Characterize metric distribution and quantiles
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
Your chosen KPI is per-video watch time (seconds). Based on the following 20-sample dataset collected from a pilot: [3, 5, 6, 6, 7, 8, 9, 10, 12, 15, 16, 20, 24, 30, 35, 45, 60, 90, 120, 180].
Tasks: (1) Describe the likely distribution shape (skewness/heaviness of tail) and sketch it verbally. (2) Compute the sample median, mode, and the 95th percentile using the linear interpolation method for empirical quantiles; show steps. (3) Compare mean vs median for this data and argue which is the more decision‑robust location estimator and why. (4) If we winsorize at the 99th percentile, explain qualitatively how that would change variance and statistical power in an A/B test on watch time.
Quick Answer: This question evaluates a data scientist's competency in descriptive statistics and robust metric analysis within the Statistics & Math domain, focusing on distribution characterization, empirical quantiles, measures of central tendency, and the effects of outlier handling on variance and experimental power.