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Statistics Hacks by Bruce Frey

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Hack #21. Choose the Honest Average

Data-driven decisions, such as whether you can afford to buy a house in a new town or who the core market is for your business, often rely on the "average" as the best description for a large set of data. The problem is that there are three completely different values that can be labeled as the "average," and the different averages often result in different decisions. Make your decisions using the correct average.

When most people hear a statement like "the average price for a house in this town is $290,000" (which might sound low, high, or just right, depending on where you call home), they imagine that this figure was determined by adding up all of the sales prices from all of the houses in the town, and then dividing that sum by the number of houses. But statisticians know there is more than one way to determine the "average," and sometimes one kind is better than another.

Whether that $290,000 really represents the typical housing price depends on whether the average is actually the mean, median, or mode. It also depends on the shape of the distribution of all the numbers that are averaged. Wise folks will make sure they are making their decisions using the best summary value. Here's when to trust each type of average.

Measures of Central Tendency

The purpose of determining an average for a set of values—whether those values are house prices, grades from a final exam, or the number of students in a yoga class—is to efficiently communicate the ...

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