Free CFA Quantitative Methods Practice Questions & Answers
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Question 361
The elbow method helps identify:
Select an option first.
Correct answer: A — A good number of clusters for K‑means
Explanation: Why A is right: The “elbow” shows diminishing returns in reducing within‑cluster variance. Why others are wrong: B/C/D: Not determined by the elbow method.
Question 362
A cluster with very high internal variance suggests:
Select an option first.
Correct answer: A — The cluster may contain multiple subgroups
Explanation: Why A is right: High variance means the cluster is not compact. Why others are wrong: B/C: Opposite. D: Not implied.
Question 363
A cluster with very low internal variance suggests:
Select an option first.
Correct answer: A — Points are tightly grouped
Explanation: Why A is right: Low variance = compact cluster. Why others are wrong: B: Opposite. C/D: Not implied.
Question 364
K‑means++ improves K‑means by:
Select an option first.
Correct answer: A — Choosing better initial centroids
Explanation: Why A is right: K‑means++ spreads out initial centroids to improve results. Why others are wrong: B/C/D: Not part of K‑means++.
Question 365
A cluster that contains only one point in K‑means likely indicates:
Select an option first.
Correct answer: A — An outlier
Explanation: Why A is right: Single‑point clusters often represent outliers. Why others are wrong: B: Not ideal. C/D: Not implied.
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In hierarchical clustering, the choice of linkage method affects:
Select an option first.
Correct answer: A — How distances between clusters are computed
Explanation: Why A is right: Linkage defines how clusters are compared. Why others are wrong: B/C/D: Not affected.
Question 367
Complete linkage tends to produce clusters that are:
Select an option first.
Correct answer: A — Compact and tight
Explanation: Why A is right: Complete linkage avoids chaining and produces compact clusters. Why others are wrong: B: Single linkage produces elongated clusters. C/D: Not true.
Question 368
Single linkage tends to produce clusters that are:
Select an option first.
Correct answer: A — Long and chain‑like
Explanation: Why A is right: Single linkage can create “chaining” effects. Why others are wrong: B: Complete linkage is compact. C/D: Not guaranteed.
Question 369
Average linkage tends to produce clusters that are:
Select an option first.
Correct answer: A — Balanced between compactness and chaining
Explanation: Why A is right: Average linkage is a middle ground between single and complete linkage. Why others are wrong: B/C/D: Not guaranteed.
Question 370
Clusters that are very close together but internally compact may indicate:
Select an option first.
Correct answer: A — The need for fewer clusters
Explanation: Why A is right: If clusters are too close, merging them may be appropriate. Why others are wrong: B: More clusters would worsen separation. C/D: Not implied.
Question 371
Clusters that are extremely compact but very close to each other may indicate:
Select an option first.
Correct answer: A — Too many clusters
Explanation: Why A is right: If clusters are compact but nearly touching, they may represent over‑segmentation. Why others are wrong: B: Too few clusters would produce loose groups. C/D: Not implied.
Question 372
Clusters that are very spread out but far apart may indicate:
Select an option first.
Correct answer: A — Too few clusters
Explanation: Why A is right: Loose clusters often contain multiple subgroups → more clusters needed. Why others are wrong: B: Opposite. C/D: Not relevant.
Question 373
A cluster that contains points with very high internal variance likely:
Select an option first.
Correct answer: A — Should be split into smaller clusters
Explanation: Why A is right: High variance suggests multiple sub‑patterns inside the cluster. Why others are wrong: B: Merging increases variance. C/D: Not true.
Question 374
A cluster that contains points with extremely low internal variance likely:
Select an option first.
Correct answer: A — Is well‑defined
Explanation: Why A is right: Low variance = tight, compact cluster. Why others are wrong: B/C/D: Not implied.
Question 375
A distance metric that works well for high‑dimensional sparse vectors is:
Select an option first.
Correct answer: A — Cosine similarity
Explanation: Why A is right: Cosine similarity handles high‑dimensional sparse data (e.g., text). Why others are wrong: B/C: Sensitive to magnitude. D: For binary data.
Question 376
Clusters that change dramatically when features are rescaled indicate:
Select an option first.
