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M01-16

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Bunuel
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M01-16 [#permalink] New post   16 Sep 2014, 00:15
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If the list Q consists of 10 numbers, and the range of Q is zero, what is the standard deviation of Q?

A. 0
B. 1
C. 3.33
D. 5
E. 10
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A
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Bunuel
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Re M01-16 [#permalink] New post   16 Sep 2014, 00:15
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Official Solution:

If the list Q consists of 10 numbers, and the range of Q is zero, what is the standard deviation of Q?

A. 0
B. 1
C. 3.33
D. 5
E. 10


In order to have a list with a range of zero, all the elements in the list must be the same. If all the elements in the list are the same, then the standard deviation is 0.

Notice that the standard deviation of a list is always greater than or equal to zero: \(SD \geq 0\). SD is 0 if and only if the list contains all identical elements (or consists of only one element).


Answer: A
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haihai89
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Re: M01-16 [#permalink] New post   31 Oct 2014, 11:05
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Dear Bunnuel,
You explained "In order to have a set with the range of zero, all of the elements in the set must be the same. If all the elements in the set are the same, then the standard deviation is 0." but I suppose it is not always true.
For example, the range of the set consisting (-10, 1,2,....8,9,10) is still 0 but the set contains different elements.
Please correct me if I'm wrong.
Thank you!
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Re: M01-16 [#permalink] New post   01 Nov 2014, 05:54
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haihai89 wrote:
Dear Bunnuel,
You explained "In order to have a set with the range of zero, all of the elements in the set must be the same. If all the elements in the set are the same, then the standard deviation is 0." but I suppose it is not always true.
For example, the range of the set consisting (-10, 1,2,....8,9,10) is still 0 but the set contains different elements.
Please correct me if I'm wrong.
Thank you!


You are wrong.

The range is the difference between the largest element and the smallest element of a set.

So, the range of (-10, 1,2,....8,9,10) is 10 - (-10) = 20, not 0.
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Re: M01-16 [#permalink] New post   07 Sep 2020, 06:12
I think this is a high-quality question and I agree with explanation.

Posted from my mobile device
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Re: M01-16 [#permalink] New post   01 Nov 2022, 08:32
What if the set has only single element 0? Range will be 0 and SD 1?
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Re: M01-16 [#permalink] New post   02 Nov 2022, 02:50
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TBT wrote:
What if the set has only single element 0? Range will be 0 and SD 1?


Both the range and the standard deviation of a list with only one element (it does not matter what the value of that element is) is 0.

The range is the difference between the largest element and the smallest element of a set, so for a single element set both of those are the same and thus the range is 0.

The standard deviation, in a sense is a deviation from the mean, for a single element set there is not deviation at all, so the standard deviation is 0.
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Re: M01-16 [#permalink] New post   12 Aug 2023, 10:09
I think this is a high-quality question and I agree with explanation.
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Re: M01-16 [#permalink] New post   13 Aug 2023, 12:39
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M01-16 [#permalink]
13 Aug 2023, 12:39
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