Education needs better Statistics

Sample Graph to Illustrate Class Size Skewed Distribution

Average class sizes in Jersey primary schools overall remains at 24.1 pupils, which is well below the UK average of 27.

But in a fifth of all primary school classes, the Education Minister had to approve an exemption to the standing policy so that the maximum class size of 26 could be breached.

At the same time, the average number of pupils in secondary school classes was 21.6 – a figure above the UK average, but well below the department’s class-size limit.

(Bailliwick Express on Education Report)

I’ve downloaded the actual report and looked at it - and one thing is glaringly missing – median class size.

Class Size, as a UK report shows, is a left skewed distribution. That is to say it is not a Bell shaped normal curve, but has usually lots more pupils in higher class sizes. That means that the smaller sizes classes bring down the average. That is why, incidentally, the average size is only 24.1 and yet a fifth of classes breach that class size.

The policy in breaching 26 is a safeguard against just relying on just teacher – pupil ratio (average) precisely because that is weighted down by the smaller classes.

It is the opposite to wage distributions, which are skewed right towards the lower wages so that average wage is invariably higher than median.

This UK report gives at least graphic giving the kind of spread – a skewed distribution, even though it doesn’t give median. I've taken a graph of class size from this report and put it at the top of this blog by way of illustration.

www.gov.uk/government/uploads/system/uploads/attachment_data/file/183364/DFE-RR169.pdf

Yet the median is the better measure of central tendency for skewed data.

Whenever the average is calculated it is important to be aware of certain outliers in the data set that could potentially skew the results and make the data unrepresentative.

The alternative statistic is a "trimmed mean", that is to say the mean with the very extreme outliers removed. But it is really not as good as a median.

In fact – and rather badly – there seem to be relatively few statistics out there on class size! There’s one example I’ve seen here, and that’s about it! And it is an an examination question about different statistical measures on class size:

http://college.cengage.com/mathematics/brase/understandable_statistics/9780618949922_ch03.pdf

It also explains that - in general, when a data distribution is mound-shaped symmetrical, the values for the mean, median, and mode are the same or almost the same. For skewed-left distributions, the mean is less than the median and the median is less than the mode. For skewed-right distributions, the mode is the smallest value, the median is the next largest, and the mean is the largest.

So while is report from Education is informative, it is not as informative as it should be. There should be graphic illustrations of the spread of class size, and the median class size, as well as the mean, should be given. Next time, the authors need to do a little more homework!