Analyze User Comment Distribution and Sampling Effects

Q: Analyze User Comment Distribution and Sampling Effects

This question evaluates understanding of right‑skewed distributions, measures of central tendency and percentiles, and the effects of aggregation and sampling on distributional shape and spread.

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Question

Scenario

You are analyzing daily comment counts per user. The per-user distribution of counts is right-skewed (many zeros/low counts and a long right tail).

Tasks

Sketch and label the distribution of individual users' daily comment counts when it is right-skewed. Mark the locations of the mean, median, and the 95th percentile (p95).
Now repeatedly take many random user groups of equal size n (users per group) and compute each group's average daily comments. Describe the distribution of these group averages. How do the mean, median, and 95th percentile of this sampling distribution compare to those of the original per-user distribution?

Hint: Invoke the Central Limit Theorem. Sample means trend toward normal; the mean stays constant; the median approaches the mean; higher percentiles shrink as n grows.

Analyze User Comment Distribution and Sampling Effects

Scenario

Tasks

Solution

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