StATS: What is a mean? (sample mean/population mean)

The mean is simply the average of all the items in a sample. To compute a sample mean, add up all the sample values and divide by the size of the sample.

• The cotinine values for seven smokers are: 73, 58, 67, 93, 33, 18, and 147. If you added up these values you would get a sum of 489. Divide that sum by 7 to get a mean of 69.9.

We will sometimes make the distinction between the sample mean and the population mean. The population mean (often represented by the Greek letter mu) is simply the average of all the items in a population. Because a population is usually very large, the population mean is usually an unknown constant. The formula for the population mean is:

where N is the number of items in the population. Usually N is very large in the thousands, millions, or sometimes even infinity. The greek letter sigma indicates that you should add the values together.

The sample mean (often represented by the symbol XBAR) is the average of all the items in a sample. The sample mean is a lot easier to compute because the size of the sample is usually quite manageable. If the sample is chosen carefully, the sample mean is a good estimate of the population mean. The formula for the sample mean is

where n is the number of items in the sample.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Definitions, Category: Descriptive statistics.