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Parameter and Statistic

Any statistical measure relating to the population which is based on all units of the population is called parameter, e.g., population mean ().1), population S.D. (cr), moments µr, µr ‘ etc.

 

Any statistical measure relating to the sample which is based on all units of the sample is called statistic, e.g., sample mean (.X), sample variance, moments mr, m'r etc. Hence the value of a statistic varies from sample to sample. This variation is called 'sampling fluctuation'. The  parameter has no fluctuation and it is constant. The probability distribution of a statistic is called 'sampling distribution'.

 

The standard deviation (S.D.) in the sampling distribution is called 'standard error' of the statistic.

 

Example 1. For a population of jive units, the values of a characteristic x are given below :

8, 2, 6, 4 and 10.

Consider all possible samples of size 2 from the above population and show that the mean of

the sample means is exactly equal to the population mean.

 

Solution. The population mean, )µ = 30/5 =  6

 

Random samples of size two (Without Replacement)

:. Mean of sample means =(31+29)/10 = 60/10 = 6 which is equal to the population mean.