Analyze Central Limit Theorem in User Comment Distribution

Quick Overview

This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Analyze Central Limit Theorem in User Comment Distribution states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Analyze Central Limit Theorem in User Comment Distribution

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Onsite

##### Scenario You are analyzing the distribution of user comments per post on a social platform to report key statistical properties to product managers. ##### Question Explain how the Central Limit Theorem applies when sampling average comments per user. Define and compute the expected value of the number of comments across all users. Differentiate population standard deviation from sample standard deviation in this context. Construct a 95% confidence interval for the mean number of comments. ##### Hints Link CLT to sample mean; use E[X]=μ; σ vs. s; CI = x̄ ± 1.96*s/√n.

Quick Answer: This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Analyze Central Limit Theorem in User Comment Distribution states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025, 10:55 AM
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Analyze Central Limit Theorem in User Comment Distribution

Comments per User — CLT, Expectation, SD, and 95% CI

Context

You are measuring how many comments each user makes in a fixed time window (e.g., one week). Let X be the random variable "number of comments made by a randomly selected user in that window." You sample n users uniformly at random and record X1, X2, …, Xn.

Tasks

  1. Central Limit Theorem (CLT): Explain how it applies to the sample mean of comments per user.
  2. Expected Value: Define E[X] and explain how to compute/estimate the expected number of comments across all users.
  3. Population vs. Sample Standard Deviation: Differentiate σ (population) from s (sample) in this context.
  4. 95% Confidence Interval: Construct a 95% CI for the mean number of comments.

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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