Statistics Made Easy: 3 Averages

I love statistics. And whoever told you maths wouldn’t be useful in the real world is a big fat liar! Here’s statistics made easy, looking at 3 averages: mean, median and mode, as well as why they’re important.

Mean

So-called (possibly? It’s how you remember it anyway!) because it’s the meanest calculation to do… You take your data set, sum it all up and then divide by the number of data points you have. Sounds confusing, so let’s introduce an example.

Let’s take 5 peoples’ salaries in order of size for ease:

• Jim with £20,000
• Sarah with £25,000
• Yasmin with £33,000
• Edwina with £75,000
• Perry with £1,000,000

The mean is the sum of the salaries divided by 5, which is £1,153,000/5 = £230,600. This is what most people would regard as the average, but it’s not necessarily as indicative of a total population, so real-world applications may make better use of the other 2 Ms… Darn you, major outlier Perry! At least you’ll be paying a bomb in tax…?

Median

A median is obtained by lining every piece of data up, and taking the item of data that is halfway through… I’ve not got a good moniker for this other than the slightly limp median/medium/middle…! Don’t meddle with the middle? Something like that. 👌

Using our data above, Yasmin is the median – the one in the middle. As an aside, if you have, say 6 pieces of data, you take the average/mean of data points 3 & 4 – the midway point.

As mentioned, the mean of £230,600 is artificially high because of Perry. £33,000 still isn’t everyone’s salary (it’s too high for Jim and Sarah, but too low for Edwina), but it’s more appropriate than £231k each.

Mode

The modal piece of data is the most common. In the above data set, all 5 salaries are unique, so there is no mode. However, if Jim was also on £25k, that would mean both he and Sarah were on £25k and there would be a salary more common than any of the others, so this would be the modal figure. When we’re looking at salaries, in real life there would be more in the late twenties, so we’d maybe use that figure for the UK average salary, as it’s more appropriate for more people, but that wouldn’t adequately represent people who earn more.

The 3Ms

The reason we have multiple ways of calculating an average is because no method is perfect. Hopefully you’ll see the real-world application and be able to take proclaimed “averages” with a pinch of salt!

There’s statistics made easy: 3 averages! By now you should know what they are… Not muggles, mildew and… muppets (thanks Francis).

So you don’t think I’m a total geek, I’m not a fan of mechanics – it’s my worst maths subject, despite clever friends trying to teach me. I just hit a brick wall. What even are you, mechanics??

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