Dogs and the central limit theorem
At school/University I had vaguely heard of the Central Limit Theorem (CLT) but never properly understood it or looked it up. My understanding was pretty much along the lines of ‘most measurements are normally distributed’.
This isn’t quite right (although as we’ll see not totally wrong). The CLT actually states that sample means taken from a distribution of measurements are normally distributed, irrespective of how the full distribution of all the measurements is distributed. So if we take large enough batches of samples of a measurement repeatedly and calculate their average, those averages will be normally distributed (with the same variance as the full distribution).