What's your A-level worth?

How many bits of information are there in your A-level result? See the graph below. Note that N grades ceased to be awarded in 2002, explaining the sharp fall in that year.

What is a ‘bit of information’? Well, suppose the exams had two grades, pass or fail. If everyone always passes, and someone says to you ‘I passed my exam’, that would convey no information to you. If 99 percent of people pass, saying ‘I passed my exam’ conveys very little information to you: you were almost sure that was the case anyway. If someone says ‘I failed my exam’, then that is surprising, and hence informative. But it won’t happen very often, and so on average you don’t get much information. The situation is similar if the pass rate of the exam is 1 percent.

However, if the pass rate if 50 per cent, then a priori you know nothing about someone’s likely result before they tell you: in this case, telling you the result gives you the most information.

If there are several different possible grades, the most informative situation is where they are allocated in equal proportions. The further the distribution of grades deviates from that, the less informative the result. For a more precise definition of ‘information entropy’ and a look at the mathematics involved, see this Wikipedia article. If there are seven different grades, as there were before 2002, the maximum possible entropy is about 2.81 bits; if there are six grades, as there were from 2002 onwards, the maximum is about 2.58 bits.

Data source: http://www.bstubbs.co.uk/a-lev.htm