During the last twenty years statistics has become an integral part of the mathematics curriculum at all levels. In this chapter we propose various real and well-based applications that can be taught from primary school onwards.

We start with a discussion of Zipf s law, an empirical law in linguistics which permits us to show the pupils how to gather and analyze data. Since this is at secondary school level, we illustrate in section 4.2 that the same processes of thought can be explained at an early age. After all, children like to tabulate things and this can be taken advantage of in order to introduce them to meaningful, although very simple, statistics, while at the same time encouraging team-work. In section 4.3 codes and code-breaking methods, using frequency tables, are discussed. The methods we use were practical before the advent of computers, and are still a necessary introduction to the subject. In our experience this subject has always elicited an enthusiastic response. The mathematical knowledge required has been kept to a minimum.

The basic notions of mean, variance, and standard deviation are introduced, starting from a discussion of average height, in section 4.4.

In section 4.5 we emphasize that statistics is a way to describe observations, and that probability is a mathematical model to explain the regularities we find in statistical data. We discuss probabilities of events, probability measure on finite sample spaces, independent events, random variables, and expectation. We discuss, at a level suitable for advanced high school students, the law of large numbers, which shows that the probability model fits the observed data.