Hi, there. I'm happy to help with this.
Standard Deviation is a measure of spread --- that is to say, a measure of how far apart numbers on a list are from each other.
Every list of numbers has a mean. The distance from any entry on the list to the mean is called the "deviation from the mean."
The standard deviation is a "typical" size deviation from the mean. It's not strictly an average of the deviations from the mean --- technically, you square all the deviations from the means, average those squares, and then take a square-root to get the standard deviation. For the GMAT, you probably not need to know the details of calculating the standard deviation, except for a high high 700+ level question.
Some rules for standard deviation
1) On a list where all entries are identical, standard deviation = 0
2) On a list where all entries are the same distance from the mean (e.g. the set {2,2,2,8,8,8}, where every item is 3 away from the mean of 5), then the standard deviation equals that distance.
3) If you multiply every item on the list by a number, the standard deviation is multiplied by the absolute value of that number.
In this question, Statement #1 says each volume was decreased by 30%. That means, each volume was multiplied by 0.7. This means the standard deviation was also multiplied by 0.7.
New standard deviation = 0.7*(old standard deviation) = 0.7*10 = 7
Therefore, Statement #1 is
sufficient to answer the prompt.
Statement #2 tells us the new mean. Knowing just the mean, nothing else, doesn't give us bupkis toward finding the standard deviation. Statement #2 is
insufficient.
Answer =
A
Here's another free DS question on standard deviation, for more practice.
https://gmat.magoosh.com/questions/937
Does all this make sense? Please let me know if you have any questions.
Mike
