Characterize metric distribution and quantiles

The KPI you have selected is watch time per video, measured in seconds. A pilot produced the following 20 observations: [3, 5, 6, 6, 7, 8, 9, 10, 12, 15, 16, 20, 24, 30, 35, 45, 60, 90, 120, 180].

Tasks: (1) Describe the probable shape of the distribution, including skewness and tail weight, and give a verbal sketch. (2) Calculate the sample median, mode, and 95th percentile with the linear interpolation approach for empirical quantiles, showing your work. (3) Compare the mean and median for this dataset, and make the case for which one is the more decision-robust measure of location, explaining why. (4) If the data are winsorized at the 99th percentile, describe qualitatively how variance and statistical power would change in an A/B test on watch time.

Overview: This question tests a data scientist's skills in descriptive statistics and robust metric analysis under Statistics & Math, with emphasis on characterizing distributions, computing empirical quantiles, central tendency measures, and how outlier treatment affects variance and experimental power.