The difference between a parameter and a statistic lies in the group they describe and their nature:
- Parameter : A parameter is a numerical value that describes a characteristic of an entire population -the complete set of individuals or items under study. Parameters are fixed but usually unknown because it is often impractical to measure the whole population. Examples include the population mean (μ), population proportion (P), or population standard deviation (σ)
- Statistic : A statistic is a numerical value that describes a characteristic of a sample , which is a subset of the population. Statistics are calculated from the sample data and are used to estimate the corresponding population parameters. They vary depending on the sample chosen. Examples include the sample mean (xˉ\bar{x}xˉ), sample proportion (p^\hat{p}p^), and sample standard deviation (s)
Key distinctions:
Aspect| Parameter| Statistic
---|---|---
Describes| Entire population| Sample (subset of population)
Nature| Fixed, usually unknown| Variable, known from sample data
Purpose| True value to estimate| Estimate of the parameter
Notation| Greek letters (μ, σ, P)| Latin letters or symbols with hats
(xˉ\bar{x}xˉ, s, p^\hat{p}p^)
Example| Mean income of all U.S. residents| Mean income of a surveyed sample
of U.S. residents
Summary
- A parameter summarizes a whole population.
- A statistic summarizes a sample drawn from that population.
- Statistics serve as estimates for parameters since measuring the entire population is often impossible
This distinction is fundamental in statistics because it underpins sampling theory and statistical inference.
