Characterize metric distribution and quantiles

Q: Characterize metric distribution and quantiles

This question evaluates a data scientist's competency in descriptive statistics and robust metric analysis within the Statistics & Math domain, focusing on distribution characterization, empirical quantiles, measures of central tendency, and the effects of outlier handling on variance and experimental power.

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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

KPI Analysis: Per-Video Watch Time (seconds)

You are evaluating a pilot dataset for the KPI "per‑video watch time" (in seconds). The dataset (n = 20) is sorted ascending:

3, 5, 6, 6, 7, 8, 9, 10, 12, 15, 16, 20, 24, 30, 35, 45, 60, 90, 120, 180

Tasks

Distribution shape
- Describe the likely distribution shape (skewness and tail heaviness) and sketch it verbally.
Summary statistics with interpolation
- Compute the sample median, mode, and the 95th percentile using the linear interpolation method for empirical quantiles. Show steps.
Mean vs. median
- Compare the mean versus the median for this data and argue which is the more decision‑robust location estimator and why.
Winsorization and power
- If you winsorize at the 99th percentile, explain qualitatively how that would change variance and statistical power in an A/B test on watch time.

Characterize metric distribution and quantiles

KPI Analysis: Per-Video Watch Time (seconds)

Solution

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Characterize metric distribution and quantiles

Overview

KPI Analysis: Per-Video Watch Time (seconds)

Solution

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