Every week this term I am taking a couple of one hour sessions with first year students that are designed to improve their understanding of basic statistical concepts – you might know this already because you might be one of those students (or you might be saying to yourself “so that’s what it’s all about”). This week’s session (Number 5 in a series of 9) is all about exploring the difference between population statistics (i.e. statistics obtained when the whole population has been measured – such as the mean height of all students at the university) and sample statistics (statistics obtained when it is only possible or practical to measure a subset of the whole population – such as the mean height of 100 randomly chosen students at the university). Usually it is only possible to measure sample statistics but what we really want to know are the corresponding population statistics.
So, the session involved taking an entire population of measurements (the 31 maximum daily August temperatures in Plymouth in 2003 as it happens) and calculating the mean and standard deviation for this population. Then small samples of varying size (2, 4, 8 and 16 values) were selected randomly from the population and the sample mean and standard deviation for the sample were calculated in each case. When you do this lots of times you find that the statistics obtained with the small sample sizes vary a lot and can be a long way off the population statistics but when the sample sizes are larger there is less variation and the values are close to the population values (which is a fairly obvious result but still a nice one to demonstrate). Anyway, the fun part revolved around how the students obtained their random samples from the population. To do this I gave small groups of students a strip of printed numbers (1 through to 31) which they ripped up into 31 small pieces of paper (each with one number on) then folded (to obscure the numbers) and then randomly picked however many numbers they needed. It is such a simple process but at the end of a busy day (for them) it was a joy to watch them all merrily ripping up their paper strips, mixing up the numbers, drawing them out and then doing the calculations. They were smiling and laughing and joking when they messed things up and I was instantly struck by the thought that this must undoubtedly be the most fun you can have with 31 small pieces of paper. Unless that is, you know otherwise…
Tim O'Hare 