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10.3 Parameter And Statistic:

In order to avoid verbal confusion with the statistical constants of the population, viz., mean (μ), variance σ2, etc., which are usually referred to as parameters, statistical measures computed from the sample observations alone, eg., mean (x bar), variance s2, etc., have been termed by Professor R.A Fisher as statistics.

In practice, parameter values are not known and the estimates based on the sample values are generally used. Thus statistic which may be regarded as an estimate of parameter, obtained from the sample, is a function of the sample values only. It may be pointed out that a statistic, as it is based on sample values and as there are multiple choices of the samples that can be drawn from a population, varies from sample to sample. The determination or the characterization of the variation that may be attributed to chance or fluctuations or sampling is one of the fundamental problems of the sampling theory.

10.3.1 Sampling distribution of a statistic:

If we draw a sample of size n from a given finite population of size N, then the total number of possible samples is:

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