A parameter is a number that describes a whole population. A statistic is the same kind of number calculated from a sample.
Why it matters
We almost never know the parameter. We use the statistic to estimate it, and we must remember it can be off.
Key ideas
- Parameter: population mean μ, proportion π
- Statistic: sample mean x̄, proportion p
- Parameters are fixed but unknown
- Statistics change from sample to sample
- Inference connects the two
Real-life research example
The true mean hemoglobin of all pregnant women in a district is the parameter. The mean of 200 women you measured is the statistic.
When to use
- Say "parameter" when talking about the population
- Say "statistic" when reporting your sample result
When NOT to use
- Don't write μ for a sample mean
- Don't treat x̄ as if it were exactly μ
Mini example
Population mean μ = 50.5 (unknown to you) Sample of 5 gives x̄ = 58.6 Another sample gives x̄ = 44.0
Quick takeaway
Parameter describes the population. Statistic describes the sample and estimates the parameter.
Try it yourself
Draw several samples below. Which number is the parameter and which are statistics?
Model answer
50.5 is the parameter (fixed). Every sample mean is a statistic and changes with each draw, but they cluster around 50.5.