I hope this is the proper forum to ask this question.
In November I will be giving a short talk on Statistics to a Science group, and will be including a warning about how averages can mislead. One amusing example, from a BBC4 TV programme, is that the average number of legs in the population is about 1.998, since a few people have one or no legs, but no one has three or more. So nearly all the population has more than the average number of legs.
For a more serious example I remember from years ago reading that the average level of radioactivity on a beach near Dounreay Nuclear Site, after a series of accidents there, was (whatever), well within safety limits. I thought then that the real danger would be intensively radioactive particles that could be ingested, but averaged out over an area would give this reassuringly safe value.
I cannot find a reference to this, all that I can find is the shameful story of failure to deal with the admitted problem of huge numbers of these particles.
Can anyone help me with figures to illustrate this, or a similar example, or a reference to the original reports?