### The difference between percentage and percentage points

Quite often I've come across situations where it's unclear if someone knew the difference between percentage and percentage points, so I thought I'd write a post where I would try to explain the difference.

Simply put, percentage is relative, while percentage points are absolute.

For example, if we say that the number of female CEOs increase by 3%, we mean that the number increase with 3% of the current number of female CEOs.

If we say the number increases with 3 percentage points, we mean that the number of female CEOs increase with 3% of the total number of CEOs.

So if 5% of all CEOs are female (the current situation in Denmark, according to today's newspapers), a 3% increase would not be noticeable, since it increased the number of female CEOs to 5.015% of the total number of CEOs.

On the other hand, if we say that the number of female CEOs increases with 3 percentage points, it would mean that 8% of all CEOs would be female. Quite a difference.

Generally speaking, percentage points should be used to measure the difference between two percentages, since it gives a more clear view of the differences than when percentages are used.

Let me give an example of how it gives a clearer view.

Let's say that a poll in year 1 shows that 10% of the population supports slavery (to take a hoepfully absurb example). In year 2 the poll shows a 20% decrease in the support compared to year 1. However, in year 3, the same number has gone up by 25% compared to year 2.

Many people would get the impression that the number of slavery supporters in year 3 is higher than in year 1, but that's actually not the case.

In year one 10% supported slavery. The next year, the number fell by 20%. 20% of 10% is 2%, which means that 8% supports slavery. Then the number of supporters increased with 25%. 25% of 8% is 2%, so the total is back up to 10%.

If we have used percentage points, we could just say that in year 2, the number of supporters fell by 2 percentage points, and that the number of supporters increased by the same amount of percentage points in year 3. Thus making it much clearer that the amount of supporters was the same in year 1 and year 3.

Simply put, percentage is relative, while percentage points are absolute.

For example, if we say that the number of female CEOs increase by 3%, we mean that the number increase with 3% of the current number of female CEOs.

If we say the number increases with 3 percentage points, we mean that the number of female CEOs increase with 3% of the total number of CEOs.

So if 5% of all CEOs are female (the current situation in Denmark, according to today's newspapers), a 3% increase would not be noticeable, since it increased the number of female CEOs to 5.015% of the total number of CEOs.

On the other hand, if we say that the number of female CEOs increases with 3 percentage points, it would mean that 8% of all CEOs would be female. Quite a difference.

Generally speaking, percentage points should be used to measure the difference between two percentages, since it gives a more clear view of the differences than when percentages are used.

Let me give an example of how it gives a clearer view.

Let's say that a poll in year 1 shows that 10% of the population supports slavery (to take a hoepfully absurb example). In year 2 the poll shows a 20% decrease in the support compared to year 1. However, in year 3, the same number has gone up by 25% compared to year 2.

Many people would get the impression that the number of slavery supporters in year 3 is higher than in year 1, but that's actually not the case.

In year one 10% supported slavery. The next year, the number fell by 20%. 20% of 10% is 2%, which means that 8% supports slavery. Then the number of supporters increased with 25%. 25% of 8% is 2%, so the total is back up to 10%.

If we have used percentage points, we could just say that in year 2, the number of supporters fell by 2 percentage points, and that the number of supporters increased by the same amount of percentage points in year 3. Thus making it much clearer that the amount of supporters was the same in year 1 and year 3.

Labels: basic concepts

## 10 Comments:

Honestly, I don't see that distinction ever "sticking" with people. The terms are too similar and the difference can't be intuited by applying a layman's common sense.

Better to just call the statistic "percent of total" versus "percent of [subset]",

thanks, although its basic concept but i was confused about it.Now i know the difference.

meba

hey thanks for the insights. i know many layman don't see the difference!

Thanks for the clarification. I had been editing some translated works and was not making the distinction, though now I see there is one. Cheers.

In your explaination using a 3% increase over 5% - wouldn't the answer be 5.15%, not 5.015%?

It should be:

5/100 * 3/100 = 15/1000 = 0.0015 * 100= 0.15%

thanks! This was really helpful! The interesting thing is that manipulation of figures in the media is rampant as people are largely unaware of this subtlety!

thanks a lot man!

I was waking up in Adelaide, Australia and reading a news item about the US Presidential candidates. I suddenly realised I had no idea what the difference was and had never asked. Your description was clear and helpful.

Oh, and when I said 'news item', I actually meant the latest xkcd comic.

Thanks for the explanation! It's quite clear :D

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