# Never exclude the idea that numbers tell different stories

14th September 2018 at 00:00
The debate on social media about the DfE’s figures on permanent exclusions demonstrates how the same set of figures can be interpreted differently, writes Christian Bokhove

I would argue that a good and transparent knowledge of numbers is an important skill to have for any person, but particularly teachers and school leaders.

This became apparent when the Department for Education published its yearly figures on exclusions. These numbers led to passionate debates on social media about whether they should give rise to concerns. Most of these discussions seemed related to absolute and relative numbers.

Let’s have a closer look at the figures for permanent exclusions.

For 2015-2016 to 2016-2017, the absolute number of permanent exclusions rose from 6,685 to 7,720 – an absolute increase of 1,035 pupils, and an increase of 15 per cent over that year.

Both the absolute and relative numbers are correct, but people pointed out that the number of pupils increased, too. Some suggested that the numbers were deceitful. I disagree. They were correct – but, indeed, one should take into account total pupil numbers to draw firm conclusions.

Pupil numbers rose from 7,916,225 to 8,025,075, according to the DfE – an absolute increase of 108,850 and a relative increase of 1.4 per cent. So yes, the total number of pupils increased, but not as much – relatively – as the number of permanent exclusions.

Perhaps a better way of representing the number of permanent exclusions is the “overall rate of permanent exclusions” – the number of permanent exclusions divided by the total number of pupils. As this number is relatively tiny, I have seen several commentators argue that it’s a small number, so why would we worry about it?

Because of the small numbers, it is interesting that depending on how you round off the quantities, you get a different picture: at one decimal place the rate in 2015-2016 was (6,685/7,916,225) 0.1 per cent and in 2016-2017 it was (7,720/8,025,075) 0.1 per cent. No increase! But at two decimal places, both respectively are 0.08 per cent and 0.10 per cent, still tiny but an increase of 25 per cent!

Numbers can tell a number of different stories. We need to be aware of this in research, reporting on your school, or simply in life.

Another example is time span. If you want to convey the message that things cost a lot of money, try using a long time span. Total numbers will be bigger. If you want to convey the message that something is cheap, just recalculate to one day (“Just £1 a day to help ...”).

It is not really possible to say one is right and the other wrong, we need all these numbers and then to be aware of absolute/relative and the units of measurement. We need the nuanced picture. And that is something for which we should always strive.

Christian Bokhove is an associate professor in mathematics education at the University of Southampton and a specialist in research methodologies