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# Which of the following pairs of numbers, when added to the set above,

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: Which of the following pairs of numbers, when added to the set above,  [#permalink]

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09 Dec 2017, 04:37
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alexkarpava wrote:
Hi guys,

I am a little bit confused here. Why does the II variant increase the SD? we already have 9 and 21 in our set, so what difference will the same numbers make? I am using the Manhattan Word Problems book and i couldn't find the answer there. Heeeelp!

Say we have a single-element set {10}. The standard deviation of a single-element set is 0. Now, consider adding another element 10 to the set: {10, 10}. The standard deviation of {10, 10} is more than 0. So, adding elements which are already in the, not always, but could increase the SD.

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Re: Which of the following pairs of numbers, when added to the set above,  [#permalink]

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23 Aug 2018, 09:59
alexkarpava wrote:
Hi guys,

I am a little bit confused here. Why does the II variant increase the SD? we already have 9 and 21 in our set, so what difference will the same numbers make? I am using the Manhattan Word Problems book and i couldn't find the answer there. Heeeelp!

If it's still actual:

The "step" in set 9,12,15,18,21 from the mean (15) is 3.
SD is approximately the "step" because members of the set are evenly scattered. Everything that will be out of the 15 +- 3 (step) will increase SD. Hence 9 and 21 will uncrease SD.
Re: Which of the following pairs of numbers, when added to the set above,   [#permalink] 23 Aug 2018, 09:59

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