Title: Percentages
Course: UGQuants (SSPS) > Section: Maths Self Test

Percentages

An understanding of percentages is absolutely fundamental if you want to be able to perform and interpret even the most basic quantitative analysis. Percentages are simply a very common way of standardizing proportions to express them as units per hundred. E.g. to convert 600 women out of 1,000 students into a percentage, we need to divide both numbers by 10 to get units per hundred as opposed to units per thousand: 60 per cent, or 60%. To convert a percentage to a proportion we always divide by 100: 60/100 gives us our original proportion of 0.6.

Quantitative analysis sometimes involves more complex processes of standardization so when you encounter these it is useful to remember that percentages are just a very familiar form of standardization, and other ways of standardizing data are not ways of ‘distorting’ data, they are just less familiar to us.

To calculate a percentage of a single number we multiply by the percentage and then divide by 100. E.g.

- If there are 800 pupils in a school and we decide that we would like to test a new educational initiative on 20% of the pupils, then 20% of 800 = (800 x 20) ÷ 100 = 16,000 ÷ 100 = 160.
So we can say that 20% of 800 is 160 If the percentage may be easily converted into quitea simple fraction or proportion (e.g. in this case 20% = 1/5) then it may be simpler just to calculate the required proportion: i.e. one-fifth of 800 is 160, therefore 20% of 800 is 160. But this approach does not work so well when percentages do not convert so easily into simple common fractions (e.g. 17%; 38%; 81% etc.)

To calculate one number as a percentage of another, it is usually easiest to first calculate the proportion and then multiply by 100. Click the arrow to see an example.