Analyze Video View Distribution: Mode, Median, Mean Comparison

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 Video View Distribution: Mode, Median, Mean Comparison states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Analyze Video View Distribution: Mode, Median, Mean Comparison

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Onsite

##### Scenario You are analyzing user engagement on a short-video sharing product. The team needs statistical insights into how views and shares behave across users and videos. ##### Question 1. Given a distribution of video views, how would you compute, interpret, and compare its **mode**, **median**, and **mean**? What relationship do you expect between them for this kind of data, and which should you report? 2. Each video a user watches has a **10% chance** of being shared. What is the probability that **at least one** of ten independently watched videos is shared? 3. You observe that **average watch length per video is increasing while the average share count (share rate) per video is decreasing**. Propose possible hypotheses for this divergence and outline how you would test them, distinguishing causal from correlational explanations. ##### Hints Apply descriptive statistics for skewed distributions, binomial probability, and a structured causal/experimental-design framework for diagnosing a metric divergence.

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 Video View Distribution: Mode, Median, Mean Comparison 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 Video View Distribution: Mode, Median, Mean Comparison

Scenario

You are analyzing user engagement on a short-video sharing product. The team needs statistical insights into how views and shares behave across users and videos.

Question
  1. Given a distribution of video views, how would you compute, interpret, and compare its mode , median , and mean ? What relationship do you expect between them for this kind of data, and which should you report?
  2. Each video a user watches has a 10% chance of being shared. What is the probability that at least one of ten independently watched videos is shared?
  3. You observe that average watch length per video is increasing while the average share count (share rate) per video is decreasing . Propose possible hypotheses for this divergence and outline how you would test them, distinguishing causal from correlational explanations.
Hints

Apply descriptive statistics for skewed distributions, binomial probability, and a structured causal/experimental-design framework for diagnosing a metric divergence.

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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