DA0-002 Data Analysis Practice Question
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?
⚠ Common exam trap
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.
Answer choices
Why each option matters
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.
Answer analysis
Option-by-option breakdown
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.
- ✗
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.
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