A parameter describes a population. A statistic describes a sample.
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The relations depend on what measures. The sample mean is an unbiased estimate for the population mean, with maximum likelihood. The sample maximum is a lower bound for the population maximum.
A parameter is a numerical measurement of a population; a statistic is a numerical measurement of a sample.
A parameter is a number describing something about a whole population. eg population mean or mode. A statistic is something that describes a sample (eg sample mean)and is used as an estimator for a population parameter. (because samples should represent populations!)
Population Parameter
parameter