Interview: 'you have to pick k for the executive team — walk me through it.'

medium

Answer

$(1) Business first: how many actionable groups can marketing / product operate?$
$Usually 3-8 in practice.$
$(2) Compute silhouette, gap statistic, BIC (if GMM) across k = 2-15.$
$(3) Plot metrics — find plateau / knee.$
$(4) Choose k that satisfies business AND metrics (e.g. silhouette > 0.3 acceptable, gap not too noisy).$
$(5) Stability check: does the top-k survive resampling?$
$(6) Present 2-3 candidates with pros/cons; let the exec team choose the interpretation.$

Check yourself — multiple choice

Random
Business constraint (3-8 actionable) + silhouette / gap / BIC across k=2-15 + stability check + present 2-3 candidates with pros/cons
Just elbow
Not real

Pick k: business constraint + metrics + stability + present options.

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214 interview questions in this topic.