# How to remember which way the skewness goes

OK, this is a quick and dirty trick of the sort that I love and the Mathematical Ninja hates. He doesn’t have much time for stats at all, truth be told, least of all skewness.

However, I’ve had several students struggle to remember ‘which way is which’ when it comes to skewness.

### What is skewness?

Skewness is a measure of the *asymmetry* of a distribution: if you’ve got a box and whiskers plot that’s perfectly symmetrical, that has zero skewness by definition. If it’s bunched up to one side or the other, then you’ve got some skewness going on. If it’s bunched up to the left, that’s positive skewness; to the right is negative. As far as I know, there’s no reason for it, it’s just a convention.

### How do you remember which is which?

Imagine you have a pub quiz team. It’s a perfectly normal quiz team: the people on it are normally distributed in intelligence (however that’s measured). That has zero skewness, by definition. But imagine one of you brings Stephen Fry along with them: I don’t care how good your team is, he’s going to make it *much* better.

In terms of the box and whiskers plot, (ignoring the fact that he’s an outlier), you suddenly have a big whisker on the right hand side - everything else is bunched up to the left - which is positive skew; you’re now much more likely to win the pub quiz than you were.

Steve (as we call him) has increased the *mean* substantially, but the median has only gone up a little bit; an alternative definition of positive skewness is that the mean is higher than the median.

### And negative skew?

Let’s suppose one of your teammates, for reasons inexplicable, is friends with Iain Duncan Smith and - despite everyone’s objections - brings him along to the quiz. Obviously, he drags down your chances of winning, because his answer to everything is “SLASH BENEFITS!”, which is really only the answer to “What happens when Axl Rose declines royalties from Guns ‘n’ Roses songs?”

Ahem.

So, instead of lovely Steve giving us a nice positive whisker on the right, we’ve got this muppet IDS giving us a horrid negative whisker on the left ((perhaps the only time he’s ever going to be on the left)). Everyone else is bunched up to the right - meaning negative skew, due to a very negative man. He’s brought the mean down significantly, but the median not so much; for negative skew, the mean is below the median.

Edited April 9, 2014, to correct where IDS’s whisker is. Thanks, Josh.