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# A list of numbers has a mean of 8 and a standard deviation

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A list of numbers has a mean of 8 and a standard deviation [#permalink]  01 Dec 2015, 18:48
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90% (00:23) correct 9% (00:51) wrong based on 86 sessions
A list of numbers has a mean of 8 and a standard deviation of 2.5. If x is a number in the list that is 2 standard deviations above the mean, what is the value of x ?

[Reveal] Spoiler: OA
13

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Question: 13
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2934 [1] , given: 394

Re: A list of numbers has a mean of 8 and a standard deviation [#permalink]  01 Dec 2015, 18:52
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Solution

This is a question that requires knowledge of standard deviation. Given that mean of the list is 8 and standard deviation is 2.5.

Now if x was one standard deviation above mean that would mean that $$x = 8 +2.5 =10.5$$.

However x is given to be two standard deviations above the mean so $$x = 8 +2.5 + 2.5 = 13$$.

Hence the answer is $$13$$.
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Re: A list of numbers has a mean of 8 and a standard deviation [#permalink]  30 Apr 2019, 16:37
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sandy wrote:
A list of numbers has a mean of 8 and a standard deviation of 2.5. If x is a number in the list that is 2 standard deviations above the mean, what is the value of x ?

[Reveal] Spoiler: OA
13

--------ASIDE-----------------------
A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc

So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
----------------------------------------

We're told that the mean is 8, and the standard deviation is 2.5
We're also told that x is 2 standard deviations ABOVE the mean

So, x = 8 + 2(2.5)
= 8 + 5
= 13

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Re: A list of numbers has a mean of 8 and a standard deviation [#permalink]  15 Sep 2020, 23:45
GreenlightTestPrep wrote:
--------ASIDE-----------------------
A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1

etc

Hi Brent, I didnt get the highlighted part?
1.5 SD = 4+1.5 = 5.5 and
0.25 SD = 4+0.25 = 4.25 why these values are wrong?
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Re: A list of numbers has a mean of 8 and a standard deviation   [#permalink] 15 Sep 2020, 23:45
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