Meet the Averages: Mean, Median, and Mode

Imagine five friends compare their quiz scores: 6, 9, 7, 6, and 12. Their teacher wants ONE number to represent the whole group. But which number should it be? Should it be the middle score? The most common score? Or a fair share if you split all the points equally? There are actually three different answers — and every one of them is called an average. Each average tells a slightly different story about the same data. Today you will learn all three, and you will never be tricked by a misleading 'average' again.

An average is a single number that represents a whole set of data. There are three main types: mean, median, and mode. **Mean** — the 'fair share' average. Add all the values together, then divide by how many values there are. The mean of a data set is written as x̄ (called 'x-bar') in many textbooks, but you can simply call it the mean. **Median** — the 'middle' average. Arrange all values in order from smallest to largest. The median is the value right in the middle. If there is an even number of values, the median is the mean of the two middle values. **Mode** — the 'most popular' average. The mode is the value that appears most often in the data set. A data set can have one mode, more than one mode, or no mode at all (if every value appears only once). **Why does it matter which one you use?** Each average suits different situations. The mean uses every value, so one very large or very small value (called an outlier) can pull it away from the rest. The median is not affected by outliers. The mode is most useful for non-numerical data, such as the most popular shoe size in a shop.