Sample and Parametric Means

The sample mean is what you estimate from your data. It is known as a sample statistic because it is calculated from a sample of observations. The symbol for a sample mean is (pronounced 'y bar'). You will usually wish to use this sample statistic to estimate the mean of the entire population it represents. This 'population' is all of the observations you could potentially make.

For example, you might measure the number of animal species on ten islands. Those ten numbers would be a sample. The 'population' you wish that sample to represent depends upon what you are studying. If you wish to work out the average number of animal species living on islands around the world, those islands are the population of interest. Or you may be interested in just the Pacific Islands. Or you might only be interested in the ten islands you have studied. In which case, that is your population.

The mean of the population is called a population parameter. The symbol used for the population mean is μ (pronounced 'mew').

Sample means are unbiased estimates of the true, or parametric mean. Thus, is an unbiased estimate of μ. But it is subject to error. The larger the sample size, the smaller that error is likely to be. Unfortunately, no matter how large your sample is, your measurement is always subject to some error.

Although the sample mean is an unbiased estimate of the parametric mean, this is by no means true for many of the statistics you may calculate. Hence you will often have to correct the sample estimate for bias.