Correct answer: A — The model is sensitive to feature magnitude
Explanation: Why A is right: Distance‑based clustering (like K‑means) depends heavily on scale. Why others are wrong: B: Opposite. C/D: Not implied.
Question 377
A cluster that contains points from multiple natural groups likely indicates:
Select an option first.
Correct answer: A — Under‑clustering
Explanation: Why A is right: Too few clusters cause unrelated points to be grouped together. Why others are wrong: B: Over‑clustering splits groups too much. C/D: Not relevant.
Question 378
A cluster that contains only one or two points in K‑means often indicates:
Select an option first.
Correct answer: A — Outliers
Explanation: Why A is right: Tiny clusters usually represent outliers. Why others are wrong: B: Not ideal. C/D: Not implied.
Question 379
A cluster that contains points with very different scales across features suggests:
Select an option first.
Correct answer: A — Scaling was not applied
Explanation: Why A is right: Unscaled features distort distance calculations. Why others are wrong: B/C/D: Not the cause.
Question 380
A cluster that is extremely elongated may be caused by:
Select an option first.
Correct answer: A — Single linkage
Explanation: Why A is right: Single linkage creates “chaining,” producing long, thin clusters. Why others are wrong: B: Produces compact clusters. C/D: Middle‑ground or centroid‑based.
Question 381
A cluster that is extremely compact may be caused by:
Select an option first.
Correct answer: A — Complete linkage
Explanation: Why A is right: Complete linkage avoids chaining and produces tight clusters. Why others are wrong: B: Produces elongated clusters. C/D: Not specifically compact.
Question 382
A cluster that appears in a dendrogram but disappears when cutting at a certain height indicates:
Select an option first.
Correct answer: A — The cluster merges with others at that height
Explanation: Why A is right: Cutting at different heights changes the number of clusters. Why others are wrong: B/C/D: Not implied.
Question 383
A cluster that contains points with very high pairwise distances suggests:
Select an option first.
Correct answer: A — Poor clustering
Explanation: Why A is right: High internal distances mean the cluster is not cohesive. Why others are wrong: B: Opposite. C/D: Not implied.
Question 384
A cluster that contains points with very low pairwise distances suggests:
Select an option first.
Correct answer: A — Strong cohesion
Explanation: Why A is right: Low distances = tight, cohesive cluster. Why others are wrong: B/C/D: Not implied.
Question 385
A cluster that is extremely sensitive to small changes in initialization suggests:
Select an option first.
Correct answer: A — K‑means instability
Explanation: Why A is right: K‑means can produce different results depending on initial centroids. Why others are wrong: B: Opposite. C/D: Not the cause.
Question 386
A cluster that contains points with very different densities suggests:
Select an option first.
Correct answer: A — K‑means may not be appropriate
Explanation: Why A is right: K‑means struggles with varying densities; DBSCAN handles this better. Why others are wrong: B: Opposite. C/D: Not relevant.
Question 387
A cluster that contains points with very different shapes suggests:
Select an option first.
Correct answer: A — K‑means assumptions are violated
Explanation: Why A is right: K‑means assumes spherical clusters; irregular shapes break this assumption. Why others are wrong: B: Opposite. C/D: Not implied.
Question 388
A cluster that contains points with very different orientations (e.g., diagonal vs horizontal) suggests:
Select an option first.
Correct answer: A — K‑means may not capture the structure
Explanation: Why A is right: K‑means cannot capture rotated or oriented clusters well. Why others are wrong: B: Opposite. C/D: Not relevant.
Question 389
A cluster that contains points with very different densities and shapes may be better handled by:
Select an option first.
Correct answer: A — DBSCAN
Explanation: Why A is right: DBSCAN handles arbitrary shapes and densities. Why others are wrong: B: Assumes spherical clusters. C/D: Not clustering algorithms.
Question 390
The main advantage of DBSCAN over K‑means is that DBSCAN:
Select an option first.
Correct answer: A — Can detect clusters of arbitrary shape
Explanation: Why A is right: DBSCAN identifies clusters of any shape and handles noise well. Why others are wrong: B: DBSCAN does not require k. C: No centroids. D: Scaling helps but is not a requirement.
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