LinkedIn Data Scientist Statistics Fundamentals
You are asked a series of statistics fundamentals questions in a data science technical screen.
Constraints & Assumptions
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Explain the intuition first, then add formulas or technical terms only where useful.
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State any assumptions, such as equal teller skill, independent arrivals, or the population being discussed.
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For distribution questions, describe the shape and the reason for that shape.
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For regularization, connect bias to out-of-sample performance rather than stopping at a definition.
Clarifying Questions to Ask
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Should I answer qualitatively, sketch the distributions, or derive a formal result?
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Are we assuming teller service rates are identical?
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For heights, are we discussing adults in the United States only?
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For LinkedIn connections, are there platform-imposed limits or sampling filters?
Part 1 - Queueing
A bank with 5 tellers can be organized two ways:
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System A: all 5 tellers share one common queue.
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System B: each teller has their own separate queue.
Assume customer arrivals are random, tellers are similarly but not necessarily identically skilled, customers are served first-come-first-served within a line, and some customers take much longer than others.
As a customer, which system would you rather join, and why? Compare expected waiting time, variance of waiting time, and fairness.
What This Part Should Cover
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The pooled queue usually has lower or no worse expected waiting time because idle capacity is shared.
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The pooled queue has lower variance because customers do not bear line-selection risk.
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Fairness is better because service order is closer to global first-come-first-served.
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Caveats for low utilization, visible shortest-line choice, heterogeneous tellers, and express lanes.
Part 2 - Height Distributions
Sketch or describe the distribution of adult male heights in the United States and, separately, adult female heights in the United States.
What This Part Should Cover
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Each distribution is roughly bell-shaped and approximately normal.
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Female and male distributions have different centers and overlap substantially.
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Real populations have finite tails and may deviate slightly from perfect normality.
Part 3 - Pooled Height Distribution
If you pool men and women together and ignore sex, what does the combined height distribution look like?
What This Part Should Cover
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The pooled distribution is a mixture of two overlapping distributions.
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It may be wider and can look slightly bimodal or shoulder-shaped depending on the separation and variance.
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Pooling can obscure meaningful subgroup structure.
Part 4 - Network Degree Distribution
On a social network such as LinkedIn, describe the distribution of the number of connections per user. Is it symmetric, left-skewed, or right-skewed?
What This Part Should Cover
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The distribution is right-skewed or heavy-tailed.
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Many users have modest numbers of connections, while a smaller group has very high counts.
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The shape is driven by network effects, professional behavior, account age, and platform limits.
Part 5 - Summary Statistics
For the connections distribution, how do the mean, median, and mode compare, and why? If asked for the likely scale of the mean, what factors would determine it?
What This Part Should Cover
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For a right-skewed distribution, the usual ordering is mode < median < mean.
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The right tail pulls the mean upward.
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The mean depends on the sampled population, active-user definition, geographic or industry mix, account age, and platform constraints.
Part 6 - Regularization Bias
Are L1-regularized lasso and L2-regularized ridge estimators unbiased? Why or why not?
What This Part Should Cover
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Both are generally biased because they shrink coefficients toward zero.
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L1 can set coefficients exactly to zero; L2 shrinks continuously.
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The bias can reduce variance and improve prediction error on unseen data.
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The answer should distinguish coefficient estimation bias from predictive performance.
What a Strong Answer Covers
A strong answer uses clear intuition, states assumptions, compares distribution shapes, explains how skew affects summary statistics, and links regularization bias to the bias-variance trade-off.
Follow-up Questions
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When would separate queues be operationally preferable despite higher variance?
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How would you empirically check whether the pooled height distribution is bimodal?
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Why can the mean be a poor summary for connection counts?
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How does regularization strength affect bias and variance?