Characterize metric distribution and quantiles

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.