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If a certain sample of data has a mean of 20.0 and a

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If a certain sample of data has a mean of 20.0 and a [#permalink] New post 11 Apr 2012, 00:46
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69% (01:30) correct 31% (00:43) wrong based on 54 sessions
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Apr 2012, 00:56, edited 1 time in total.
Edited the question
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Re: In a certain sample of data has mean = 20 and standard de [#permalink] New post 11 Apr 2012, 00:55
Expert's post
sapna44 wrote:
In a certain sample of data has mean = 20 and standard deviation = 3 , which of the following values is more than 2.5 standard deviation from mean ?

A. 12
B. 13.5
C. 17
D. 23.5
E. 26.5


Question should read:
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5

Value is more than 2.5SD from the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 20-7.5=12.5 or more than 20+7.5=27.5.

Answer: A.

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Re: If a certain sample of data has a mean of 20.0 and a [#permalink] New post 25 Feb 2013, 19:51
So from the mean means below the mean?
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink] New post 25 Feb 2013, 19:57
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fozzzy wrote:
So from the mean means below the mean?


No. 'Away from the mean' means either 'below the mean' or 'above the mean'.
(Bunuel has mentioned that the answer will be a value either less than 12.5 or greater than 27.5, in the post above.)
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink] New post 25 Feb 2013, 20:22
Hi,

I thought that a SD of 2.5 from a MEAN of 20 would be a value dispersed 2.5 units away from 20, So I subtracted 2.5 from 20 and got the answer wrong.

Can you please explain why did we multiply SD with 2.5?

Cheers
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink] New post 25 Feb 2013, 20:40
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sanman wrote:
Hi,

I thought that a SD of 2.5 from a MEAN of 20 would be a value dispersed 2.5 units away from 20, So I subtracted 2.5 from 20 and got the answer wrong.

Can you please explain why did we multiply SD with 2.5?

Cheers


There are two different things here:

SD is 3.
We need to find values which are 2.5 SD away from the mean.

When we say that a value is at mean, it is 20.
When we say that a value is 1 SD away from mean, it means the value is 3 away from mean (because 1 SD is 3). So it can be either 17 or 23.
When we say that a value is 2 SD away from mean, it means that the value is 2*3 away from mean (because 2 SD is 6). So it can be either 14 or 26.
When we say that a value is 2.5 SD away from mean, it means that the value is 2.5*3 away from mean. So it can be either 12.5 or 27.5.

Since we want a value which is more than 2.5 SD away, the value must be less than 12.5 or greater than 27.5.
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink] New post 19 Nov 2013, 14:51
2.5 * 3 = 7.5

20 - 7.5 = 12.5
20 + 7.5 = 27.5

Limits: 12.5 and 27.5

Ans A (12 is out of the limits)
Re: If a certain sample of data has a mean of 20.0 and a   [#permalink] 19 Nov 2013, 14:51
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