True Population Parameter#
The fixed, usually unknown quantity (mean, proportion, coefficient) that estimation targets.
Important
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What it is#
A true population parameter is a fixed (but usually unknown) number that describes a whole population. The word true stresses that the value exists even though we seldom observe it. The familiar ones are written with Greek letters: \(\mu\) (mean), \(\sigma\) (standard deviation), \(p\) (proportion) and \(\rho\) (correlation).
Parameter vs statistic#
Because we rarely measure an entire population, we draw a sample and compute a statistic to estimate each parameter:
mean — parameter \(\mu\), statistic \(\bar{x}\)
standard deviation — \(\sigma\), statistic \(s\)
proportion — \(p\), statistic \(\hat{p}\)
correlation — \(\rho\), statistic \(r\)
The statistic is random (it depends on which sample you draw); the parameter is fixed but unknown. This single distinction underlies every “true vs sample” page in statistics.
Example#
The parameter \(p\) might be the real fraction of all U.S. voters who support candidate A; a survey of 1,000 gives the statistic \(\hat{p} = 0.52\), an estimate of that unknown \(p\).
Inference is about parameters#
We never know a parameter exactly without a census, so we infer it: a confidence interval brackets it (“95% confident the true parameter lies in this range”), and a hypothesis test evaluates a claim about it (\(H_0 : \mu = 100\)). Estimators, standard errors, intervals and tests all exist to pin down population parameters from sample data.
Theme: Probability & Statistics Foundations · All terminology
Hint
Mind map — connected ideas
True Mean (Population Mean) · True Conversion Rate · Sample Mean · Sample Standard Deviation · Parameter(s) of Interest · Proportion
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More in Probability & Statistics Foundations
Beta Distribution · Confidence Level · Correlation · Critical Value · Cumulative Distribution Function (CDF) · Frequentist · IID (Independent and Identically Distributed) · Likelihood · Margin of Error (MoE) · Mean · Median · Normal Distribution · Outlier · Population Proportion
See also
Source article Adapted (context, re-expressed) in our own words from: True Population Parameter (insightful-data-lab.com).