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siddhantvarma
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The standard deviation of which of the following can be the same as th 20 Nov 2024, 08:29
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E
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75% (hard)

Question Stats:

33% (00:53) correct 67% (00:53) wrong based on 230 sessions

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The standard deviation of which of the following can be the same as the standard deviation of A, B and C?

I. |A|, |B| and |C|
II. 3A+3, 3B+3 and 3C+3
III. A-30, B-30 and C-30

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II and III
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E
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Shreyzzz
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The standard deviation of which of the following can be the same as th 21 Nov 2024, 00:38
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In the second option, wont the standard deviation multiply by 3 as well? then it wont be the same
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Bunuel
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The standard deviation of which of the following can be the same as th 21 Nov 2024, 00:53
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Shreyzzz
In the second option, wont the standard deviation multiply by 3 as well? then it wont be the same
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Notice what the question asks:

The standard deviation of which of the following can be the same as the standard deviation of A, B and C?

The keyword is can, not must.
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siddhantvarma
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The standard deviation of which of the following can be the same as th 21 Nov 2024, 03:39
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Official Explanation:

The question asks whether I, II, or III “can” have the same standard deviation.
We know I can have the same standard deviation as A, B, and C. Option III: A-30, B-30, and C-30 will also have the same standard deviation. A set's standard deviation remains the same if you shift all elements by the same constant.

For II,
If A=B=C are equal, they will have zero standard deviation, II. 3A+3, 3B+3 and 3C+3 will have zero standard deviation.

Hence all three can have the same standard deviation as A, B and C.

The correct answer is E.
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trepsixore
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The standard deviation of which of the following can be the same as th 04 Dec 2024, 04:29
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I still don't understand how 3A+3, 3B+3 and 3C+3 can be relevant. Multiplying or dividing the numbers in set, WILL definitely change the stdv, how can we conclude that it's zero? Please, explain :(

Thanks.
siddhantvarma
Official Explanation:

The question asks whether I, II, or III “can” have the same standard deviation.
We know I can have the same standard deviation as A, B, and C. Option III: A-30, B-30, and C-30 will also have the same standard deviation. A set's standard deviation remains the same if you shift all elements by the same constant.

For II,
If A=B=C are equal, they will have zero standard deviation, II. 3A+3, 3B+3 and 3C+3 will have zero standard deviation.

Hence all three can have the same standard deviation as A, B and C.

The correct answer is E.
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siddhantvarma
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The standard deviation of which of the following can be the same as th 04 Dec 2024, 06:22
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Hi trepsixore

Let's make sure we understand the question correctly. The question asks, "The standard deviation of which of the following can be the same as the standard deviation of A, B, and C?"

Then, I'm given three sets to evaluate:

I. |A|, |B| and |C|
II. 3A+3, 3B+3 and 3C+3
III. A-30, B-30 and C-30

I want to see if the standard deviation of any of these sets can be equal to that of set A, B and C. In other words, can there be a scenario where 3A+3, 3B+3 and 3C+3 can have the same standard deviation as A, B and C? Well yeah, if A, B and C are all equal to 0, the standard deviation of A, B and C is 0. The standard deviation of 3A+3, 3B+3 and 3C+3 will also be 0 because this set reduces to {3,3,3}. I hope that makes sense. :)
trepsixore
I still don't understand how 3A+3, 3B+3 and 3C+3 can be relevant. Multiplying or dividing the numbers in set, WILL definitely change the stdv, how can we conclude that it's zero? Please, explain :(

Thanks.
siddhantvarma
Official Explanation:

The question asks whether I, II, or III “can” have the same standard deviation.
We know I can have the same standard deviation as A, B, and C. Option III: A-30, B-30, and C-30 will also have the same standard deviation. A set's standard deviation remains the same if you shift all elements by the same constant.

For II,
If A=B=C are equal, they will have zero standard deviation, II. 3A+3, 3B+3 and 3C+3 will have zero standard deviation.

Hence all three can have the same standard deviation as A, B and C.

The correct answer is E.
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