Title: Showing increases and decreases with percentages.
Course: UGQuants (SSPS) > Section: Maths Self Test

Examples of showing increases and decreases with percentages.

Percentages are also often used to describe increases or decreases, e.g. between two different time periods. When this is done some care must be taken in presenting and interpreting percentages because there are two different ways such changes may be described:

When we say simply that there has been an x% increase in something over a certain time period then this increase is conventionally expressed as a percentage of the figure that comes first. i.e. a percentage of the figure at the earlier point in time. E.g. If we observe that the number of women MPs in a parliament increased from 150 to 180 between 2005 and 2010, then we first calculate the difference between the two time points (180-150 = 30) then express this difference as a percentage of the figure at the first time point (30 ÷ 150 = 0.2 = 20%).

Therefore, we can say that there was a 20% increase in the number of women MPs between 2005 and 2010.

1. But note that the figure calculated in the example in 1) does not necessarily tell us anything about what happened to the overall percentage of women MPs over the same time period. The number of women MPs clearly increased, but perhaps the overall number of MPs also increased (or fell) over the same period? When we want to express the change in thepercentage as opposed to the change in the number over a certain time period, we usually express this as an increase or decrease in percentage points. E.g.
  1. Say that in fact the overall number of MPs in the parliament remained the same in 2010 as it was in 2005: 600 MPs. An increase in the number of women MPs over that period from 150 to 180 would be an increase from 25% to 30% (because 180 ÷ 600 = 0.3 = 30%).

We could therefore say that the percentage of women MPs had increased by 5 percentage points over the period 2005-2010. Note that this is a very different figure compared to the statement that ‘the number of women MPs increased by 20% between 2005 and 2010’, but both statements are equally true.

Politicians, the media, and others are not always so precise in differentiating between these two ways of expressing percentage change, and this can result in misleading presentation of data and arguments. If you understand the difference, you will not be misled!

Another important dimension to the difference between 1) and 2) is that it is possible to have a percentage increase or decrease of more than 100%, but it is not possible to have an increase or decrease of more than 100 percentage points. E.g.

- If the number of women MPs in a parliament increased from 30 to 90 between two elections then we could say that the number of women MPs had increased by 200% (because the difference between the two numbers – 60 – as a percentage of the starting number – 30 – is 200%). However, if we assume that the total number of MPs remained at 600 at both elections, then we could say that there had been an increase in the percentage of women of 10 percentage points (i.e. from 5% of all MPs to 15%).

The first figure (200%) sounds much more dramatic than the second (10 percentage points) but in fact each one reflects an essential and important feature of the data. The 200% increase reflects the fact that, relative to the number of women MPs in 2005, there were a lot more women MPs in 2010; the 10 percentage point increase reflects the fact that, because there were so few women MPs in 2005, the increase in 2010 still represents a relatively modest increase in the proportion of women MPs in the parliament.