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Free Questions › CFA › Quantitative Methods
Free CFA Quantitative Methods Practice Questions & Answers
1,200 exam-style Quantitative Methods questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 541
A key limitation of hierarchical clustering is that it:
Select an option first.
Correct answer: A — Cannot be undone once clusters merge
Explanation: Why A is right: Hierarchical clustering is greedy; merges cannot be reversed. Why others are wrong: B: No k needed. C: Dendrograms exist. D: Works with any distance metric.
Question 542
The “elbow method” is used to:
Select an option first.
Correct answer: A — Choose the number of clusters in K‑means
Explanation: Why A is right: The elbow point indicates diminishing returns in reducing within‑cluster variance. Why others are wrong: B/C/D: Not related.
Question 543
Silhouette scores measure:
Select an option first.
Correct answer: A — How well each point fits within its cluster
Explanation: Why A is right: Silhouette scores evaluate cluster cohesion and separation. Why others are wrong: B/C/D: Not silhouette metrics.
Question 544
A silhouette score close to +1 indicates:
Select an option first.
Correct answer: A — Well‑separated clusters
Explanation: Why A is right: High score = strong cluster assignment. Why others are wrong: B/C/D: Not correct.
Question 545
A silhouette score near 0 indicates:
Select an option first.
Correct answer: A — Overlapping clusters
Explanation: Why A is right: Score near 0 means points lie between clusters. Why others are wrong: B: Would be near +1. C/D: Not relevant.
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Question 546
The main objective of clustering is to:
Select an option first.
Correct answer: B — Group similar observations
Explanation: Why B is right: Clustering groups data points based on similarity without labels. Why others are wrong: A: That’s forecasting. C/D: Preprocessing steps, not clustering.
Question 547
K‑means clustering works best when clusters are:
Select an option first.
Correct answer: A — Roughly spherical and similar in size
Explanation: Why A is right: K‑means assumes clusters are compact and evenly shaped. Why others are wrong: B/C: K‑means struggles with irregular or overlapping clusters. D: K‑means requires numeric data.
Question 548
The K in K‑means refers to:
Select an option first.
Correct answer: A — The number of clusters
Explanation: Why A is right: K is the number of clusters the user chooses. Why others are wrong: B/C/D: Not what K represents.
Question 549
K‑means uses which measure to assign points to clusters?
Select an option first.
Correct answer: A — Distance to centroids
Explanation: Why A is right: Points are assigned to the nearest centroid. Why others are wrong: B: No probabilities in basic K‑means. C/D: Not relevant.
Question 550
A major drawback of K‑means is that it:
Select an option first.
Correct answer: A — Is sensitive to initial centroid placement
Explanation: Why A is right: Poor initialization can lead to poor clustering. Why others are wrong: B: K‑means scales well. C: It requires numeric data. D: Dendrograms are for hierarchical clustering.
Question 551
Hierarchical clustering produces:
Select an option first.
Correct answer: A — A tree‑like structure of clusters
Explanation: Why A is right: Hierarchical clustering outputs a dendrogram. Why others are wrong: B/C/D: Not outputs of hierarchical clustering.
Question 552
Agglomerative clustering merges clusters based on:
Select an option first.
Correct answer: A — Minimum distance between clusters
Explanation: Why A is right: Agglomerative clustering merges the closest clusters first. Why others are wrong: B/C/D: Not used in clustering.
Question 553
Single linkage clustering defines cluster distance as:
Select an option first.
Correct answer: A — The minimum distance between any two points
Explanation: Why A is right: Single linkage = nearest‑neighbor distance. Why others are wrong: B = complete linkage C = average linkage D = centroid linkage
Question 554
Complete linkage clustering defines cluster distance as:
Select an option first.
Correct answer: A — The maximum distance between any two points
Explanation: Why A is right: Complete linkage = farthest‑neighbor distance. Why others are wrong: B = single linkage C = average linkage D = centroid linkage
Question 555
Average linkage clustering defines cluster distance as:
Select an option first.
Correct answer: A — The average distance between all pairs of points
Explanation: Why A is right: Average linkage uses the mean of all pairwise distances. Why others are wrong: B/C/D: Other linkage methods.
