What's your A-level worth?

Quinapalus Home :: Things Technical :: What's your A-level worth?
This page is no longer maintained.

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 is 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.

graph of entropy of A-level results against year for a range of subjects

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

This page most recently updated Fri 5 Jan 10:25:27 GMT 2024
Word Matcher

Type a pattern, e.g.
into the box and click ‘Go!’ to see a list of matching words. More...

Qxw screen
Qxw is a free (GPL) crossword construction program. New! Release 20200708 for both Linux and Windows. Non-Roman alphabets, batch mode, multiplex lights, answer treatments, circular and hex grids, jumbled entries, lots more besides. More...

You can order my book, ‘Practical Signal Processing’, directly from CUP or via Hive, Amazon UK or Amazon US.
Practical Signal Processing front cover
“Probably the best book on signal processing ever written” — review at Goodreads.
Wydanie polskie.

If you find this site useful or diverting, please consider a donation to NASS (a UK registered charity), to KickAS (in the US), or to a similar body in your own country.

Copyright ©2004–2024.
All trademarks used are hereby acknowledged.