Sketch distributions and compare mean/median/mode
Quick Overview
This question evaluates understanding of distributional shape, central tendency (mean, median, mode), skewness, outliers, and the effects of combining subpopulations in real-world data.
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Feb 16, 2026, 7:49 AM
Data Scientist
Technical Screen
Statistics & Math
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Distribution sketches and summary-stat comparisons
Answer the following conceptual statistics questions. Assume you have a large random sample and you are sketching shape only (no need for exact parameters).
Part A — Human heights
- Sketch the distribution of adult male heights in the US .
- Sketch the distribution of adult female heights in the US .
- If you combine men and women into a single population, what does the height distribution look like? Explain why.
Part B — Social network connections
Consider the distribution of number of connections/friends per user on a professional social network (e.g., LinkedIn).
- Sketch the distribution of “number of connections.”
- Describe what you expect for the mean relative to most users (i.e., will the mean be close to a typical user’s value?).
- For this distribution, compare mean vs median vs mode and explain your reasoning.
(You may assume standard data issues like outliers and heavy tails can occur.)
Solution
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