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# A set consists of 20 different numbers whose average is 10. Which of t

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A set consists of 20 different numbers whose average is 10. Which of t  [#permalink]

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06 Jun 2017, 09:53
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25% (medium)

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62% (00:43) correct 38% (01:20) wrong based on 93 sessions

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A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15

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Re: A set consists of 20 different numbers whose average is 10. Which of t  [#permalink]

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07 Jun 2017, 11:22
number closer to the average will make the SD shrink,,
option C 10,10 is the best option out of these

ans C
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Re: A set consists of 20 different numbers whose average is 10. Which of t  [#permalink]

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07 Jun 2017, 11:34
Bunuel wrote:
A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15

Standard deviation reduces when the new elements are closer to the mean than the value of standard deviation

Hence standard deviation reduces my maximum amount when new terms are equal to the mean which is 10 here

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Re: A set consists of 20 different numbers whose average is 10. Which of t  [#permalink]

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07 Jun 2017, 17:38
The SD will change if the numbers are closer to mean
SD increases as the difference between the additional number and mean increases
SD decreases as the difference between the additional number and mean decreases

So option C and E are close to the mean.

Option C decreases SD more than Option E since, both the numbers are closer to mean
Option C
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Re: A set consists of 20 different numbers whose average is 10. Which of t  [#permalink]

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08 Dec 2019, 20:42
Bunuel wrote:
A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15

The standard deviation is a measure of how far the data values of a set are located from the average. When new values that are equal to the average are added to the set, the standard deviation is decreased because these new values have no deviation from the average.

In the given data set, since the average is 10, when 10 and 10 are added to the set, the standard deviation will decrease.

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Re: A set consists of 20 different numbers whose average is 10. Which of t   [#permalink] 08 Dec 2019, 20:42
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