X is Not a Number

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Next, I want to introduce the idea of understanding a key element of statistical formulas. And that is understanding what is this x that we keep seeing. In all of our statistical formulas, we always see the letter x. And if you’re like me, and you took algebra, you know that x is a variable. And in statistics and data analysis, x is also a variable, but it has a little bit of a different meaning. And this tends to trip people up. So I want to set the record straight on what on Earth x is. Specifically, x is not a number. When I took algebra, I learned that x was a number and I had to find x.

And x was, like, a single number. Well, that is no longer the case. x is now a set of numbers. So I want to show you what that means. Because when I do operations with x in a formula, I’m really saying you need to do an operation to many different numbers, which makes sense when we’re analysing data because we have records for many people. So let’s see how this might work in practise. Here’s a data set with four people. I’ve got information on their sex, information on their ages, how many years they’ve been in the company. If x was age, x would represent all those numbers.

So for instance, it would represent the age of the first person, 30, the age of the second person, the age of the third person, and the age of the fourth person. So if I’ve got these ages, I could do operations with x. But I’m not going to do them just to one number, but to every number. So for instance, if I put in a statistical formula x plus 1, I wouldn’t just add 1 to the first score, I would add 1 to all the scores. So keep in mind when you’re working with data, you’ve got many numbers. And we’re going to repeat whatever operation we do to all of them in that variable, all of the numbers in that column.

So remember x is not a number. It’s a set of numbers. [LOGO MUSIC PLAYING]