The purpose of sampling is to obtain

The

A sample may be selected

There are several

One appealing feature of simple random sampling is the lack of bias in the selection of the sample.

After a simple random sample is selected and the selected elements measured or interviewed, it is reasonable to use the (ordinary) sample mean of a variable as an estimate of the unknown population mean of that variable, and the (ordinary) proportion of sampled elements in a category as an estimate of the proportion of elements in the population in the same category. To estimate the population totals or numbers, multiply these estimates by the population size,

It can never be guaranteed (with certainty) that an estimate will be equal to, or within a given interval from the corresponding population characteristic (unless, of course, sampling is with replacement and the sample size equals the population size).

Imagine an experiment whereby a large number of simple random samples of the same size are selected from a known population, and from each such sample a sensible estimate is made of the population characteristic. It will be observed that the average value of these sensible estimates is equal to the population characteristic. In other words, in the long run and on average the sensible estimate neither under-estimates nor over-estimates, but is equal to the population characteristic. An estimate with this property is called an

The property can be confirmed mathematically to hold in general. That is, the ordinary sample mean (total) and proportion (number) are unbiased estimates of the corresponding population mean (total) and proportion (number).

It can be shown, however, that the sensible estimates are

Stratified and two-stage random sampling require that the population elements be divided into groups according to some criterion. The sample is called