Simple example of a sampling distribution Suppose that a population consisted of five families and we wish to estimate the average household income based on a sample of size 2. Both of these values refer to individual units in the population. For example, think back to sampling from StatVillage. Of course we hope that they are representative of what would happen in the population. Similarly, the sampling distribution of s refers to the variation of s over all possible samples from the population.
Lets look at the sampling distribution of and s in more detail.
Notice that some values of are above the population mean, and some values of are above the population mean. We don't have any guarantee from a single sample if we are above or below the true value of the population parameter. We say such estimators are unbiased . This must be read carefully. We say that s is a biased estimator.