: Deciles split ordered data into 10 equal parts.
Q103. Deciles are the values which divide a data set
into:
A. Two equal parts
B. Four equal parts
C. Ten equal parts ✓ Correct Answer
D. Hundred equal parts
Explanation: By definition, deciles create ten equal-sized groups of
data.
Q104. The nine values that divide a distribution into
ten equal parts are called:
A. Quartiles
B. Percentiles
C. Deciles ✓ Correct Answer
D. Median
Explanation: Nine dividing points (d1 to d9) create ten equal parts —
these are the deciles.
Q105. d5 is the value below which the following
percentage of observations lie:
A. 25%
B. 50% ✓ Correct Answer
C. 75%
D. 100%
Explanation: The 5th decile marks the halfway point, i.e. 50% of the
data lies below it.
Q106. d3 is the value below which the following
percentage of observations lie:
A. 25%
B. 30% ✓ Correct Answer
C. 60%
D. 100%
Explanation: Each decile represents 10% increments, so the 3rd decile
marks 30%.
Q107. q2 is equal to:
A. Median
B. P50
C. d5
D. All of these ✓ Correct Answer
Explanation: The second quartile is identical to the median, the 50th
percentile, and the 5th decile.
Q108. The area above d9 is:
A. 10% ✓ Correct Answer
B. 25%
C. 75%
D. 100%
Explanation: Since d9 marks the 90% point, only 10% of the data lies
above it.
Q109. d7 is equal to:
A. P30
B. P70 ✓ Correct Answer
C. d3
D. None
Explanation: The 7th decile corresponds to the 70th percentile, i.e.
P70.
Q110. Quantiles that divide the arrayed data into 100
equal parts are called:
A. Quartiles
B. Percentiles ✓ Correct Answer
C. Deciles
D. Median
Explanation: Percentiles split ordered data into 100 equal parts.
Q111. Percentiles are the values which divide a data
set into:
A. Two equal parts
B. Four equal parts
C. Ten equal parts
D. Hundred equal parts ✓ Correct Answer
Explanation: By definition, percentiles create one hundred equal-sized
groups of data.
Q112. The 99 values that divide a distribution into
hundred equal parts are called:
A. Quartiles
B. Percentiles ✓ Correct Answer
C. Deciles
D. Median
Explanation: Ninety-nine dividing points (P1 to P99) create one
hundred equal parts — the percentiles.
Q113. P50 is the value below which the following
percentage of observations lie:
A. 25%
B. 50% ✓ Correct Answer
C. 75%
D. 100%
Explanation: By definition, the 50th percentile marks the point below
which 50% of the data lies.
Q114. P3 is the value below which the following
percentage of observations lie:
A. 2%
B. 3% ✓ Correct Answer
C. 6%
D. 10%
Explanation: Each percentile represents 1% increments, so P3
corresponds to 3%.
Q115. P50 is equal to:
A. Median
B. q2
C. d5
D. All of these ✓ Correct Answer
Explanation: P50 is identical to the median, Q2, and d5 — they all
mark the same middle point.
Q116. P70 is equal to:
A. P30
B. d7 ✓ Correct Answer
C. d3
D. None
Explanation: P70 aligns exactly with the 7th decile, d7.
Q117. P5 is a value below which the following
percentage of observations lie:
A. 0.5%
B. 5% ✓ Correct Answer
C. 50%
D. None
Explanation: By definition, P5 marks the point below which 5% of the
observations lie.
Q118. If d5 = 10.5, then median =
A. 0.5
B. 10.5 ✓ Correct Answer
C. 10
D. None
Explanation: Since d5 always equals the median, median = 10.5.
Q119. If d3 = 6, then P30 =
A. 5
B. 6 ✓ Correct Answer
C. 30
D. None
Explanation: d3 and P30 mark exactly the same point in the data, so
P30 = 6.
Q120. If P25 = 9, then q1 =
A. 5
B. 6
C. 9 ✓ Correct Answer
D. None
Explanation: P25 and Q1 mark exactly the same point, so q1 = 9.
