In statistics, the mean is the mathematical average of a set of numbers. The average is calculated by adding up two or more scores and dividing the total by the number of scores.

Consider the following number set: 2, 4, 6, 9, 12. The average is calculated in the following manner: 2 + 4 + 6 + 9 + 12 = 33 / 5 = 6.6. So the average of the number set is 6.6.

### Why Psychologists Care About the Mean

If you are taking a psychology class, you might be wondering why your instructor wants you to know so much about statistical concepts such as the mean, median, mode, and range. The reason for this is that psychologists utilize such numbers to help make sense of data that is collected through research.

Imagine, for example, that a psychologist is doing research on sleep habits among college students. She hands out a form to a random sample of 100 university students and has them track how much they sleep each night for a period of 30 days.

Once data has been collected, a researcher has a great deal of information. But now she needs to make sense of this information and determine how to present it in a meaningful way. A mean can help do that.

The first thing this psychologist might do is take a look at the data collected from each individual student. She might want to look at things such as the range of data (the smallest amount of sleep the student got to the most amount of sleep the student reported), but one of the most helpful numbers she might want to look at is the average amount of sleep that the student got per night over the course of the month.

In order to accomplish this, she would start by adding up each number and then dividing by the total number of data points. In this case, the month had thirty days, so she would add up the hours of each night sleep and then divide that total number by 30. This value represents the mean, or average number, of hours of sleep that each particular student reported over the course of the month.

Once she has calculated a mean for each student, she might want to then report the range of values, the median (or most frequently occurring number), or even combine all of the numbers into an overall mean for the entire group.

### Measures of Central Tendency

The mean is just one type of measure of central tendency. In other words, psychologists are often interested in looking at how data points tend to group around a central value. By understanding this central value, researchers are able to get a better idea about what is considered expected or normal for a particular group as a whole.

The mean can be influenced by extreme data points. If most tend to fall within a certain range, but a few data points are either very high or very low, the mean might not be a good reflection of what is really happening with the data.

Consider your own grades on exams in your psychology class, for example. Imagine that you have taken four tests so far with scores of 96 percent, 98 percent, 94 percent, and 100 percent. Unfortunately, you were not feeling well before your last exam and did not have enough time to prepare and ended up flunking the test with a score of just 14 percent. While the rest of your exams scores represent solid work, that one extremely low score drags your mean score down to 80.4 percent. For this reason, research might also look at the median score, or the most frequently occurring score in a data set, as a means of determining central tendency.