Definition
The mean (also called the arithmetic average) is the sum of all values in a dataset divided by the number of values. It is the most commonly used measure of central tendency in statistics and gives you a single number that represents the "center" of your data.
How to Calculate the Mean
The formula is straightforward: add up every value, then divide by how many values you have.
A teacher records quiz scores for 5 students: 72, 85, 90, 68, and 95.
Step 1: Add the scores: 72 + 85 + 90 + 68 + 95 = 410
Step 2: Divide by the count: 410 / 5 = 82
The mean quiz score is 82.
Why It Matters
The mean is everywhere - from your grade point average to economic reports about average household income. It is the foundation of many advanced statistical methods, including hypothesis testing and regression analysis. Understanding the mean helps you summarize data quickly and compare groups.
However, the mean has an important limitation: it is sensitive to outliers. A single extreme value can pull the mean far from what is typical. For example, if one student scored 20 instead of 95, the mean drops from 82 to 67 - even though most students scored much higher. When your data is skewed, the median often gives a more accurate picture.
The mean is the go-to measure for symmetrical data without extreme values. When outliers are present, consider using the median instead.