After a contribution to a previous thread I thought some more about what I actually wanted to say, so here is a much more succint version:

The average of any distribution or even worse of a dataset is not a sufficient description without a statement about the distribution.

So often research results are reported as a simple average with a standard deviation. The educated statistician will recognise these two numbers as the first two modes of a distribution. But these two modes completely describe a distribution if it is a normal distribution. Though the central limit theorem gives us justification to use it in quite a number of cases, in general we need to make sure that the dataset has no higher modes. The most obvious case is of a dataset dominated by a single binary random variable.

This statement then, that not all datasets are normally distributed, holds for any field, be it solid state physics, astrophysics, biochemistry, evolutionary biology, population ecology, welfare economics or psychology. To assume that any average together with a standard deviation derives from a normal distribution or even worse that there is no more information in the dataset or the underlying phenomenon is a grave scientific mistake.