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M01-16

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Math Expert
Joined: 02 Sep 2009
Posts: 49437

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16 Sep 2014, 00:15
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5% (low)

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91% (00:19) correct 9% (00:35) wrong based on 161 sessions

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$$Q$$ 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. 10

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Math Expert
Joined: 02 Sep 2009
Posts: 49437

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16 Sep 2014, 00:15
2
Official Solution:

$$Q$$ 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. 10

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.

Notice that the standard deviation of a set is always more than or equal to zero: $$SD \geq 0$$. SD is 0 if and only if a set contains all identical elements (or the set consists of only 1 element).

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Joined: 09 May 2013
Posts: 35
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.28

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31 Oct 2014, 11:05
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!
Math Expert
Joined: 02 Sep 2009
Posts: 49437

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01 Nov 2014, 05:54
2
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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15 May 2017, 05:46
Dear Sir,

I have a doubt. What happens if my set is (1,3,6,7,7,7,8,9,9,11)
Math Expert
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15 May 2017, 05:59
Manoraaju wrote:
Dear Sir,

I have a doubt. What happens if my set is (1,3,6,7,7,7,8,9,9,11)

Your doubt is not clear. The range is the difference between the largest element and the smallest element of a set.

So, the range of (1,3,6,7,7,7,8,9,9,11) is 11 - 1 = 10, not 0 as given in the stem.
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19 Jul 2018, 19:31
What if the smallest number in the set is 0 and the largest number is 10? The range becomes 0 in this case and not all numbers are required to be 0.
Math Expert
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Posts: 49437

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19 Jul 2018, 20:28
premprabhs111 wrote:
What if the smallest number in the set is 0 and the largest number is 10? The range becomes 0 in this case and not all numbers are required to be 0.

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

The range of the set in which the smallest element is 0 and the largest element is 10, is 10 - 0 = 10, not 0.
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Re: M01-16 &nbs [#permalink] 19 Jul 2018, 20:28
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