Question 556
Centroid linkage clustering defines cluster distance as:
Select an option first.
Correct answer: A — Distance between cluster centroids
Explanation: Why A is right: Centroid linkage uses the distance between cluster means. Why others are wrong: B/C/D: Other linkage definitions.
Question 557
A dendrogram cut at a higher height produces:
Select an option first.
Correct answer: A — Fewer clusters
Explanation: Why A is right: Higher cuts merge more branches → fewer clusters. Why others are wrong: B: Lower cuts produce more clusters. C/D: Not correct.
Question 558
A dendrogram cut at a lower height produces:
Select an option first.
Correct answer: A — More clusters
Explanation: Why A is right: Lower cuts separate branches earlier → more clusters. Why others are wrong: B: Opposite. C/D: Not correct.
Question 559
A distance matrix must be:
Select an option first.
Correct answer: A — Symmetric
Explanation: Why A is right: Distance from A to B equals distance from B to A. Why others are wrong: B: It can be triangular, but full matrices are common. C/D: Not required.
Question 560
K‑means clustering minimizes:
Select an option first.
Correct answer: A — Within‑cluster sum of squared distances
Explanation: Why A is right: K‑means optimizes compactness within clusters. Why others are wrong: B: Not the objective. C/D: Not relevant.
Question 561
Clusters that are well‑separated will have:
Select an option first.
Correct answer: A — High between‑cluster distances
Explanation: Why A is right: Good clustering = large separation between clusters. Why others are wrong: B: Indicates overlap. C/D: Not relevant.
Question 562
A poor clustering result may show:
Select an option first.
Correct answer: A — Points close to centroids of other clusters
Explanation: Why A is right: Points near other clusters indicate misassignment. Why others are wrong: B/C/D: Indicate good clustering.
Question 563
K‑means is most sensitive to:
Select an option first.
Correct answer: A — Outliers
Explanation: Why A is right: Outliers distort centroids significantly. Why others are wrong: B: Unsupervised → no labels. C/D: Not specific issues.
Question 564
Hierarchical clustering is computationally:
Select an option first.
Correct answer: A — More expensive than K‑means
Explanation: Why A is right: Hierarchical clustering often requires O(n²) or worse. Why others are wrong: B: Opposite. C/D: Impossible for clustering.
Question 565
A cluster containing only one observation in hierarchical clustering indicates:
Select an option first.
Correct answer: A — That point is highly dissimilar from others
Explanation: Why A is right: Single‑point clusters often represent outliers or unique patterns. Why others are wrong: B: Not a failure. C/D: Not implied.
Question 566
A cluster that contains points very far from all other clusters likely represents:
Select an option first.
Correct answer: A — An outlier group
Explanation: Why A is right: A distant cluster often indicates unusual or outlier observations. Why others are wrong: B: Balanced clusters are not far from others. C/D: Not implied.
Question 567
K‑means clustering is most appropriate when:
Select an option first.
Correct answer: A — Data is numeric and roughly evenly scaled
Explanation: Why A is right: K‑means relies on numeric distances. Why others are wrong: B: Requires numeric encoding. C: Needs vectorization first. D: Impossible to cluster.
Question 568
A major advantage of hierarchical clustering is that it:
Select an option first.
Correct answer: A — Does not require choosing the number of clusters upfront
Explanation: Why A is right: You can choose clusters after viewing the dendrogram. Why others are wrong: B: No clustering method guarantees perfection. C: Works with any distance metric. D: Centroids are for K‑means.
Question 569
A major disadvantage of hierarchical clustering is that it:
Select an option first.
Correct answer: A — Cannot reverse merges once made
Explanation: Why A is right: Hierarchical clustering is greedy; merges are permanent. Why others are wrong: B: No k needed. C: Dendrograms exist. D: Not true.
Question 570
Clusters that overlap heavily will likely produce:
Select an option first.
Correct answer: A — Low silhouette scores
Explanation: Why A is right: Overlap reduces cluster separation → low silhouette values. Why others are wrong: B: High scores require clear separation. C/D: Not necessarily.
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