Analyze Distribution of Daily Page Shares Per User
Overview
This question evaluates skills in statistical distribution analysis, percentile-based summarization, cohort dynamics, and temporal persistence modeling for engagement metrics such as daily page shares and time-on-site.
Meta
Jul 12, 2025, 6:59 PM
Data Scientist
Onsite
Statistics & Math
77
0
Engagement Distributions and Cohort Dynamics
You are analyzing per-user, per-day engagement. Assume a day-level panel with all users included (inactive days count as zeros) and no bots.
Task
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Daily page shares per user
- Sketch (describe) the distribution and indicate: mean, median, p1, and p99.
- What overall shape do you expect and why?
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Persistence/regression
- For users at the 50th and 95th percentiles of today’s distribution, predict their average daily shares two weeks from now (i.e., their expected per-day rate during the following 14 days). Explain directionally and how you would estimate it.
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Cohort trajectories by day-1 activity
- For the cohort with exactly 2 shares on day 1, describe the expected trend of their average shares over days 2–30.
- Repeat for the cohort with exactly 5 shares on day 1. Which cohort will have larger variance? What distributional family do you expect to fit best?
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Time spent per user
- Repeat the above style of analysis for daily time-spent-per-user. Comment on the stability of the mean and tail behavior (e.g., p95/p99) over three weeks.
Hints: Engagement metrics are typically heavy-tailed; cohorts regress toward the overall mean while retaining right-skewed structure.
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