A parameter describes a whole population; a statistic describes a sample. The average height of all adults in a country is a parameter — one fixed, true value, almost never actually measurable. The average height of the 1,000 adults you surveyed is a statistic — computable, and a little different with every new sample. Statistics are how we estimate parameters we cannot reach.
In everyday English a parameter is a limit — the edges within which something may vary, like the stops on the mixing desk in the scene above. Statistics borrowed the word for the fixed truths of a whole population: the real mean, the real proportion — values that exist whether or not anyone can afford to measure every member. A statistic is the working substitute: compute the same quantity on a sample and use it to estimate the parameter. That is the entire relationship — one number is the target, the other is the shot at it — and the notation keeps them apart: Greek letters (μ, σ) for parameters, Latin (x̄, s) for statistics.
parameter
A parameter comes from Greek para- (beside) and metron (measure): a measure set alongside, a limit you agree to work within. In the plural it usually means the boundaries of a task — 'within the parameters of this study' — the agreed scope no one should overstep. In its technical sense a parameter is a variable factor whose value you can set, like a constraint you choose rather than one imposed. Either way it defines a space: fix the parameters and you fix where the work may go.
statistic
A statistic is one number distilled from many — an average, a percentage, a count — that stands in for a whole mass of measurements. The word shares its root with 'state', since such figures were first gathered to describe nations: their populations, harvests, and taxes. A single statistic can clarify or mislead, which is why careful readers ask how it was collected before they let it settle an argument. The plural, statistics, also names the entire discipline of analysing such data.
| parameter | statistic | |
|---|---|---|
| Describes | the whole population | one sample |
| Value | fixed — one true number | varies from sample to sample |
| Computable? | rarely — you would need everyone | yes — that is its job |
| Symbols | Greek: μ, σ, π | Latin: x̄, s, p̂ |
| Role | the target being estimated | the estimate doing the work |
| Example | mean height of all adults | mean height of 1,000 surveyed |
The stops and the summary. A parameter is the pair of stops on the desk: a fixed fact about the whole system, set whether or not you ever look at it. A statistic is the glowing number in the corner of the chart: computed from the readings you actually collected, and different the next time you collect. Ask one question — was every member measured, or just a sample? Whole population: parameter. Sample: statistic.
parameter
- iThe true unemployment rate for the whole country is a parameter no survey ever sees directly.
- iiMean body temperature across all living adults is a parameter; no thermometer will ever reach it.
- iiiA census aims at parameters: it tries to measure everyone, not a sample.
statistic
- iThe poll's 43% approval figure is a statistic drawn from 1,200 voters.
- iiEach new sample of bulbs gives a slightly different failure-rate statistic.
- iiiThe clinic reports a sample statistic: average recovery time among its own patients.
Two housekeeping notes keep the pair tidy. First, everyday English uses parameter loosely for any limit or factor ('within the parameters of the budget') — that sense, the one this site's parameter page animates, is separate from the statistical one, and in essays it is almost always the one you want. Second, the pair travels with two companions: population and sample. Hold all four together and the topic is essentially held — which is why the one-sentence summary in the first question below is worth memorising outright.
The stats sense surfaces in TOEFL reading passages on research methods: when a passage says a statistic was computed, it is flagging sample-based evidence, with all the uncertainty that implies — a favourite setup for inference questions. In your own writing, keep the register straight: essay 'parameters' are scopes and limits, not population values, and IELTS Task 1 numbers are statistics only in the loose sense of figures — no sampling theory required.