Describe the data before modeling
Summary statistics describe different aspects of a distribution; one number rarely tells the whole story.
The idea
Two groups can have the same average but very different spread, so the average alone can hide important structure.
Location measures such as mean or median summarize center, while variance or standard deviation summarize spread. Shape and outliers also matter.
How it works
- Inspect data types, ranges, missingness, duplicates, and impossible values.
- Summarize center with mean/median and spread with variance, standard deviation, IQR, or quantiles as appropriate.
- Visualize distributions and relationships.
- Reason about sampling uncertainty, dependence, and whether the sample represents the target population.
Mean and population variance
Sample estimators may use n−1 for an unbiased variance estimate under standard assumptions. The right statistic depends on the question and sampling process.
μ = (1/n)Σxᵢ, σ² = (1/n)Σ(xᵢ−μ)²
Check your understanding
If two datasets have the same mean, what can still differ?
- Their spread and shape
- Nothing at all
- Their sample count must be identical
- Their labels must match
Answer and explanation
Equal means do not imply equal distributions. Spread, skew, outliers, sample size, and other structure can differ.
A common misconception
A larger dataset does not automatically remove bias; it can estimate the wrong population very precisely.
Data & AI Foundations
Understand distributions, projections, evaluation, and explanations so model outputs are easier to reason about.