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Chapter 5

# Deviating from the Average

IN THIS CHAPTER

Finding out what variation is all about

Working with variance and standard deviation

Exploring R functions that calculate variation

Here’s a well-known statistician joke: Three statisticians go deer hunting with bows and arrow. They spot a deer and take aim. One shoots and his arrow flies off ten feet to the left. The second shoots and his arrow goes ten feet to the right. The third statistician happily yells out, “We got him!”

Moral of the story: Calculating the mean is a great way to summarize a set of numbers, but the mean might mislead you. How? By not giving you all the information you typically need. If you rely only on the mean, you might miss something important about the set of numbers.

To avoid missing important information, another type of statistic is necessary — a statistic that measures variation. Think of variation as a kind of average of how much each number in a group of numbers differs from the group mean. Several statistics are available for measuring variation. They all work the same way: The larger the value of the statistic, the more the numbers differ from their mean. The smaller the value, the less they differ. ...

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