I started with the easy part, explaining why mean is misleading here and median is more representative, but then kind of fumbled when they pushed on P1 and P99 specifically.
Start by acknowledging the heavy-tail nature of page share counts and the limitations of the mean. Then, propose a robust annotation strategy using median and percentiles (P1, P99) to capture central tendency and tail behavior, and outline a forecasting method that accounts for extreme values, such as a log-transform or a heavy-tailed model.
Pro tip: Emphasize that the mean is misleading for heavy-tailed data; instead, use the median and percentiles to communicate typical and extreme behavior. Also, consider that P1 might be more informative than P99 for understanding the 'long tail' of low-engagement pages.
Confirm the heavy-tail nature by plotting the distribution (e.g., histogram on log scale) and computing skewness/kurtosis. Discuss why the mean is not representative.
Choose median as the central tendency measure, and P1 and P99 to capture the lower and upper tails. Explain what each statistic reveals about user engagement.
Annotate these statistics on a box plot or violin plot, and possibly on a log-scale histogram. Highlight how they provide a more complete picture than the mean alone.
Propose a forecasting approach that handles heavy tails, such as log-transforming the data before applying time series models (e.g., ARIMA) or using a generalized Pareto distribution for extreme values.
Suggest backtesting the forecast and monitoring key percentiles over time to detect shifts in the distribution, which could indicate changes in user behavior or product features.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.