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This content is taken from the Royal Holloway, University of London 's online course, Survival Statistics: Secrets for Demystifying Numbers. Join the course to learn more.
1.4

## Royal Holloway, University of London

Skip to 0 minutes and 10 seconds Numbers in the media usually involve percentages, so it’s important to know exactly how these work. Most of you probably do. But I just don’t want to leave this vital detail to chance. Imagine that we’ve got 2,000 people signed up for this course. Then, like magic, word leaks out that the course opens with a delightful little clip on percentages. Out of nowhere, 400 new people join in. Hooray! I’d just like to pause briefly here and say thank you to all 400 of you for your wonderful vote of confidence. Now we’ve just gone from a base of 2,000 up to a new total of 2,400. That is, our population of students has increased by 20%, which we calculate as follows.

Skip to 1 minute and 4 seconds 2,400 minus 2,000, that is the change in the number of students, divided by 2,000, which is our starting point or base for calculation. As a detail, we then multiply by 100 to put our number on a scale from zero to 100%. The base from which we move is crucial. To get the point, let’s consider the same move but in reverse. That is, now we’re a community of 2,400 students. But before the beautiful buzz I generated with my triumphant Playing With Percentages video, we had only 2,000 students. So without this gem, our numbers would be almost 17% lower than they actually are. That is, 2,400 minus 2,000, the same change of 400 we had in the last calculation.

Skip to 2 minutes and 1 second But now divided by 2,400, not divided by 2,000, because 2,400 is now the base number for this thought experiment. And then again, we multiply by 100. That is, cutting this video would cost me about 16.7% of my potential clientele. But adding it to the course grows my numbers by about 20%.

Skip to 2 minutes and 33 seconds It’s all a matter of what comparison you make. There’s not really a practical difference here, but this example hints at a bigger and more important truth. By playing with the base for calculation we can shrink or expand our percentages. We’ll return to that subject, but two final thoughts before finishing. One, it’s impossible for something to decrease by more than 100% as long as the thing we’re talking about can’t be negative. Imagine that last year I drank 70 shots of vodka. Then I decide to improve my health by cutting back my vodka consumption by 150%. Unfortunately, that’s not going to happen unless I manage to vomit up some of last year’s shots.

Skip to 3 minutes and 25 seconds But the size of my bank account can actually decrease by more than 100%. I’ll leave that one as an exercise. And finally, my last point about percentages. Doubling something, for example, going from 70 vodka shots in 2018 to 140 vodka shots in 2019, is 100% increase. Tripling, for example, going from 70 shots to 210 shots, is a 200% increase. Quadrupling is a 300% increase. Again, we’ll clarify with an exercise. I think you’ll find that as with the whole of this course, it makes perfect sense once you think about it.

# Playing With Percentages

Here are some examples of the sorts of calculations mentioned in the video.

### Percentage change

The general form of these calculations is:

((NewValue – BaseValue) / BaseValue) x 100

For example, the Crystal Palace Eagles (The Pride of South London), won 14 games during the 2018-19 Premiership football season. Suppose they win 24 games in 2019-2020. This would be a 71.4% increase in games won. How so?

Baseline value – 14

New value – 24

((24 – 14) / 14) x 100 = 71.4%

Go Eagles!

### 100% decrease

Suppose that the Eagles win 0 games in 2019 -2020. Of course, this would never happen but let’s just suppose it does for the sake of argument. This would be a 100% decrease (or, in other words, an increase of negative 100 percent):

((0 – 14) / 14) x 100 = -100%

### Decreases of more than 100%

Suppose I have £1,000 in my bank account at the beginning ot the 2019-2020 season. I quit my job, planning to live off of income from my FutureLearn course but no such money materializes. So I survive the year on a diet of Palace Ale which costs me a total of £800 while losing a further £700 betting on The Pride of South London. I tap into the credit allowance of my bank account, leaving a balance of -£500 by the end of the season. My bank balance has suffered a 150% decrease:

((-500 – 1000) / 1000) x 100 = -150%

### A factor-of-seven increase

The 2019-20 Eagles exceed all expectations, winning the Premiership and pulling my bank account up to £7,000 despite my increased intake of Palace Ale. This is a 600% increase:

((7000 – 1000) / 1000) x 100 = 600%