Practice Library
All MCQs
Browse exam-wise, subject-wise, and country-wise MCQs with explanations.
Choose an option to check your answer.
A.
An ECDF
B.
A dendrogram
C.
A grouped bar chart of unrelated categories
D.
A network graph
Show Answer
Correct Answer: A. An ECDF
Explanation:
At x = 20, the ECDF's vertical value is the observed cumulative proportion.
Choose an option to check your answer.
A.
It hides exact observations
B.
It cannot compare groups
C.
It always appears smooth
D.
It avoids arbitrary bin boundaries
Show Answer
Correct Answer: D. It avoids arbitrary bin boundaries
Explanation:
An ECDF uses every observed value directly.
Choose an option to check your answer.
A.
A theoretical distribution only
B.
The average of all histogram bin widths
C.
The cumulative proportion of observed sample values
D.
A regression residual plot
Show Answer
Correct Answer: C. The cumulative proportion of observed sample values
Explanation:
The empirical CDF increases by the observed sample proportion at each value.
Choose an option to check your answer.
A.
Percentiles are random labels
B.
Different interpolation conventions may be used
C.
Software changes the raw data automatically
D.
Percentiles are defined only for normal data
Show Answer
Correct Answer: B. Different interpolation conventions may be used
Explanation:
A finite sample may not contain an observation exactly at the desired position.
Choose an option to check your answer.
A.
A percentile that divides ordered data into four parts
B.
A mean computed from four observations
C.
A graph with four panels
D.
A probability that must equal 0.25
Show Answer
Correct Answer: A. A percentile that divides ordered data into four parts
Explanation:
The first, second, and third quartiles correspond approximately to the 25th, 50th, and 75th percentiles.
Choose an option to check your answer.
A.
The 25th percentile
B.
The 75th percentile
C.
The 100th percentile
D.
The 50th percentile
Show Answer
Correct Answer: D. The 50th percentile
Explanation:
The median divides ordered data into lower and upper halves.
Choose an option to check your answer.
A.
Exactly 90 observations exist
B.
The value is 90% larger than the mean
C.
About 90% of observations are at or below that value
D.
Only 10% of values are below it
Show Answer
Correct Answer: C. About 90% of observations are at or below that value
Explanation:
A percentile is a threshold in the ordered distribution.
Choose an option to check your answer.
A.
F(a) + F(b)
B.
F(b) - F(a)
C.
F(b) / F(a) in every case
D.
1 - F(a) - F(b)
Show Answer
Correct Answer: B. F(b) - F(a)
Explanation:
F(b) includes probability up to b, while F(a) includes probability up to a.
Choose an option to check your answer.
A.
As a step function
B.
As a set of isolated circles with no connection
C.
As a perfectly straight line in every case
D.
As a bar chart of means
Show Answer
Correct Answer: A. As a step function
Explanation:
The CDF jumps at values with positive probability mass.
Choose an option to check your answer.
B.
The sample mean
C.
The variance
D.
1
Show Answer
Correct Answer: D. 1
Explanation:
Eventually the threshold includes the entire probability space.
Choose an option to check your answer.
A.
It must be symmetric
B.
It must have constant slope
C.
It is nondecreasing
D.
It must be negative for small x
Show Answer
Correct Answer: C. It is nondecreasing
Explanation:
Accumulated probability cannot decrease when the threshold increases.
Choose an option to check your answer.
A.
The probability that the variable equals its mean
B.
The probability that the random variable is less than or equal to x
C.
The density only at x
D.
The number of observations above x
Show Answer
Correct Answer: B. The probability that the random variable is less than or equal to x
Explanation:
The CDF accumulates probability from the lower tail through x.
