The 3 Ms of Central Tendency Mean, Median, and Mode

Which one should you use? Why Does It Matter?

Consider the following example:

You live in a town of 1,000 people where the mean annual income is $25,000 and the median annual income is about the same, a place not unlike Damascus, Virginia.

Now, suppose Warren Buffett decides to move to your town, and his earnings last year were a billion dollars.

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Now the mean income is $1,023,976, but the median income is still about $25,000.

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A popular magazine runs a story about “The Town of Millionaires.”

It is a wonderful story about this whole town of millionaires who are so frugal they live in ordinary homes. What a great example of America!

Why is this misleading?

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Most people in this town are still pretty poor.

The mean does not give a good picture of the “typical” resident. Nothing changed except that one new person moved to town.

This could be a big deal if the town loses government services because of its income level…but we will hope whoever is in charge of those numbers does a little better research than the magazine did.

Now let’s see if you can pick the correct M given some sample situations.

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Which measure would be the best for the favorite movie of college students?

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I hope you chose mode. Mode is a good choice for non-numerical data items and for frequent occurrences.

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Which measure would be the best for the distances students in your class travel to school?

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This time we choose median. One student may live much further than everyone else from the school having the same effect on the mean distance that Warren Buffett’s income had in our earlier example. When an outlier may significantly influence the mean, it is best to use median.

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Which measure would be the best for the daily high temperature during a week in July?

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This time we can use mean since daily temperatures are not likely to have outliers.

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To sum up, when data have no outliers, we typically use mean. If data have outliers, we choose median. If we are interested in the frequency of particular values or we want to summarize non-numeric data, we use mode.

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Now, for some practice on the affect of outliers on measures of central tendency, the three Ms, go to the Khan Academy site whose web address appears on the next slide and work with the data to achieve the requested values for the mean and median.

This will help you determine the effect changes in data have on those measures.

Knowing this will help you figure out which M works best with your data!

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Below is a sample problem from the Khan Academy website whose address appears above. Go the site and click on the data dots and drag them until you achieve the requested mean and median.