Analyze daily comments distribution and sampling
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
You are given daily counts of comments per active user. (1) Define and compute mean, median, and 95th percentile (P95) for a day; write explicit formulas, including how to compute P95 from a sorted empirical distribution. (2) Explain the Central Limit Theorem (CLT) and why the sampling distribution of the sample mean tends toward normality; specify required conditions. (3) If you repeatedly sample 200 independent simple random samples of size n from the same day’s user-level comments, what n is sufficient for the sample mean to be approximately normal, and how does the sampling distribution’s variance change with n? (4) Show how the plots of daily mean, median, and P95 change as n increases, and why. (5) If comments/user increased week-over-week, list at least three plausible statistical or product reasons and how you would test each.
Overview: This question evaluates proficiency in statistical inference, descriptive statistics (mean, median, percentiles), sampling theory and the Central Limit Theorem within the Statistics & Math domain for data scientist interviews.
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