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Question 1

Explain the Fermi estimation method. Illustrate with an example, e.g., estimating the number of cats in Norway.

Answer 1

Fermi Estimation Method:
➤ A quick, rough approach to estimate difficult quantities by breaking problems into simpler parts.
➤ Accepts order-of-magnitude accuracy (within about 10x).
➤ Uses logical assumptions and known info to make manageable estimates.
➤ Cross-checks with different methods to increase confidence.

Example: Estimating Number of Cats in Norway

Norway population ≈ 5.4 million

Average household size ≈ 2.2 people

Total households ≈ 5.4M ÷ 2.2 ≈ 2.5 million

Assume 30% households own pets → 2.5M × 0.30 = 750,000 pet-owning households

Cats vs dogs equally popular → 750,000 × 0.50 = 375,000 cat-owning households

Average cats per cat-owning household ≈ 1.5

Total cats ≈ 375,000 × 1.5 = 560,000 cats

Cross-Check Approaches:

15% of households own cats → 2.5M × 0.15 = 375,000 households × 1.5 cats = 560,000 cats

Per capita: 1 cat per 10 people → 5.4M ÷ 10 = 540,000 cats

Final Estimate:
~500,000 to 600,000 cats in Norway

Why It Works:
➤ Breaks complex problem into smaller, intuitive parts
➤ Uses logical assumptions and available knowledge
➤ Cross-checking gives confidence in estimate
➤ Rough but useful accuracy for practical purposes

Applications in Project Management:
➤ Early cost/resource estimates without detailed data
➤ Risk and feasibility assessments
➤ Quick, reasonable approximations to guide decisions

Simple Explanation:
Fermi estimation splits a big, hard guess into smaller easy guesses, combines them, and checks with different angles to get a quick, useful estimate.

Question 2

Define project cost overruns and the key disagreement in its definition

Answer 2

Project Cost Overrun:
➤ When actual project cost > expected cost.
Example: Expected $4M, actual $5M → overrun = $1M (25%).
➤ Not all cost increases count as overruns—adjustments may exclude inflation, scope changes, or material price changes.

Key Disagreement:
➤ Which cost estimate to compare actual costs against?

Flyvbjerg (2002): Use cost estimate at project sanction (start).

Love & Ahiaga-Dagbui (2018): Use latest estimate after last major scope change.

Consequences:
➤ Flyvbjerg’s method → 90% projects show overruns.
➤ Love & Ahiaga-Dagbui’s method → only ~33% show overruns.
➤ Definition choice affects perception of project success/failure and can lead to unfair blame or misleading stats.

Simple Explanation:
Cost overruns mean spending more than planned. But whether we compare costs to the original budget or a later one changes how often overruns seem to happen.

Question 3

Flyvbjerg’s 3 root causes of cost overruns and statistical inference

Answer 3

Root Causes:

Random error: Honest mistakes, some projects over, some under budget.

Cognitive bias: Overly optimistic estimates, consistent underestimation but moderate.

Strategic misreporting: Deliberate underestimation to secure approval, large and frequent overruns.

How to Infer Cause Using Statistics:
➤ Random error → balanced distribution of overruns and underruns.
➤ Cognitive bias → consistent small underestimations.
➤ Strategic misreporting → systematic, large, one-sided overruns.

What Flyvbjerg Found:
➤ 90% of projects had overruns, often large and one-sided → rules out random error, indicates bias or strategic misreporting (likely the latter).

Simple Explanation:
Looking at many projects shows if overruns are random or mostly one-sided. Most are one-sided and big, meaning people likely underestimate costs on purpose.

Question 4

Steps to create a histogram

Answer 4

Collect data: Gather values (e.g., project costs).

Decide bins: Number of intervals, often √(number of data points).

Determine intervals: Find min & max, divide range evenly by bins.

Count frequency: Number of data points per bin.

Calculate relative frequency: Frequency ÷ total observations.

Calculate density (optional): Relative frequency ÷ bin width (for unequal bins).

Plot histogram: Bars with heights = frequency or density, bars touch (no gaps).

Simple Explanation:
A histogram shows how data points spread across ranges by grouping them into bins and drawing bars to represent how many fall into each group.