M11 q28

Question

Is the standard deviation of set  S  greater than the standard deviation of set  T  ?

1. The range of set  S  is greater than the range of set  T 
 2. The mean of set  S  is greater than the mean of set  T

OA: (E)

Can someone please explain me this one?

hamm0 · Answer

Where did you get tripped up?

Quite simply,
1: No information about the Mean or number of terms, hence insufficient.

2: No information about the number of terms, hence insufficient.

The question you're asking yourself is "do the data points in set S deviate further from the mean of set S than the data points in set T deviate from their mean?"

Bunuel · Answer

For the GMAT you only need to understand the concept of SD: you won't be asked to actually calculate the standard deviation of a set on the GMAT. So, what is the main thing you should know about it? Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. Now, (1) says that the range of S is greater than the range of T, so the biggest and smallest numbers in S are more widespread than the biggest and smallest numbers in T. But what about the other numbers of these sets? SD of {0, 10} is greater than SD of {0, 9}, but SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than SD of {0, 9}. Not sufficient. (2) The mean of set S is greater than the mean of set T. Info about the mean is totally useless to get how widespread the given sets are. Not sufficient. (1)+(2) Statement (2) gives absolutely no new info for (1), so even taken together they are still insufficient to answer the question. Answer: E. Check this for more: math-standard-deviation-87905.html PS questions on SD: ps-questions-about-standard-deviation-85897.html DS questions on SD: ds-questions-about-standard-deviation-85896.html Hope it helps.

teal · Answer

Thanks a lot Bunuel and hammo!

Bunuel - thanks for providing all the info.

teal · Answer

SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than SD of {0, 5}

How did you reach that conclusion? Isn' the std dev. higher for the first set?
What is the best way ( most efficient) to compare the std dev. of given sets without calculating the actual std. dev. ( MGMAT guide covers this topic a little bit)?

Bunuel · Answer

It should be SD of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less than SD of {0, 9}. Anyway the given sets are just examples to demonstrate the point. Follow the links in my previous post for the staff you need to know about SD. The GMAT SD questions are pretty straightforward and to answer them you just need to understand its concept.

M11 q28

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