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# If a certain sample of data has a mean of 15 and a standard deviation

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Math Expert
Joined: 02 Sep 2009
Posts: 43812
If a certain sample of data has a mean of 15 and a standard deviation [#permalink]

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06 Dec 2016, 10:12
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94% (00:20) correct 6% (00:06) wrong based on 65 sessions

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If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?

A. 10
B. 12
C. 16
D. 18
E. 19
[Reveal] Spoiler: OA

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Manager
Joined: 02 Nov 2013
Posts: 95
Location: India
Re: If a certain sample of data has a mean of 15 and a standard deviation [#permalink]

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07 Dec 2016, 00:26
If a data distribution is normal then the 68% data values are within one standard deviation of the mean (i.e., μ ± σ), and about 95 percent are within two standard deviations (μ ± 2σ).
Here, mean = 15 and standard distribution is 2.
Numbers which are within two standard distribution will be in the range of 15±(2*2) i.e. 11 to 19.

Only only which does not follow this range is 10, i.e. Answer A.
Director
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Posts: 646
Re: If a certain sample of data has a mean of 15 and a standard deviation [#permalink]

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07 Dec 2016, 01:52
Bunuel wrote:
If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?

A. 10
B. 12
C. 16
D. 18
E. 19

One SD= mean-SD to mean + SD.
here we have SD=2
so one SD range will be 13 to 17
two SD range will be 11 to 19
only value that do not fall under this is 10.Hence A.
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Re: If a certain sample of data has a mean of 15 and a standard deviation [#permalink]

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07 Dec 2016, 08:22
Bunuel wrote:
If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?

A. 10
B. 12
C. 16
D. 18
E. 19

$$Range = Mean$$ + $$2SD$$

Or, $$Range = 15$$ + $$2*2$$

Or, $$Range = 15$$ + $$4$$

Thus the range of data is { 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ,19 }

Among the given options only (A) 10 doesn't come within the range of data...

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Re: If a certain sample of data has a mean of 15 and a standard deviation [#permalink]

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10 Dec 2016, 05:30
Bunuel wrote:
If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?

A. 10
B. 12
C. 16
D. 18
E. 19

We are given that a certain sample of data has a mean of 15 and a standard deviation of 2. So data values that fall within two standard deviations of the mean are values from 15 - 2(2) = 11 to 15 + 2(2) = 19, inclusive. We can see that the only answer choice that does not fall within two standard deviations of the mean is 10.

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Re: If a certain sample of data has a mean of 15 and a standard deviation [#permalink]

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13 Sep 2017, 07:57
Bunuel wrote:
If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?

A. 10
B. 12
C. 16
D. 18
E. 19

To be within 2 standard deviations, the value should be between 15-4 and 15+4 inclusive.
Only value in option which is not between 11 and 19 (inclusive ) is 10

Ans:A
Re: If a certain sample of data has a mean of 15 and a standard deviation   [#permalink] 13 Sep 2017, 07:57
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