Lies, damn lies and averages

Q It makes me really mad when I read that the average pupil:teacher ratio is 22.5 in state primaries and 16.9 in state secondary schools. Newspapers quote it as if to say "what are teachers complaining about? In my day we had classes of 30 or more!". Most of my classes number about 30 pupils and in some years there were 36 in the top set. So where do these figures come from?

A First there is a difference between pupil:teacher ratio and class size. For class size a random sample of different class sizes from a number of schools would have to be collected and analysed. There would be differences due to location, type of school, ability of children and so on. For the pupil:teacher ratio, the statistics are simply a ratio of the number of pupils to the number of teachers.This is irrespective of whether the teachers have a full timetable commitment.

To find a school's pupil:teacher ratio, divide the number of pupils by the number of teachers. The figures quoted in newspapers where averages are concerned, whether average salaries, house prices or, here, pupil:teacher ratios, rarely define the statistic being quoted. The reader does not always know which central tendency is being quoted (whether mean, median, or mode). In school we teach the pupils that they must make this distinction, and that for the report to have meaning the accompanying measure of dispersion (standard deviation, interquartile range and range respectively) should also be quoted.

Another important statistic is a description of the sample and its size. A large sample can provide a different picture - my 95 year old grandfather smoked 40 cigarettes a day and it didn't do him any harm! But as a sample of one, how valid is this view?. I have provided what I hope is an interesting example that will illustrate these points.

Try working out each of the central tendencies in the table, you could do this with your pupils as a lesson starter leading to a lesson on measures of dispersion.

Alternatively, or as well, you might like to show the data as a histogram. I found two great interactive websites where the data can be entered and differently shape histograms created: http:illuminations.nctm.orgmath6-8BarChartstudent and www.shodor.orginteractivateactivitieshistogram Email your questions to Mathagony Aunt at write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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