The meaning of statistical functions.

What is the meaning of a standard deviation? It has a definition which can be taught, but what its meaning is is a different question. This is something that cannot be taught. It is a concept that someone only picks up through usage. A sample’s position relative to the standard deviation and the mean says something about that sample, and where it fits within a distribution… but so what? What are the implications of the sample’s position? That will vary from sample to sample, and be different in the case of a pharmaceutical tablet and in the case of an orange. It is this interpretation of the data, which varies from situation to situation that makes teaching and learning statistics so very challenging. Principally we have a chicken and egg situation. The pupil has to use the concept, to learn it, and only after having used it (for a period of 9 months or so) will they begin to develop the understanding of what it actually means, what its implications are in various scenarios. At Puppet Maths we teach statistics via scenarios which we create with our puppets. This we have found is the optimal way of conveying the meaning of the various concepts that exist in statistics.