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
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.
Measuring Variation
Suppose you measure the heights of a group of children and you find that their heights (in inches) are
48, 48, 48, 48, and 48
Then you measure another group and find that their heights are
50, 47, 52, 46, and 45
If you calculate the mean of each group, you'll find they're the same ...
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