Meta: Determine Key Statistics for Article Comment Distribution Analysis

Determine Key Statistics for Article Comment Distribution Analysis

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Onsite

##### Scenario Analyzing distribution of the number of comments each article receives on a content website. ##### Question You receive the full distribution of comment counts per article. Which summary statistics would you compute and why? When might the mean be misleading compared with the median? How would you detect and treat outliers in the comment counts? If product managers want to know whether a recent UI change increased engagement, which statistical test would you choose and why? ##### Hints Think about skewed count data, heavy-tailed distributions, robust statistics, and basic hypothesis testing.

Overview: Meta statistics prompt on analyzing article comment-count distributions, including robust summaries, skew and outliers, exposure-adjusted rates, heavy-tailed count data, and tests for UI-change impact.

Community answers

Answer by SS

Absolutely! Let’s go deeper and reason through each part of the answer. I’ll explain both what the measures/tests are and why/how they are used in this context. 1. Summary Statistics to Compute and Why a) Mean Definition: Sum of all comment counts divided by the number of articles. [ \text{Mean} = \frac{\sum_{i=1}^N X_i}{N} ] Reason to compute: Gives the “average” engagement. Useful for overall trend analysis. Caveat: Sensitive to extreme outliers. If a few articles have extremely high comments, the mean will overstate typical engagement. b) Median Definition: The middle value when all articles are sorted by comment counts. Reason to compute: Provides a robust measure of “typical” engagement that is less affected by extreme articles. c) Percentiles (p1, p25, p75, p95) Definition: Percentile pX is the value below which X% of observations fall. Reason to compute: Helps understand distribution spread and tail behavior. For example, the 95th percentile shows the high-comment articles that are extreme but real signals. d) Interquartile Range (IQR) Definition: Difference between 75th percentile (Q3) and 25th percentile (Q1). [ \text{IQR} = Q3 - Q1 ] Reason to compute: Measures spread of the middle 50% of data. Robust to extreme values and helps detect outliers. e) Standard Deviation Measures overall variability but is sensitive to outliers, unlike IQR. f) Count of zeros Since comment counts can be zero-inflated, counting zeros tells us how many articles had no engagement, which is

Analyze Comment Counts per Article

You are analyzing the distribution of the number of comments each article receives on a content website. You have comment counts for all articles in a defined period.

Constraints & Assumptions

Comment counts are non-negative integers and may be zero-inflated and heavy-tailed.
Articles differ in exposure, age, topic, author, placement, and traffic source.
Product stakeholders may care about typical article engagement, total comment volume, and whether a UI change increased engagement.
Separate descriptive analysis from causal impact analysis.

Clarifying Questions to Ask Guidance

What time window and article cohort are included?
Are counts raw comments, approved comments, unique commenters, or comments per article view?
Do we have pageviews, article age, topic, author, and traffic source?
Was the UI change randomized, rolled out gradually, or launched to everyone at once?

What a Strong Answer Covers Guidance

Summary statistics: count, zero rate, mean, median, percentiles, max, variance, standard deviation, IQR, trimmed or winsorized mean, and concentration among top articles.
Explanation of why the mean can be misleading when a few viral articles create a long right tail.
Exposure-adjusted metrics such as comments per 1,000 views or per active reader.
Outlier detection using percentiles, robust z-scores on log1p(count) , IQR rules, topic/traffic review, and data-quality checks.
Treatment of outliers: investigate first, correct data errors, analyze with and without outliers, cap/winsorize for robustness, or use models suited to heavy-tailed count data.
Statistical testing for a UI change: randomized A/B test if available; otherwise difference-in-differences, regression adjustment, permutation/bootstrap tests, or count models such as negative binomial.
Guardrails around comment quality, moderation load, spam, and user retention.

Follow-up Questions Guidance

Would you report mean or median to product managers, and why?
How would you compare articles with very different pageviews?
What if the UI change increases comments but also increases spam?
How would you choose between a t-test, Mann-Whitney test, and negative-binomial regression?