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## Standard Deviation On the GMAT

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There are a handful of questions in the GMAT pool that test your knowledge of standard deviation. As usual, because the GMAT is a standardized test, the way in which this content area is tested is predictable.

Every statistical measurement has something to do with the characteristic of sets of numbers. For instance, the average (arithmetic mean) and median are two ways of indicating the middle of the numbers in a set.

By contrast, standard deviation (like range, which isn't as descriptive) measures *dispersion*. Consider the following two sets of numbers:

- {28, 29, 30, 31, 32}
- {10, 20, 30, 40, 50}

Both sets have averages and medians of 30, but that hardly means that they are identical. For instance, the range of the first set is 4, while the range of the second set is 40. The standard deviation is much different, as well.

**Understand Standard Deviation, Don't Calculate It**

This brings us to an important point. While it's important to understand what standard deviation *means*, it is not important to know how to calculate it. To read more about the nitty-gritty of standard deviation, which might be enough to make you thankful that you don't need to understand it that thoroughly, try the relevant wikipedia article here.

Here's what you need to know about standard deviation:

- It is a measure of dispersion.
- To calculate it, you need to know how far every number is from the mean of the set.
- The closer numbers are to the mean, the smaller the standard deviation, and vice versa.

**Advanced Standard Deviation Principles**

That's it. Of course, the GMAT has plenty of ways to make questions a little harder, even based on those principles. Here are some tips to handle those questions:

- The actual numbers don't matter. For standard deviation, it's all about how far each term is from the mean. For instance, the set {10, 20, 30} has the same standard deviation as {150, 160, 170}. In other words, if you add or subtract the same amount from every term in the set, the standard deviation doesn't change.
- If you multiply or divide every term in the set by the same number, the standard deviation
*will*change. For instance, if you multiply {10, 20, 30} by 2, you get {20, 40, 60}. Those numbers, on average, are further away from the mean. - When you multiply or divide every term in a set by the same number, the standard deviation changes
*by that same number*. In the example I just gave, the standard deviation of {20, 40, 60} is exactly double that of the standard deviation of {10, 20, 30}. (The same is true of range, incidentally.)

These aren't all simple concepts, but they are simpler than the alternative of mastering the standard deviation of a statistics textbook. As always, understanding the parameters of the test is an important aspect of beating it.

**About the author:** *Jeff Sackmann has written many
GMAT preparation books, including the popular Total GMAT Math,
Total GMAT Verbal, and GMAT 111. He has also created
explanations for problems in The Official Guide, as well as
1,800 practice GMAT math questions.*

Total GMAT Math
The comprehensive guide to the GMAT Quant section. It's "far and away the best study material
available," including over 300 realistic practice questions and more than 500 exercises! |