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Browse exam-wise, subject-wise, and country-wise MCQs with explanations.
Choose an option to check your answer.
A.
Observations are well matched to their own clusters and separated from others
B.
Every cluster has the same size
C.
The data are normally distributed
D.
The chosen k is necessarily the true value
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Correct Answer: A. Observations are well matched to their own clusters and separated from others
Explanation:
Silhouette compares within-cluster cohesion with nearest-cluster separation.
Choose an option to check your answer.
A.
How p-values change with sample size
B.
How survival probability changes over time
C.
How histogram bins change with width
D.
How within-cluster variation decreases as k increases
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Correct Answer: D. How within-cluster variation decreases as k increases
Explanation:
Adding clusters always reduces within-cluster variation.
Choose an option to check your answer.
A.
Arbitrarily shaped nested clusters
B.
Clusters defined only by category labels
C.
Compact, roughly spherical clusters
D.
Groups separated solely by time censoring
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Correct Answer: C. Compact, roughly spherical clusters
Explanation:
Nearest-centroid assignment partitions space into convex regions.
Choose an option to check your answer.
A.
Outliers always create missing values
B.
Means and squared distances give extreme observations strong influence
C.
The algorithm uses only medians
D.
Outliers change category names
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Correct Answer: B. Means and squared distances give extreme observations strong influence
Explanation:
An extreme point can pull a centroid far from the cluster's main concentration.
Choose an option to check your answer.
A.
Different starts can converge to different local solutions
B.
It changes the raw observations
C.
It makes the algorithm supervised
D.
It guarantees the global optimum
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Correct Answer: A. Different starts can converge to different local solutions
Explanation:
The k-means objective is not convex over assignments and centroids together.
Choose an option to check your answer.
A.
Standardization creates the true cluster labels
B.
K-means accepts only negative values
C.
It guarantees spherical clusters
D.
Variables with larger scales would otherwise dominate distance calculations
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Correct Answer: D. Variables with larger scales would otherwise dominate distance calculations
Explanation:
K-means commonly relies on Euclidean distance.
Choose an option to check your answer.
A.
The most distant point in the dataset
B.
A categorical response label
C.
The mean vector of observations assigned to a cluster
D.
The first observation in each cluster
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Correct Answer: C. The mean vector of observations assigned to a cluster
Explanation:
Each centroid summarizes a cluster's center in feature space.
Choose an option to check your answer.
A.
A response label for every observation
B.
The number of clusters k
C.
A time-to-event variable
D.
A null hypothesis
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Correct Answer: B. The number of clusters k
Explanation:
Standard k-means requires the desired number of clusters as an input.
Choose an option to check your answer.
A.
To minimize within-cluster squared distances to cluster centroids
B.
To maximize the number of clusters automatically
C.
To predict a labeled response
D.
To estimate a survival function
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Correct Answer: A. To minimize within-cluster squared distances to cluster centroids
Explanation:
K-means assigns observations to the nearest centroid and updates centroids iteratively.
Choose an option to check your answer.
A.
To sort observations for display only
B.
To estimate a kernel bandwidth
C.
To generate a normal Q-Q plot
D.
To assess a null distribution by rearranging labels or values under exchangeability
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Correct Answer: D. To assess a null distribution by rearranging labels or values under exchangeability
Explanation:
Permutation breaks the association specified by the alternative while preserving other data features.
Choose an option to check your answer.
A.
Assuming every variable is uniform
B.
Deleting half the sample repeatedly
C.
Repeated resampling from the observed data with replacement
D.
Drawing only from a known population
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Correct Answer: C. Repeated resampling from the observed data with replacement
Explanation:
Bootstrap samples approximate the estimator's sampling distribution empirically.
Choose an option to check your answer.
A.
After seeing which direction gives a smaller p-value
B.
Before analysis, when only one direction is scientifically relevant and the opposite would not support the claim
C.
Whenever the sample is small
D.
Whenever the data are skewed
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Correct Answer: B. Before analysis, when only one direction is scientifically relevant and the opposite would not support the claim
Explanation:
Choosing direction after inspecting results inflates false positives.
