##### Question Sketch the distribution of daily page shares per user, indicating mean, median, p1, and p99. What shape do you expect and why? For users at the 50th and 95th percentiles of today’s distribution, predict their average shares two weeks from now. For the cohort with exactly two shares on day 1, describe the expected trend of average shares over days 2–30. Repeat for the cohort with five shares; which cohort will have larger variance and what distribution do you expect? Repeat the above style of analysis for daily time-spent-per-user; comment on stability of mean and tail behavior over three weeks. ##### Hints Engagement metrics are typically heavy-tailed; cohorts regress toward the overall mean while retaining right-skewed structure.

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.

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This is a medium difficulty Statistics & Math question, commonly asked during Onsite rounds at Meta.

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This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

Analyze Distribution of Daily Page Shares Per User

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

Daily page shares per user
- Sketch (describe) the distribution and indicate: mean, median, p1, and p99.
- What overall shape do you expect and why?
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.
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?
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.

Task

Daily page shares per user

Sketch (describe) the distribution and indicate: mean, median, p1, and p99.
What overall shape do you expect and why?

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.

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?

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.

Analyze Distribution of Daily Page Shares Per User

Quick Overview

Engagement Distributions and Cohort Dynamics

Task

Solution

Comments (0)

Analyze Distribution of Daily Page Shares Per User

Quick Overview

Engagement Distributions and Cohort Dynamics

Task

Solution

Comments (0)