Hi All,
As a math subject, Standard Deviation comes from the broader category of statistics. It's essentially about how "spread out" a group of individual numbers is, relative to the average of that group. There's a lot of interesting ways that Standard Deviation can impact decision-making processes in big business, but that's something you'll learn about in Business School. In real life, calculating the Standard Deviation of a group of numbers involves a big calculation (and you probably would NOT want to do that calculation by hand). Thankfully, the GMAT will NEVER ask you to actually calculate the Standard Deviation of a group of numbers. You're likely to be tested on the CONCEPT though.
Any time you're given the average (arithmetic mean) of a group of numbers and the Standard Deviation, then you can easily calculate Standard Deviations "away" from the mean.
In this question, we're given an average of 20 and an S.D. of 2. Standard Deviations go in "BOTH directions" on a Number Line, so.....
1 Standard Deviation "up" = 20 + 2 = 22
1 Standard Deviation "down" = 20 - 2 = 18
2 Standard Deviations "up" = 20 + 2 + 2 = 24
2 Standard Deviations "down" = 20 - 2 - 2 = 16
Etc.
The above example is a common way for the GMAT to test you on the concept.
Another way to test you is to see if you understand how to "increase" or "decrease" an S.D. by adding in new numbers to an existing group of numbers.
Using this same prompt as an example, since we have an average of 20, if we were to include ANOTHER value that = 20 (or was really close to it), then the overall group of numbers would be LESS "spread out" and the S.D. would decrease. In that same way, if we were to include ANOTHER value that was FAR from 20, then the overall group of numbers would be MORE "spread out" and the S.D. would increase.
Standard Deviation is not a big part of the GMAT, but you'll likely see it in one question. As such, it's not a big "point gainer" or "point loser" on this Test. The ways in which the GMAT will Test you on the concept are relatively simple though, so this can be an easy pick up on Test Day as long as you're clear on the concepts.
GMAT assassins aren't born, they're made,
Rich
_________________
Rich Cohen
Co-Founder & GMAT Assassin