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gmatter0913
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GMAT 1: 680 Q49 V34
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Statistics 28 Jan 2012, 09:18
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1. If a subset of a set has the same standard deviation as that of the set, then can we say that all the elements in the set are the same?


2. If the standard deviation of two sets is the same, can the range be different?



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Statistics 28 Jan 2012, 09:58
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bsaikrishna
1. If a subset of a set has the same standard deviation as that of the set, then can we say that all the elements in the set are the same?
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Not necessarily:
The SD of {1, 2, 3, 4, 5, 6, 7, 4, 7} is 2;
The SD of {1, 2, 3, 4, 5, 6, 7} is also 2.
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Statistics 28 Jan 2012, 09:59
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bsaikrishna
2. If the standard deviation of two sets is the same, can the range be different?
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Yes:
The SD of {1, 2, 3, 4, 5, 6, 7} is 2 and the range is 6;
The SD of { 1, 1, 5, 5 } is 2 and the range is 4.
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Statistics 28 Jan 2012, 10:15
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To summarize, there is no relationship between the standard deviation and the range of a set, you should be aware of for the GMAT, other then both measure the spread of the set in one way or another.

All you need to know is:
The range of a set is the difference between the largest and smallest elements of a set.

As for SD: you won't be asked to actually calculate the standard deviation of a set on the GMAT. You just need to understand the concept of 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.

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.



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