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Percentages
By Abigail Walker on June 3, 1998:

I dont understand persantages at school and i am doing my A-levels and could you please help me.

By Harry Smith on June 4, 1998:

Dear Abigail

Most people have a very rough idea of what a certain percentage means. I doubt many people couldn't tell you that 50 percent(%) was a half for example; the question is, what exactly does the number mean. The word 'cent' means one hundred, and percent means precisely that; per hundred. So 50% means 50 per hundred. That is to say, if we were to say 20% of the people in the world had ginger hair, that would mean that of every hundred people in the world we took, we could expect twenty of them to have ginger hair. If we were to divide our number by 100, giving us
20/100=0.2, we would have the probability that any one person in the world had ginger hair. If we had fewer people in our group, a class of twenty say (to keep David Blunkett happy), and we had the same percentage (20% of them have ginger hair), we can work out how many people in the class have ginger hair by supposing that we had a hundred of them. If we divided everyone in the class into five exact copies of themselves, we would have a
hundred people (looking remarkably similar), and we could expect twenty of them to have ginger hair. If we take the copied people and squashed them back together, we would have 20/5=4 people with ginger hair. 4 is 20 percent of 20.

My biggest problem with percentages was always knowing how to calculate them, but there is a very easy method. If we have a certain sized group (like our class of twenty), and we want to know what percentage of them exhibit a certain property (like having ginger hair), we work out:

(No. of things which have that property)
________________________________________ x 100
(No. of things in the entire group)


This will give us the percentage required. There are more interesting questions in percentages. For example, when we say "we can expect 20 people out of a hundred to have ginger hair" how sure can we be. It is not actually very likely that exactly twenty people will have ginger hair, but we know that the number with ginger hair will be around that value. In order to know what are chances are of finding exactly twenty people with ginger hair we need more information about gingerness than simply (20% of people have ginger hair). If you'd like to know more about this please let me know.

Percentages are often overused in newspapers and on television to make events or stories believable. The media loves to say things like "30% of criminals re-offend" or "25% of people in Britain are at risk of heart disease" without knowing what the figure actually mean. I even once saw "reports show that 50% of British drivers are of a below average standard"! I presumed the other fifty percent were above average and decided only to go out on the roads every other day!

Yours

Harry Smith