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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.

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This is a medium difficulty Statistics & Math question, commonly asked during Take-home Project rounds at Boston Consulting Group.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Boston Consulting Group during technical interviews.

Compute averages and binomial/Poisson probabilities | Boston Consulting Group Interview Question

Quick Overview

This question evaluates proficiency in streaming summary-statistics updates and probability calculations, specifically computing an updated mean from aggregated summaries and comparing Binomial versus Poisson probability computations within the Statistics & Math domain.

Streaming Mean and Binomial vs Poisson Approximation

Part A — Streaming Mean Update

You have an existing dataset of N = 1,000 observations with mean 12.4. You:

Remove r = 50 observations whose mean is 20.1, then
Append a = 30 new observations whose mean is 9.8.

Without recomputing from raw data, compute the exact new mean. Show the formula you use and report the final value to 3 decimal places.

Part B — Binomial vs Poisson Approximation

Let X ~ Binomial(n = 40, p = 0.07).

Compute P(X = 0), P(X ≤ 2), and P(X ≥ 3) exactly. Report each to 4 decimal places.
Approximate the same three quantities using a Poisson(λ = n·p) model (use continuity only if appropriate), and report absolute errors for each quantity (|exact − approx|).
Briefly justify when the Poisson approximation is appropriate here, and how you would tighten the approximation if p were larger.

Streaming Mean and Binomial vs Poisson Approximation

Part A — Streaming Mean Update

You have an existing dataset of N = 1,000 observations with mean 12.4. You:

Remove r = 50 observations whose mean is 20.1, then
Append a = 30 new observations whose mean is 9.8.

Without recomputing from raw data, compute the exact new mean. Show the formula you use and report the final value to 3 decimal places.

Part B — Binomial vs Poisson Approximation

Let X ~ Binomial(n = 40, p = 0.07).

Compute P(X = 0), P(X ≤ 2), and P(X ≥ 3) exactly. Report each to 4 decimal places.
Approximate the same three quantities using a Poisson(λ = n·p) model (use continuity only if appropriate), and report absolute errors for each quantity (|exact − approx|).
Briefly justify when the Poisson approximation is appropriate here, and how you would tighten the approximation if p were larger.

Compute averages and binomial/Poisson probabilities

Quick Overview

Streaming Mean and Binomial vs Poisson Approximation

Part A — Streaming Mean Update

Part B — Binomial vs Poisson Approximation

Solution

Comments (0)

Compute averages and binomial/Poisson probabilities

Quick Overview

Streaming Mean and Binomial vs Poisson Approximation

Part A — Streaming Mean Update

Part B — Binomial vs Poisson Approximation

Solution

Comments (0)