Why do you need the mean in maths?

Answer 1

The mean is one of the measures of central tendency. The other standard ones are the median and the mode. They each have their strengths and weaknesses. For the mean, also called the average, the idea of central tendency is this: every number that has gone into calculating the average has the same unweighted effect on the final average. Of course, the numbers that are out at the extremes can seem to have more pull, but you don't actually do anything different with those numbers. They are all treated exactly the same. You add all the data points together, and then divide that sum by the number of data points. So the mean represents equally each of the data points used in its calculation.

This is a very important idea in statistics, where you figure out how to use measures of central tendency and other measures to say some surprisingly powerful things about the data you collect.