Mean Compared to Sample Mean Understanding the Differences

The mean and sample mean are both measures of central tendency. They measure the average of a set of values. For example, the mean height of fourth graders is an average of all the varying heights of fourth grade students.

Definition

The terms “mean” and “sample mean,” when used without further specification, both refer to the arithmetic mean, also known as the average.

Differences

“Mean” usually refers to the population mean. This is the mean of the entire population of a set. Often, it’s not practical to measure every individual member of a set. It’s more practical to measure a smaller sample from the set. The mean of the sample group is called the sample mean.

Example

Suppose you want to know the average height of fourth grade students in New York City. The population consists of all the fourth graders in the city. You would calculate a mean by adding the height of every fourth grader in the city and dividing it by the total number of fourth graders. For a sample mean, you’d calculate the mean for a smaller set of fourth graders. Whether that number approximates the mean for all fourth graders in the city depends on how well the sample matches the total population.