This weeks Birmingham Post has an article entitled “Soaring expulsion rate is ‘blip’”. Apparently:
A huge increase in the number of children permanently expelled from Birmingham schools is an unexplainable one-off blip, education chiefs have insisted. Just over 80 pupils were regarded as so disruptive that they were removed from mainstream education by city head teachers in a single term. The figure, for Autumn 2009, represented a 40% increase on the same period in the previous year
By the standards of some reporting of statistics, this isn’t a bad article. However, it still provides no context, without which we cannot make a judgement. For example, what if the history of school expulsions in recent terms was like this?
Very little change, and then the rate shoots up. This could be something serious. However what if it was like this?
Suddenly, the jump is just part of a history of wide fluctuations. Also, notice how in both graphs the penultimate data point is missing. The article tells us that over 80 (I called it 81) pupils were expelled in Autumn 2009, a 40% increase “on the same period last year” i.e. Autumn 2008. What was the figure for Spring 2009? We have no idea, it could be anything. For all we know it could be higher than 81, in which case the most recent figures are part of an encouraging trend.
Finally, what is the figure in percentage terms? I couldn’t immediately find the school age population of the city so I crunched some numbers. Wikipedia tells us that in the 2001 Census the population of Birmingham was 1,113,000. Of these, 23.4% were under 16. This calculates as 260,442. If we assume that there are equal numbers in all of the year groups under 16 (obviously false, but I’m a busy guy), then we can say that 11/16ths of this figure are at school – about 180,000. So, last term, about 0.045% of pupils were expelled, against 0.031% a year before. Obviously these population figures are derived from figures that are nearly 10 years out of date, and have rounding errors and incorrect (but reasonable) assumptions thrown in. Nevertheless, the figure is very very small.
When reading an article about figures, always ask yourself what you are NOT being told. Not that you are being mislead, but what different backgrounds could actually cast the results in a different light, as we have done here?
Posted by Pete Collins 
