Direct comparison
Parameter Vs Statistic: Key Differences & Comparison | CASRAI
A parameter and a statistic are both numerical summaries, but of different groups. A parameter describes a whole population and is usually unknown; a statistic describes a sample and is calculated from observed data. Statistics are used to estimate parameters, and the two are conventionally written with Greek and Roman symbols respectively.
Side-by-side comparison
| Dimension | Parameter | Statistic |
|---|---|---|
| Describes | A whole population | A sample drawn from the population |
| Known or unknown | Usually unknown — the true value sought | Calculated directly from observed data |
| Fixed or variable | Fixed for a given population | Varies from one sample to the next |
| Symbol — mean | μ (mu) | x̄ (x-bar) |
| Symbol — std dev | σ (sigma) | s |
| Symbol — proportion | p or π (pi) | p̂ (p-hat) |
| Notation convention | Greek letters | Roman letters |
| Role | The target being estimated | The estimator used to infer the parameter |
| Example | The mean income of all UK households | The mean income of 2,000 surveyed households |
Common questions
FAQ
How do I remember which is which?+
A handy mnemonic: parameter and population both start with "p", while statistic and sample both start with "s". So a parameter summarises a population, and a statistic summarises a sample. You calculate a statistic to estimate a parameter.
Why are parameters usually unknown?+
Because they describe an entire population, which is rarely measured in full — doing so would require a complete census of every member. Instead, researchers take a sample, compute a statistic, and use it to estimate the unknown parameter, along with a margin of uncertainty.
Why use Greek and Roman letters?+
It is a long-standing convention that keeps the two clearly distinct. Greek letters (μ, σ, π) denote population parameters, while Roman letters (x̄, s, p̂) denote the matching sample statistics. Seeing the symbol tells you immediately whether a value refers to the whole population or to a sample estimate.
Going deeper
