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# Standard deviation and Mean problem

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Manager
Joined: 27 Feb 2010
Posts: 105
Location: Denver
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Kudos [?]: 276 [0], given: 14

Standard deviation and Mean problem [#permalink]

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23 Apr 2010, 17:02
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83% (01:30) correct 17% (00:00) wrong based on 13 sessions

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if a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the folllowing 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

Can someone please explain the solution for this problem?
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 246 [1] , given: 31

Re: Standard deviation and Mean problem [#permalink]

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23 Apr 2010, 17:05
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zz0vlb wrote:
if a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the folllowing 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

Can someone please explain the solution for this problem?

3*2.5 = 7.5

Low end: 12.5
Upper end: 27.5

All fall within range except A
Manager
Joined: 27 Feb 2010
Posts: 105
Location: Denver
Followers: 1

Kudos [?]: 276 [0], given: 14

Re: Standard deviation and Mean problem [#permalink]

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23 Apr 2010, 17:13
Thank you for the quick reply lagomez. +1 Kudos to you.
SVP
Status: Graduated
Affiliations: HEC
Joined: 28 Sep 2009
Posts: 1637
Concentration: Economics, Finance
GMAT 1: 730 Q48 V44
Followers: 98

Kudos [?]: 593 [0], given: 432

Re: Standard deviation and Mean problem [#permalink]

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06 Jul 2010, 15:35
Expert's post
The mean (average) equals 20, and the standard deviation equals 3. For standard deviation, remember to consider numbers above and below the mean.

One standard deviation includes all numbers that fall into 17 to 23. This is determined by adding and subtracting 3 from 20. In other words, 20 + 3 = 23, and 20 - 3 = 17. We can eliminate C.

Two standard deviations identifies the set of numbers that fall into 14 ( 20 - 3 - 3) to 26 (20 + 3 + 3). We can eliminate D.

2.5 standard deviations results in 12.5 to 27.5. We can eliminate B and E. Hence, A.

Lagomez, of course, has already shown us a faster way.
_________________
Re: Standard deviation and Mean problem   [#permalink] 06 Jul 2010, 15:35
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# Standard deviation and Mean problem

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