Mean

Instead of using the mode, the mean is the most useful measure of what a typical score is doing because it is, by definition, the average. We have symbols for it. We’ve talked about these before. But let’s review. Our symbol in our sample is typically going to be x bar, or x with a bar over it. However, if you’re writing up results, maybe putting a Word document or PowerPoint deck together, you’re probably not going to want to use that. So we often just use an italicised capital M. It’s intuitive. M stands for Mean. The other thing I want to mention is that the mean can happen at two levels.

If you’re dealing with a sample or a small set of data from which you want to make some generalisations, we will use these symbols just fine. However, sometimes you actually have all the data of interest. Say, for instance, you go to a popular shopping website and look at their data. They may have every record of every thing ever done on that website, in which case there’s no need to generalise from the data. You have all the data. And in that case, we actually use a different symbol. We call that the population. And that would be if you have every score of interest. And the symbol for that would be mu, which is actually just a Greek letter M.

Regardless of which level we calculate the mean, the formula is going to be the same. You’re going to add up all the scores, sigma x, and you’re going to divide by the number of scores, n. It is the average. It is easy to calculate. And it is the most common summary statistic we’re going to calculate when working with data.