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4003 Variations Questions and Verified Answers 2026-2027 BANK
QUESTIONS WITH DETAILED VERIFIED ANSWERS EXAM
QUESTIONS WILL COME FROM HERE (100% CORRECT
ANSWERS A+ GRADED
1. The primary difference between common cause and special cause
variation is that common cause variation is:
A. Always attributable to a specific operator error
B. Inherent to the process and predictable within limits
C. Caused by external factors outside the process design
D. Eliminated by adjusting the process mean
Answer: B
Explanation: Common cause variation represents the natural, inherent
variability of a stable process. It arises from the cumulative effect of
many small, unavoidable factors and is predictable within statistical
control limits. Special cause variation, by contrast, arises from specific,
identifiable sources external to the inherent process.
2. In a stable process, variation follows a normal distribution.
Approximately what percentage of data points falls within plus or
minus three standard deviations of the mean?
A. 68.3%
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B. 95.4%
C. 99.7%
D. 99.9%
Answer: C
Explanation: The empirical rule states that for a normal distribution,
roughly 68.3% of data lies within one standard deviation of the mean,
95.4% within two, and 99.7% within three. The three-sigma limit is
therefore the conventional boundary used in statistical process control
to signal a potential special cause.
3. A control chart indicates a point beyond the upper control limit. The
correct initial interpretation is that:
A. The process mean has permanently shifted upward
B. A special cause of variation is likely present
C. The process specification limit has been exceeded
D. Common cause variation has increased
Answer: B
Explanation: A point outside the control limits is the fundamental signal
of a special cause. It does not automatically mean the product is out of
specification, as control limits relate to process stability, not
specification limits. Investigating for an assignable cause is the
appropriate action.
4. Which measure of variation is most robust against outliers in a
dataset?
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A. Range
B. Variance
C. Standard deviation
D. Interquartile range
Answer: D
Explanation: The interquartile range, the difference between the 75th
and 25th percentiles, measures the spread of the middle 50% of data.
Because the lowest and highest 25% are excluded, extreme values do
not affect it, making it a robust measure of dispersion compared to the
range or standard deviation.
5. A process capability index Cpk of 0.8 indicates that the process:
A. Is highly capable and centered
B. Is capable but off-center
C. Is not capable, producing some output outside specification limits
D. Has no special cause variation
Answer: C
Explanation: A Cpk value less than 1.0 means the process spread
exceeds the specification width, or the process mean is so far from the
target that one specification limit is being violated. The process will
inevitably produce non-conforming units even if perfectly stable.
6. The coefficient of variation is best described as the ratio of the:
A. Mean to the standard deviation
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B. Standard deviation to the mean
C. Variance to the range
D. Range to the interquartile range
Answer: B
Explanation: The coefficient of variation expresses the standard
deviation as a percentage of the mean, providing a dimensionless
measure of relative dispersion. It is particularly useful for comparing
the degree of variation between datasets with different units or vastly
different means.
7. When performing an analysis of variance, the F-statistic is calculated
as:
A. Mean square error divided by mean square treatment
B. Mean square treatment divided by mean square error
C. Sum of squares treatment divided by sum of squares total
D. Standard deviation treatment divided by standard deviation error
Answer: B
Explanation: In ANOVA, the F-statistic is the ratio of the between-group
variance estimate to the within-group variance estimate. A large F-
value suggests that the variation among group means is greater than
what would be expected from random error alone.
8. A process exhibits a cyclical pattern on a control chart. This suggests
the variation is likely due to:
A. A gradual tool wear
4003 Variations Questions and Verified Answers 2026-2027 BANK
QUESTIONS WITH DETAILED VERIFIED ANSWERS EXAM
QUESTIONS WILL COME FROM HERE (100% CORRECT
ANSWERS A+ GRADED
1. The primary difference between common cause and special cause
variation is that common cause variation is:
A. Always attributable to a specific operator error
B. Inherent to the process and predictable within limits
C. Caused by external factors outside the process design
D. Eliminated by adjusting the process mean
Answer: B
Explanation: Common cause variation represents the natural, inherent
variability of a stable process. It arises from the cumulative effect of
many small, unavoidable factors and is predictable within statistical
control limits. Special cause variation, by contrast, arises from specific,
identifiable sources external to the inherent process.
2. In a stable process, variation follows a normal distribution.
Approximately what percentage of data points falls within plus or
minus three standard deviations of the mean?
A. 68.3%
,2|Page
B. 95.4%
C. 99.7%
D. 99.9%
Answer: C
Explanation: The empirical rule states that for a normal distribution,
roughly 68.3% of data lies within one standard deviation of the mean,
95.4% within two, and 99.7% within three. The three-sigma limit is
therefore the conventional boundary used in statistical process control
to signal a potential special cause.
3. A control chart indicates a point beyond the upper control limit. The
correct initial interpretation is that:
A. The process mean has permanently shifted upward
B. A special cause of variation is likely present
C. The process specification limit has been exceeded
D. Common cause variation has increased
Answer: B
Explanation: A point outside the control limits is the fundamental signal
of a special cause. It does not automatically mean the product is out of
specification, as control limits relate to process stability, not
specification limits. Investigating for an assignable cause is the
appropriate action.
4. Which measure of variation is most robust against outliers in a
dataset?
,3|Page
A. Range
B. Variance
C. Standard deviation
D. Interquartile range
Answer: D
Explanation: The interquartile range, the difference between the 75th
and 25th percentiles, measures the spread of the middle 50% of data.
Because the lowest and highest 25% are excluded, extreme values do
not affect it, making it a robust measure of dispersion compared to the
range or standard deviation.
5. A process capability index Cpk of 0.8 indicates that the process:
A. Is highly capable and centered
B. Is capable but off-center
C. Is not capable, producing some output outside specification limits
D. Has no special cause variation
Answer: C
Explanation: A Cpk value less than 1.0 means the process spread
exceeds the specification width, or the process mean is so far from the
target that one specification limit is being violated. The process will
inevitably produce non-conforming units even if perfectly stable.
6. The coefficient of variation is best described as the ratio of the:
A. Mean to the standard deviation
, 4|Page
B. Standard deviation to the mean
C. Variance to the range
D. Range to the interquartile range
Answer: B
Explanation: The coefficient of variation expresses the standard
deviation as a percentage of the mean, providing a dimensionless
measure of relative dispersion. It is particularly useful for comparing
the degree of variation between datasets with different units or vastly
different means.
7. When performing an analysis of variance, the F-statistic is calculated
as:
A. Mean square error divided by mean square treatment
B. Mean square treatment divided by mean square error
C. Sum of squares treatment divided by sum of squares total
D. Standard deviation treatment divided by standard deviation error
Answer: B
Explanation: In ANOVA, the F-statistic is the ratio of the between-group
variance estimate to the within-group variance estimate. A large F-
value suggests that the variation among group means is greater than
what would be expected from random error alone.
8. A process exhibits a cyclical pattern on a control chart. This suggests
the variation is likely due to:
A. A gradual tool wear
