## Thursday, 4 March 2010

### Error and ambiguity in reporting percentage increases

The following appeared in a report in The Times on 1 March 2010: 'The number of candidates awarded a grade C or above (in GCSE science) was predicted to rise by 2.4 per cent …'.

There are examples here of a common error and a common ambiguity in the use of percentages.

First, the error. The reporter (Greg Hurst, Education Editor) clearly cannot be referring to an increase in the number of candidates awarded a Grade C or above. This could simply be a result of changes in the population from one year to the next. He must be referring to an increase in the proportion of candidates.

But even with this understanding it is not clear what the 2.4 per cent relates to. Is it 2.4% of the proportion who were successful or 2.4% of the entire population? Here is the ambiguity.

As an example, assume that in the previous year 50% of candidates were awarded grade C or above. Does the 2.4% increase mean 2.4% of the 50%? In which case, the proportion becomes 51.2%. Or does it mean the 50% has increased to 52.4%?

I suspect that it means the latter. To make it clear the reporter should write: 'The proportion of candidates awarded a grade C or above (in GCSE science) was predicted to rise by 2.4 percentage points …'

This ambiguity can always arise when we start talking about percentage changes in data given in percentages. We need to be clear about this distinction between an increase of so much per cent, and an increase of so many percentage points.

#### 1 comment:

1. Take a look at this Derek.

http://www.express.co.uk/posts/view/157444/Mum-beats-odds-of-50m-to-one-to-have-3-babies-on-same-date-