Children writing eleven plus examinations in mathematics will probably have to learn the term `average’.
Does this mean that 100% of children have to learn what an average is? Could only 5% of eleven plus children meet a question about an average? We can use a word like `many’ children – and so we can surmise that it is possible that the proportion is possibly higher than half of the children. If we use the word `most’, then it is likely that a majority of children will meet a question on averages. Of course if we say `an average number’ then we could conjecture that about half the children will be tested on averages.
We could measure the heights of all the children writing eleven plus examination – and take their average height. This could be compared this with the average height of the children who did pass. We would then be able to describe a measurable difference between all children and the selected group of successful children.
We could be offered the average of the standardised scores for verbal reasoning in one county. It should then be able to compare this with the average of standardised scores in a different county. It is unlikely, but not impossible, that the scores would be different. Authorities, however, are careful not to publish figures like this. Imagine what some parents could make of possibly controversial data!
An arithmetic mean, however, is only accurate if the data is presented in an equal interval scale – like time, weight, area and height. When we look at a verbal reasoning test it could be valid to say that a child who needs a verbal reasoning score of 120 to pass needs to be better at doing verbal reasoning tests than a child who only reaches a standardised score of 100. We could also think that the score of 120 is 20% higher than a score of 100.
We can not however say that one person is 20% more able than the other!
We know that average is to do with a typical amount or quantity. We know too that that an average is found by adding quantities together and dividing the total by the number.
What we can not, however, say is a child who achieves a Standardised Score of 100 on a verbal reasoning test is absolutely average in ability. Than would be a mean statement!