K-Means Clustering DATA-SCIENCE-FOUNDATIONS Practice Questions (Page 2)

Questions 6–10

1. 6application · medium

   A data scientist uses silhouette analysis to evaluate K-means results for k values from 2 to 6. The average silhouette scores are: k=2: 0.55, k=3: 0.62, k=4: 0.58, k=5: 0.50, k=6: 0.45. Which k is most appropriate?

   • Ak=6
   • Bk=4
   • Ck=2
   • Dk=3
   Reveal Solution Discussion Select an answer first
2. 7application · medium

   A retail chain wants to segment its stores based on two features: annual revenue (in millions of dollars) and store size (in square feet). The data scientist runs K-means with k=3 and observes that the clusters are elongated and diagonal, with some stores assigned to a cluster whose centroid is far from them in Euclidean distance. Which change is most appropriate to improve the clustering?

   • ARemove store size from the analysis because it is highly correlated with revenue.
   • BStandardize both features to have zero mean and unit variance before running K-means.
   • CUse Manhattan distance instead of Euclidean distance.
   • DIncrease k to 5 to capture more granular store segments.
   Reveal Solution Discussion Select an answer first
4. 8application · medium

   A data scientist applies K-means to a dataset with two features. The scatter plot shows two clusters: one is a dense, spherical cluster, and the other is a long, elongated cluster. The scientist runs K-means with k=2 and finds that the elongated cluster is split into two, while the spherical cluster is merged with part of the elongated cluster. Which limitation of K-means is most directly causing this issue?

   • AK-means is sensitive to outliers, and the elongated cluster contains outliers.
   • BThe features were not standardized, causing the elongated cluster to be distorted.
   • CK-means assumes clusters are roughly spherical and of similar size, so it struggles with elongated clusters.
   • DThe number of clusters k=2 is too low for this dataset.
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5. 9application · medium

   A data scientist applies K-means to a dataset containing customer age and annual income. The resulting clusters are heavily influenced by a few customers with extremely high incomes, causing one cluster to contain only those outliers. Which preprocessing step is most likely to improve the clustering?

   • AApply log transformation to the income feature before scaling.
   • BRemove all customers with income above the 95th percentile.
   • CUse z-score normalization without any transformation.
   • DIncrease k to 5 to create a separate cluster for the high-income customers.
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6. 10foundation · easy

   Why is feature scaling important before applying K-means?

   • ATo make the algorithm converge faster.
   • BTo convert categorical variables into numeric ones.
   • CTo ensure all features contribute equally to the distance calculation.
   • DTo reduce the number of clusters needed.
   Reveal Solution Discussion Select an answer first