The mean is probably the most famous of the summaries that can be drawn from a population. It tries to express a representative value of the entire population, and this is why it is so beloved and hated. We formally compute it, in its simplest possible formulation, by dividing the sum of all the elements of the population by the number of elements themselves minus one, so that we can write it down as:

Have you noted the minus one? I don't want to be too technical about it, you should just be aware that this is the formula employed when dealing with samples and not the entire population, which is the vast majority of times. As I was saying, it is both beloved and hated. It is beloved and frequently used because of its ease of computation and its level of synthesis. Compared, for instance, with the quartiles we have seen, you do not have to show a series of numbers and describe their meaning and relations, for instance, computing the interquartile range. You just have one number, and you can describe the whole population with it.

Nevertheless, this number tends also to be hated for two main reasons:

• It does not allow the phenomenon going on within subpopulation to emerge
• Tends to be biased from the presence of outliers