X Subscripts

Next, I want to talk about a system for keeping track of the individual scores within a variable. I previously told you x was not a number, but a set of numbers. It’s a variable or column in your data. For example, it might be the four ages of four employees at a company, ages 30, 21, 59, and 45. In our statistical formulas, I’m going to tell you to do things to x like add numbers to them, square them, add them up, et cetera. But what happens if we want to refer to a single score? How can I do that? Well, we have a system for keeping track of this. It uses subscripts.

So for instance, if we need to have a way to refer to the third age score, what I’m going to do is I’m going to just put a little three at the bottom of my x. So I’ll have x3 to refer to 59. This allows me to have x be a set of numbers in general. But if I want a specific score or I need to do that in my formula for some reason, I can do that with a subscript. If I want a general way of writing this, I could put a little xi. And that i is just a placeholder for any one of those individual numbers.

So this might be useful if you’re looking at texts, and you see a little xi. It’s really just saying a score in a variable. That’s all that little xi is going to mean. Now, briefly, when we have a data set, we have both rows and columns. So if we’re not clear which variable we want to refer to, we can actually include both. So for instance, maybe I want the third row and the second column in this data set, the second column being age. Because I’ve got my sex, age, and years at company. And then my third row, to go down to that third employee, Ben. Whenever we have both rows and columns, we always note them row first, column second.

That can be a little confusing for people to remember. So just always remember, if we’re ever referring to a position in a spreadsheet like this, you always have rows, comma, columns. Annoyingly, some people leave out the comma, and they would just say x3 2 and they just assume you can figure that out. I would never do that to you. I find that confusing. So here we go– a system for referring to individual scores by subscripts.