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m01q16

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m01q16 [#permalink] New post 14 Sep 2011, 04:23
Q is a set of 10 numbers. If the range of Q is zero, then what is the standard deviation of Q ?
A.0
B.1
C.3.33
D.5
E. insufficient information
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Re: m01q16 [#permalink] New post 14 Sep 2011, 13:55
A.
If the range is zero SD will be zero. Why?
When can range be zero?
When set is one element set or all the elements of set is identical.
In either case mean of the set will be the number in the set.
What is SD?
It is the dispersion of individual element of set from mean. Now if the mean is that same identical number of set, there is no dispersion. Hence SD will be zero.

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Re: m01q16 [#permalink] New post 20 Oct 2011, 20:23
When range is zero, it means that all items in the set are same. Standard deviation is the sum of diversions from mean. Since all the items of the set are same, there will be no diversion from the mean and hence SD is zero.

I hope its clear now.
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Re: m01q16 [#permalink] New post 14 Jan 2012, 21:21
IMO - A

Range signifies standard deviation so if range is 0 SD will also be zero.
Re: m01q16   [#permalink] 14 Jan 2012, 21:21
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