Q121. Quartiles, deciles and percentiles are all
types of:
A. Quantiles ✓ Correct Answer
B. Mean
C. Mode
D. Dispersion measures
Explanation: All of these positional measures fall under the general
category of quantiles.
Q122. To select an appropriate average, which factor
is necessary to consider?
A. Type of variable
B. Purpose of the average
C. Type of the distribution
D. All of these ✓ Correct Answer
Explanation: Choosing a suitable average depends on the type of
variable, the purpose, and the shape of the distribution — all matter.
Q123. Which average is appropriate for a quantitative
variable?
A. Arithmetic mean ✓ Correct Answer
B. Median only
C. Mode only
D. Only for qualitative
(categorical) data
Explanation: For quantitative (numeric) data, the arithmetic mean is
the appropriate and most commonly used average.
Q124. Which average is suitable for qualitative
(categorical) data?
A. Mean
B. Median
C. Mode ✓ Correct Answer
D. Both median and mode
Explanation: For categorical data, only the mode (most frequent
category) makes sense as an average.
Q125. Which is the most suitable average for a
symmetrical distribution?
A. Mean
B. Median
C. Mode
D. All are equally
suitable ✓ Correct Answer
Explanation: In a symmetrical distribution, mean, median, and mode all
coincide, so all are equally suitable.
Q126. Which average is preferred in the case of a
skewed distribution?
A. Mean
B. Median ✓ Correct Answer
C. Geometric mean
D. None
Explanation: Since median isn't distorted by extreme values, it is
preferred for skewed distributions.
Q127. Which average is not affected by extreme
values?
A. Mean
B. Median ✓ Correct Answer
C. Geometric mean
D. None
Explanation: Median depends only on the position of the middle value,
so it's unaffected by extreme values.
Q128. Which average is useful for rates and ratios?
A. Mean
B. Harmonic mean
C. Geometric mean
D. Both harmonic and
geometric mean ✓ Correct Answer
Explanation: Both the harmonic mean and geometric mean are appropriate
for averaging rates and ratios.
Q129. To average the marks obtained in an
examination, which average is suitable?
A. Mean ✓ Correct Answer
B. Median
C. Mode
D. None
Explanation: Exam marks are quantitative data without extreme distortion
typically, so the arithmetic mean is suitable.
Q130. To average the growth rate of population of
different cities, which average is suitable?
A. Mean
B. Geometric mean ✓ Correct Answer
C. Mode
D. Median
Explanation: Growth rates compound multiplicatively, so geometric mean
is the correct average.
Q131. To average the height of students, which
average is suitable?
A. Mean ✓ Correct Answer
B. Geometric mean
C. Mode
D. Median
Explanation: Height is straightforward quantitative data, so the
arithmetic mean is suitable.
Q132. To average the size of agricultural holdings,
which average is suitable?
A. Median ✓ Correct Answer
B. Mode
C. Median and mode
D. Mean
Explanation: Agricultural holding sizes are often skewed by a few very
large holdings, so median is the suitable average.
Q133. To average an increase in salaries (expressed
as rates), which average is suitable?
A. Median
B. Mode
C. Geometric mean ✓ Correct Answer
D. Mean
Explanation: Since salary increases are rates of change, geometric
mean gives the correct average.
Q134. To average the volume of sales of garments,
which average is suitable?
A. Geometric mean
B. Mode
C. Arithmetic mean ✓ Correct Answer
D. Harmonic mean
Explanation: Sales volume is straightforward quantitative data, so the
arithmetic mean is suitable.
Q135. In case of an open-end class, which average is
more suitable?
A. Median ✓ Correct Answer
B. Mode
C. Arithmetic mean
D. Both median and mode
Explanation: Since open-end classes have no defined boundary, the
median (based on position) is more suitable than the mean.
Q136. Which of these is not always unique?
A. Mean
B. Median
C. Mode ✓ Correct Answer
D. Geometric mean
Explanation: A data set can have more than one mode
(bimodal/multimodal) or none at all, so mode is not always unique.
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