Meta·Data Scientist·Technical Phone Screen·Senior

Senior

May 2026

Summary

Meta DS interview with a meaty product analytics case built around group call quality and capacity decisions. One question, but it had four sub-parts that each could've been their own conversation. Felt more like a product strategy exercise than a stats exam, which I wasn't fully expecting.

Questions Asked (1)

You're deciding whether to cap the maximum number of participants in a Group Call. Given 28 days of historical group size data and a quality-of-service model where call quality degrades linearly with group size, determine: (a) how to visualize the size distribution with properly labeled axes, (b) the 95th percentile of that size distribution, (c) whether that percentile satisfies a minimum call quality threshold and what cap to set if it doesn't, and (d) the trade-offs between quality and reach, plus an adaptive capping policy and a statistical rule for monitoring the cap over time.

Product Analytics & MetricsTechnical Trade-offsA/B Testing & Experimentation

Author's notes

This one took me a second to parse because the four parts feel deceptively independent but they're really a chain.

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AI HintsAI Generated

Suggested Approach

Walk through the problem as a structured data science case: first visualize the distribution with clear axes, then compute the 95th percentile and compare it to the quality threshold, and finally discuss trade-offs and propose an adaptive cap with monitoring. Emphasize that the cap should be data-driven and revisited as usage evolves.

Pro tip: Don't just give a number—frame the cap as a product decision balancing user experience and engagement, and propose a concrete monitoring rule (e.g., alert if the 95th percentile exceeds the cap for 3 consecutive days) to show operational maturity.

1. Visualize the distribution

Plot a histogram (or ECDF) of group sizes with x-axis labeled 'Number of participants' and y-axis labeled 'Frequency' (or 'Proportion of calls'). Mention binning choices and any skew.

2. Compute the 95th percentile

Calculate the 95th percentile of the group size distribution from the 28-day data. Explain that this represents the size below which 95% of calls fall.

3. Check against quality threshold

Compare the 95th percentile to the minimum call quality threshold. If it exceeds the threshold, determine the maximum group size that still meets the threshold (e.g., solve for size where quality = threshold).

4. Discuss trade-offs and adaptive policy

Articulate the trade-off: a lower cap improves quality but reduces reach and may frustrate users. Propose an adaptive cap that adjusts based on real-time network conditions or time of day.

5. Define monitoring rule

Suggest a statistical rule to monitor the cap over time, such as tracking the 95th percentile weekly and alerting if it consistently exceeds the cap, or using a control chart.

Key Points to Mention

Use of histogram or ECDF for visualization with proper axis labels and units.
Definition and calculation of the 95th percentile (e.g., via numpy.percentile).
Linear degradation model: quality = a - b * size, and solving for size when quality = threshold.
Trade-off between quality and reach: user satisfaction vs. engagement metrics.
Adaptive capping: dynamic adjustment based on network conditions, device type, or time.
Monitoring: statistical process control, alerting on percentile shifts, or A/B testing the cap.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.