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As we have seen, every list of numbers has an average. Also as we have seen, the numbers of the list do not need to actually be anywhere near the actual average. In fact, most numbers in the list differ, or deviate from the average by some degree.

The standard deviation tells us generally how the numbers will deviate from the average. The greater the deviation, the higher the standard deviation.

	800Score Tip: While this chapter explores the intricate Standard Deviation formula, the GMAT does not require you to know it. Your goal in learning Standard Deviation should be to understand what it is, how it works, and what it represents, rather than how to calculate its value.

Formula:

Let's use a sample list of numbers to understand the standard deviation formula:

3, 8, 6, -4, 2

The average of this list is 3.

The formula for Standard Deviation is as follows:

where x is a term in the list, is the average of the list, and n is the number of numbers in the list. You will therefore follow these steps:

1. Find the average of the list of numbers

2. Subtract each term from the average

3. Square each of the differences

4. Add up the squared values

Statistics & Standard Deviation Part C