Analyze User Comment Distribution and Sampling Effects
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Onsite
##### Scenario
Analyzing distribution of user comment counts and the effect of sampling.
##### Question
Sketch the distribution of individual users’ daily comment counts when it is right-skewed and mark mean, median, and 95th percentile positions. After randomly sampling many user groups and computing each group’s average comments, describe the resulting distribution and how the mean, median, and 95th percentile change.
##### Hints
Invoke Central Limit Theorem; sample means trend toward normal, mean stays constant, higher percentiles shrink, median approaches mean.
Overview: Evaluates statistical reasoning about right-skewed user comment counts and sampling distributions. Strong answers place median, mean, and p95 correctly, then use the Central Limit Theorem to explain why group averages become less variable and more symmetric.
Community answers
Answer by fm
https://imgur.com/a/MMyk6ra
mode is most likely 0
median probably between 0 and 1, having 50% of the density distribution before and after it
mean is affected by outliers and quite high in comparison to median and mode
95th percentile wouldn't be that far in the tail as frequencies should be very low for the high comment counts in the tail
Answer by Xiaoming
The raw distribution of daily comments per user is highly right-skewed, with the median near zero, the mean pulled right by heavy commenters, and the 95th percentile far out in the tail. Once we average over random user groups, the Central Limit Theorem kicks in — the distribution of sample means becomes approximately normal, centered on the same mean, with reduced spread. The median converges to the mean, and high percentiles like the 95th move closer to the mean as the effect of outliers diminishes.