Tag Archives: averages

Above average worries

I’m not sure which of these stories is the most worrying…

Above average mortality rates in a hospital.

When it comes to encouraging girls into science, “nearly half of the co-educational state-funded schools we looked at are actually doing worse than average“.

That this nuclear plant has a safety record that is worse than average.

This older report that (in England) any school found to be below-average would fail its inspection. (I’m not sure to what extent this guidance has been followed).

Actually, what is worrying is the common thread of all of those reports. Let’s ask that mathematical wizard Mr Gove about the last point:

Q98 Chair: One is: if “good” requires pupil performance to exceed the national average, and if all schools must be good, how is this mathematically possible?
Michael Gove: By getting better all the time.
Q99 Chair: So it is possible, is it?
Michael Gove: It is possible to get better all the time.
Q100 Chair: Were you better at literacy than numeracy, Secretary of State?
Michael Gove: I cannot remember.

Indeed.

While behind many of those stories there are important issues need addressed, the issue can never be that almost half of anything are performing worst than average. Because that is the definition of average. You take a whole load of scores, find the average score – which is going to be in the middle – and then work out which scores were above or below average. Amazingly in many cases almost exactly half will be below average.  Because that is what average means.

In every case there are two issues:

1. How big is the spread between scores and if there is a broad range or outliers whose absolute scores indicate very poor performance (or very large variations in performance), can the causes be identified and can we create solutions that work.

2. More importantly, why don’t journalists and politicians appear to understand that for real world data sets almost half of anything is going to be below average. How can (the presumably well educated) people who write news for the BBC websites or who run the Education Department in the UK government not understand what an average is?