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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] New post 01 Dec 2015, 18:48
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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 ?

enter your value

[Reveal] Spoiler: OA
13


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Question: 13
Page: 150
Difficulty: easy

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Re: A list of numbers has a mean of 8 and a standard deviation [#permalink] New post 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] New post 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 ?

enter your value

[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

Answer: 13

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Re: A list of numbers has a mean of 8 and a standard deviation [#permalink] New post 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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