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Source: — Problem Solving |

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by Ian Stewart » Sat Sep 01, 2012 3:22 am
Only in two cases: if the range is 0, then the standard deviation is 0. And if your set has exactly 2 elements, then you can find the standard deviation if you know the range (the standard deviation would be exactly half the range). In all other cases, absolutely not!
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by mehaksal » Wed Sep 05, 2012 2:11 am
Ian..on one of the posts you had replied that STD cannot be more than half the range....is that not so?
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by AbhiJ » Sat Sep 08, 2012 8:49 am
Another case would be when the set is an AP and you know the number of elements.
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by Ian Stewart » Fri Sep 28, 2012 9:44 am
mehaksal wrote:Ian..on one of the posts you had replied that STD cannot be more than half the range....is that not so?
That is so, but that doesn't mean the range determines the standard deviation. If the only fact you know about a set is that its range is 10, then all you know about the standard deviation is that it is at most 5. For example, the following two lists both have a range of 10:

0, 0, 10, 10

0, 5, 5, 10

but the standard deviation of the second list is smaller than that of the first (which has a standard deviation of exactly 5), because the elements in the second list are clustered more closely around its mean. So knowing only the range does not give you enough information to find the standard deviation.
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by eski » Sat Sep 29, 2012 3:12 am
Thanx Ian , thats give clarity of thought .

However, what about set having negative number. how does that change ?
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by Ian Stewart » Sat Sep 29, 2012 4:00 am
eski wrote: However, what about set having negative number. how does that change ?
Everything I said above is true when your sets contain negative numbers - that actually doesn't make any difference.
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