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

# Measure of Center

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Author: Sophia Tutorial
##### Description:

This lesson will explain which measure of center to use.

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Tutorial

This tutorial is going to answer the question, “which measure of center should I use?” You will learn about:

1. Measures of Center
2. Median
3. Mode

## 1. Measures of Center

There are multiple measures of center:

1. The mean
2. The median
3. The mode

Each of these measurements have their own tutorials.

The mean is default that you should use if there's no real reason to use anything else.

Mean

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

The mean is the measurement best to use if possible because it's the most versatile measure of center and therefore it's the most appropriate one in the vast majority of cases.

However, there are certain situations where the mean is not appropriate gauge for center. In those cases, you should use the median. You will hardly ever use the mode.

## 2. Median

Here's an example of when the mean is a poor representation of where the center really is. Here is a table of one company’s employees and their salaries:

 Title Boss Manager Shift Worker Number of Employees 1 3 8 Salary \$200,000 \$55,000 \$42,000

How many of the employees make more than \$58,000 and how many make less than \$58,000? 11 of our 12 people make less than \$58,000. Only one employee makes more than that, and that employees makes substantially more.

The boss’s \$200,000 salary is an outlier. Therefore, the mean doesn’t make very much sense as a measurement of the middle.

In this case a better measure of center would be the median. If you took all the salaries and wrote them out from least to greatest, the median (the one in the middle) would be \$42,000. That more accurately describes what a typical worker makes.

In the presence of outliers, which are very few high or very few very, very low values the mean won't give an accurate representation of center. Use the median in cases like those.

## 3. Mode

When should you use mode? Mode isn’t used very often. It's used mainly for qualitative data sets, to determine the category that has the most values in it.

So in this case the mode is biology.

Mode is also used to describe the peak of a distribution, such as in a histogram.

The mean is our default measure of center. It's the preferred one and it's the most versatile. However, sometimes if we have outliers or a few values that can pull the mean towards them either on the high side or the low side, the mean then won't accurately represent center anymore. In those cases, the median should be used instead. Typically we reserve the mode for qualitative distributions. Mode is used mainly for qualitative data sets

Thank you and good luck!

Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS

Terms to Know
Mean

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