But what’s important about the standard deviation? Well, the take-away message is that whereas the range tells us about the overall spread of numbers in a group, the standard deviation tells us how far the numbers are spread away from the group’s mean.
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If you want to see an explanation of how to calculate the true standard deviation, check out last week’s Math Dude “Video Extra!” episode. In the last article, we also talked about an approximation to the standard deviation (which I called the quasi-standard deviation) that’s a bit easier to understand and calculate than the real thing. Clearly, these two groups are different despite having the same mean. In contrast, sophomores are generally 15 and 16 year old, so the range of the ages of sophomores is 16 – 15 = 1. So, since freshmen typically enter high school when they are 14, and seniors graduate when they are 18 (hopefully!), the overall range of the ages of high schoolers is 18 – 14 = 4. The range is simply the overall spread in a group of numbers. Clearly it’s important to distinguish whether or not two groups with similar average properties are, in fact, similar-and that’s where the concepts of range and standard deviation that we talked about last time shine.
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