Central Limit Theorem (CLT) and Normal Distribution Questions
Understand the CLT: when you take multiple random samples and calculate their means, those sample means are normally distributed (bell-shaped) even if the underlying data isn't. Know that normal distribution is parameterized by mean and standard deviation. Appreciate why this matters: it allows you to estimate population characteristics from samples and construct confidence intervals.
HardSystem Design
0 practiced
Design an architecture to compute and publish running estimates of the population mean and an approximate 95% confidence interval for a metric in a high-throughput streaming system that processes 1M events per second. Explain trade-offs in terms of latency, memory, and statistical accuracy and list sketching or sampling techniques you would consider (e.g., reservoir sampling, t-digest, streaming variance algorithms).
MediumTechnical
0 practiced
You are forecasting expected daily revenue but the raw revenue per user is extremely heavy-tailed with occasional huge values. Discuss whether the CLT justifies using sample mean-based CIs and propose robust alternatives you would use as a data scientist to provide reliable uncertainty quantification.
MediumTechnical
0 practiced
You need to determine a sample size to estimate average customer lifetime value within a margin of error of 0.5 units at 95% confidence. Population standard deviation is unknown but a pilot sample of 40 customers gives sd ≈ 4. Describe the steps to compute a recommended sample size and show the calculation using the pilot sd. Discuss any iterative steps you would take in practice.
MediumTechnical
0 practiced
Design a small dashboard or slide for a non-technical stakeholder that demonstrates the CLT using company transaction data. Specify the plots and interactive elements you would include (e.g., slider for sample size), what each element communicates, and how you would explain the practical implications for estimating average transaction value.
HardTechnical
0 practiced
You computed per-user average time-on-site from varying numbers of sessions per user and plan to use these averages as features in a downstream model. Discuss whether CLT justifies treating these per-user averages as approximately normal features, and describe strategies to handle heteroskedasticity due to varying per-user sample sizes (e.g., weighting, hierarchical modeling).
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