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Proportions are not Averages

I want to talk for a moment about proportions. Proportions are percentages, but written as a decimal, like 0.5 for 50%. People often report these and think of them like averages. And I just want to make a point that they’re actually a little bit different. They’re not averages. And I thought I would use some data from an earlier image for us to see that. By the way, if you remember from our earlier module, I really don’t like pie charts. I have a pie chart on the screen. But I’m going to always advocate that you use bar graphs. So imagine we have this following data as a bar graph. Woo! Glad we got rid of that pie chart.
On the left here, we see a situation where 80% of this sample identifies as male and 20% identifies as female. So here we have, clearly, the average or the mode, because it’s a categorical variable. We don’t have numbers here. These are just categories. The mode is male. The average score is male. And it’s 80%. On the right, we have a different data set. Now we have just over 50% of the sample as male, and the mode is also male. So here we have two situations where the average or typical score is male. That’s our summary statistic, our average for categorical variable. But the proportions are vastly different. Right?
And in the left case, clearly it’s the majority by a large margin. On the right, they’re almost equal. Proportions are useful for understanding where different areas of your data are. For example, what proportion of the sample is male or female, et cetera. However, I just want to point out that they are not averages. They are actually their own thing. If you get into more advanced statistical analyses, there are different kinds of statistics that we would have to use for proportions. If you’re wanting to do different kinds of statistical tests, with proportions as opposed to averages, there’s different equations. Everything changes when we’re dealing with proportions. We’re not going to learn all those tools in this class.
But I want you to make that really clear in your notes that, in fact, when we’re dealing with proportions, it is a different kind of thing than an average. It’s useful, and in fact, I would always recommend calculating them, especially with categorical data. But they are not the same as averages. [LOGO MUSIC PLAYING]

Proportions are percentages but written as a decimal such as 0,5 for 50%. People often think of these as averages but they’re actually a little bit different.

Example of two bar graphs showing different proportions of males vs. females

In the above example, we have two data sets. In the first one, there is a score of 80% male and 20% female. In the second one, there is a score of 52% male and 48% female. Both of these data sets have the mode of male.

Even though both data sets have the same mode, it is clear to see that the proportions are vastly different.

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Essential Mathematics for Data Analysis in Microsoft Excel

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