Beware the Average
When IQ tests are designed, they are designed so that the group pf people they are test on will get an average IQ score of 1-- with a standard deviation of 15. Test a different set of people, or even the same set of people on another day and you will get a different average IQ score and a different standard deviation.
A bigger problem is that IQ does not work across ethnic groups and cultures. Some African cultures have an IQ if 80 or so, But these cultures display great problem solving skills in their own environment. Take those Africans an subject them yo a western culture from birth - an approach discredited - and their IQ might increase to 100. Of a test gives different scores to different cultures it cannot measure innate intelligence.
Another problem is that education and diet are improving and this is contributing to higher intelligence. A group of average people taking an old IQ test may score higher than average for this reason. IT is highly undesirable to have to calculate an intelligence quotient by age and ethnic group and education and many other factors to obtain an intelligence quotient due to the quality if someones genes.
The same goes for every other sort of average and standard deviation. The average and standard deviation are always the average of a number of things. If any of the things change in any way, then the average and standard deviation Weill also change and any statistical measure use to classify this will tell something like 'we are better than average'. In these circumstance statistics becomes ridiculous.
