Quick Answer
The answer is k=4, as it yields the highest silhouette score of 0.52, indicating the best balance of cluster cohesion and separation. When using the silhouette score to choose optimal k, you select the value that maximizes the average silhouette width, which here clearly points to k=4. The elbow method supports this by showing that the within-cluster sum of squares (WCSS) drops sharply through k=4 and then levels off, meaning additional clusters beyond four add little explanatory power. On the CompTIA Data+ DA0-001 exam, this scenario tests your ability to interpret both the silhouette score and the elbow curve together—a common trap is picking k=3 because the elbow appears to bend there, but the silhouette score is the more definitive metric for cluster quality. Remember the memory tip: “Higher silhouette, better silhouette”—always prioritize the highest score when the elbow is ambiguous.
This DA0-001 practice question tests your understanding of analyzing and modeling data. Compare every option against the stated constraints before choosing — the best answer satisfies all requirements, not just the most obvious one. After answering, compare your reasoning against the explanation and wrong-answer breakdown below. Once you have made your selection, read the full explanation to reinforce the concept and understand why each distractor is designed to mislead on exam day.
A data analyst at a marketing firm is tasked with segmenting customers based on their purchasing behavior. The dataset contains 10,000 customers with features such as annual spend, frequency of purchases, recency of last purchase, and average order value. The analyst decides to use k-means clustering. After standardizing the features, the analyst runs k-means with k=3, k=4, and k=5, and computes the silhouette score for each: k=3: 0.45, k=4: 0.52, k=5: 0.48. The analyst also plots the elbow curve and observes that the within-cluster sum of squares (WCSS) decreases sharply from k=2 to k=4, then levels off. Based on these results, what is the most appropriate number of clusters?
k=4
Highest silhouette score and elbow point.
k=2
Why wrong: Not evaluated, but elbow suggests k=4 is better.
k=3
Why wrong: Silhouette score is lower than k=4.
k=5
Why wrong: Silhouette score is lower than k=4.
Answer choices
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
k=4
The silhouette score is highest at k=4 (0.52), indicating that clusters are well-separated and cohesive. The elbow curve shows WCSS decreasing sharply up to k=4 and then leveling off, suggesting that k=4 captures the optimal trade-off between model complexity and variance explained. Together, these metrics point to k=4 as the most appropriate number of clusters.
Key principle: Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option.
Answer analysis
For each option: why learners choose it and why it is or isn't the right answer here.
k=4
Why this is correct
Highest silhouette score and elbow point.
Related concept
Read the scenario before looking for a memorised answer.
k=2
Why it's wrong here
Not evaluated, but elbow suggests k=4 is better.
k=3
Why it's wrong here
Silhouette score is lower than k=4.
k=5
Why it's wrong here
Silhouette score is lower than k=4.
Common exam traps
The trap here is that candidates might rely solely on the elbow curve and pick k=3 or k=5, ignoring the silhouette score which directly measures cluster quality and clearly favors k=4.
Detailed technical explanation
Silhouette score measures how similar a point is to its own cluster compared to other clusters, ranging from -1 to 1; values above 0.5 are considered good. The elbow method uses WCSS to identify the point where diminishing returns begin, but it can be ambiguous, so combining it with silhouette analysis provides a more robust cluster selection. In practice, domain knowledge about customer segments (e.g., low, medium, high spenders) should also be considered to validate the chosen k.
Key takeaway
Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option.
Real-world example
A practitioner preparing for the DA0-001 exam encounters this exact type of scenario on the job. The correct answer here is not the most general option — it is the best answer for the specific constraint described. Answer the scenario, not the keyword: identify the specific constraint before choosing the most familiar-sounding option. Real exam questions reward reading the full scenario before eliminating options, because the constraint defines which answer fits.
What to study next
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FAQ
Analyzing and Modeling Data — This question tests Analyzing and Modeling Data — Read the scenario before looking for a memorised answer..
The correct answer is: k=4 — The silhouette score is highest at k=4 (0.52), indicating that clusters are well-separated and cohesive. The elbow curve shows WCSS decreasing sharply up to k=4 and then leveling off, suggesting that k=4 captures the optimal trade-off between model complexity and variance explained. Together, these metrics point to k=4 as the most appropriate number of clusters.
Identify which exam domain this question belongs to, review the core concept, then practise similar questions from the same domain.
Read the scenario before looking for a memorised answer.
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Last reviewed: Jun 11, 2026
This DA0-001 practice question is part of Courseiva's free CompTIA certification practice question bank. Courseiva provides original exam-style practice questions with explanations, topic-based practice, mock exams, readiness tracking, and study analytics to help learners prepare for the DA0-001 exam.
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