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Common Core: 6.SP.3 S.ID.2

# Measures of Center

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Author: Katherine Williams
##### Description:

Identify which measure of center to use given a scenario.

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Tutorial

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This tutorial covers how to select which measures center is best. Now, we've already explained what the mean, median, and mode are and how to calculate them. But what you don't know is why to use them and which one is going to be the best for your situation.

Now, with the mean, that's the most common measure of center. It's the one that's used the most often. One, I guess, downside to the mean is that it's not as good when there are extreme values. Like we saw and that tutorial, the extreme values kind of pull the mean up towards those extremes, which end up making them mean higher than a majority of the data set.

When you do have those extreme values, the median ends up being a more accurate representation of where the data lies. So the median is the best option for when there are extreme values. Now, the mode is used with nominal qualitative data, because you can only talk about the most frequent category. There's no way to report the mean or the median for something like favorite type of ice cream. There's no numbers there. And there's no ranking to it. So you would have to report mode.

Let's look at some examples. In this first example, we're going to look at a football player's salary. So for that one, it is qualitative data. So we could use the median or the mean. And we need to think about whether or not there's an extreme values. With football players, particularly in the NFL, there are some players who are those superstars that make way, way more than everyone else. So there are those extreme values. So in this case, median is going to be the best measure of center.

Now, in the second example, it says a class' favorite much. So when we're talking about this, we're talking about students choosing between hamburgers and hot dogs and pizza. This data is not quantitative. And it's not kind of ordered or ranked in any way. So we're going to have to use the mode here to report the measure of center.

This next example talks about the dress size of the average woman. Here, we're talking about numbers 2, 4, 6, 8, and 10, women's dress sizes. But we might not want to report the mean or the median. In this case, we're probably going to want to report the mode, because with dress size, we're really classifying a size, like small, kind of small, average, a little bit above average. But we could potentially use the mean or the medium. This one's got a little bit of gray area on it.

For the next example, the age of a class, I would want to use the mean. We have quantitative data, ages. And they're all kind of in the same range. Any classroom has students that are within a couple of years of each other. So the mean would be appropriate. There's no extremes.

And the last case, with a typical worker's salary. If you're working in a company where everyone makes around the same amount, then you could report the mean. However, if you're thinking about a company that has that CEO it makes a lot more than everyone else, then you'd want to report the median, in order to show what kind of a typical average person makes. So in this case, we'd be looking at the median. This has been our tutorial on how to select which measure of center.

Terms to Know
Mean

The average number in a quantitative data set; the sum of all the values, divided by the number of values.

Median

The value that is in the "middle" of a data set when the set is arranged from least to greatest.

Mode

The most frequently appearing number in a set of quantitative data or most frequently occurring category in a set of qualitative data.

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