Statistics

When children first encounter maths, they learn arithmetic. Arithmetic requires them to be precise. There are no rewards for rough answers or approximate answers. Consequently, children learn that maths is a precise science and that they have to think precisely to get it right. Then at the age of 13, after they have been indoctrinated for about 8 years, they are presented with statistics. Statistics is all about approximate answers, rough quantities, ball park figures. The output of statistical analysis is what the likely answer might be. Children find statistics so very difficult because the turn around in mindset needed to understand what it is about is so very massive.
The mean is a real maths concept, because it involves calculation which can be done with precision… but what about the mode? So many who start on statistics consider finding the mode to be not maths. There is no arithmetic involved, all one has to do is arrange the numbers and see how many of them there are. They feel that this is for kindergarten, not for serious mathematicians. It is clearly too simplistic to be of any practical use. What can its purpose possibly be? And the median? How can it be scientific just to pick the middle number irrespective of their spread and distribution?
What all these attitudes display is lack of understanding of the purpose of maths. Maths exists to provide an understanding of things that happen in the real world. Maths concepts are used where they are useful and left alone when they are not. Mean, mode and median all exist to give the mathematician a feeling for what a typical number in a distribution of numbers might be. Depending upon the distribution these values might all be similar, or they might vary dramatically. Whichever case they fall into, their relative sizes tells us something about the nature of the distribution, but it requires experience to understand what that nature.