Standard Error and Sampling Distribution

The standard deviation of the sampling distribution is called the standard error. It is called because it measures the sampling variability due to chance or random forces. Hence to clarify the term standard error it is necessary to describe a sampling variability due to chance or random forces. Hence to clarify the term standard error it is necessary to describe a sampling distribution. If we select a number of independent random samples of a definite size from a given population and calculate some statistics (like the mean, standard deviation, etc.) from each sample, we shall get a series of values of these statistics or functions. These values obtained from the different samples can be put in the form of a frequency distribution. The distribution so formed of all possible values of a statistics is called the sampling distribution or the probability distribution of that statistics. Thus if we draw 100 random samples from a given population and calculate their mean, we shall get a series of 100 means which would from a frequency distribution. This distribution will be known as the sampling distribution of the means.

An explanation of sampling distribution would be incomplete without describing the universe distribution, the sample distribution and showing the relationship of these two with the sampling distribution.

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