Class Sizes in Primary Schools – Some statistical issues

A lot of  discussion has already happened from the reporting of  the latest class size statistics. The main discussions centered around the average class size having risen.

However, the data (see here : Class Sizes by School 2006-12 for a spreadsheet – warning 9mb) strongly suggest that there is a significant skew in the data. And we know that when data are skewed then the average may be a poor metric of what the ‘norm’ is.

Here is a histogram of all classes across the years 2006-12 for all schools. We can see, from the overlay, that it is not normally and symmetrically distributed. Thus we might want to consider if we need another measure of the central location of class sizes.

pupnums

The Median can help us here. A median is a the 50th percentile – in other words it is a number that in this context tells us the class size above which and below which 50% of class sizes lie.    Imagine a set of class sizes of  8, 20, 20, 22 and 40. The average class size is 22 while the median is 20. In the data for class sizes the maximum in any one class in one year is 47 (and that is a scandal of monstrous proportions) and the minimum is 1. A median is more likely to give us a good sense of the ‘norm’ than a mean in that case.

Year Mean Median Max Min
2006  24.09  25.00 41 3
2007  23.91  25.00 42 1
2008  23.78  24.00 46 2
2009  24.12  25.00 44 1
2010  23.91  25.00 45 3
2011  24.44  25.00 47 2
2012  24.70  25.00 41 1
Total  24.14  25.00 47 1

Looking then at the median we see…. No real change over the last 6 years. Typically 50% of classes have less than 25 pupils, 50% have more.  It might not be better reporting but it would be more accurate to say “class sizes really show no change in general” or “average class sizes increase a little but data are so skewed its hard to say”

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s