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standard deviation is so mean

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standard deviation is so mean [#permalink] New post 04 Dec 2009, 03:47
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A GMAT PREP QUE


9.4, 9.9, 9.9, 9.9, 10 10.2, 10.2, 10.5
The mean and standard deviation of the 8 numbers shown are 10 and 0.3. What percent of the 8 numbers are within 1 standard deviation of the mean?

1- 90%
2- 85%
3- 80%
4- 75%
5- 70%

Last edited by ppp21 on 04 Dec 2009, 05:00, edited 1 time in total.
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Senior Manager
Senior Manager
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Joined: 30 Aug 2009
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Concentration: General Management
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Re: standard deviation is so mean [#permalink] New post 04 Dec 2009, 04:26
ppp21 wrote:
A GMAT PREP QUE


9.4, 9.9, 9.9, 9.9, 10 10.2, 10.2, 10.5
The mean and standard deviation of the 8 numbers shown are 10.3 and 0.3. What percent of the 8 numbers are within 1 standard deviation of the mean?

1- 90%
2- 85%
3- 80%
4- 75%
5- 70%


shouldn't the mean be 10 here? is OA - 4-75%
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Re: standard deviation is so mean [#permalink] New post 04 Dec 2009, 05:01
my apologies...
have corrected mean to 10.
the ans is correct D) 75%
please explain how did you get it
Senior Manager
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Re: standard deviation is so mean [#permalink] New post 04 Dec 2009, 05:08
mean = 10 and SD = 0.3

we need to find numbers which are within 1 standard deviation of the mean which will be total numbers in range of 10 +/- 0.3 i.e. in the range of 9.7 to 10.3 both inclusive. we can see all numbers except 9.4 and 10.5 fall in this range. So percent is (6/8) *100 = 75%
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Re: standard deviation is so mean [#permalink] New post 04 Dec 2009, 05:12
THANK YOU!! :-D
but can you please explain what did they mean by

within 1 standard deviation of the mean
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Re: standard deviation is so mean [#permalink] New post 04 Dec 2009, 06:27
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ppp21 wrote:
THANK YOU!! :-D
but can you please explain what did they mean by

within 1 standard deviation of the mean


"within 1 SD of the mean" means we need to consider all values which are either = or more than 9.7 and less than or equal to 10.3. These values are same as 10 (Mean) +/- 0.3 (which is 1SD)

if the question would had asked within 2 SD then the values would had been 10 (Mean) +/- 2*0.3 (which is 2 SD)

hope this helps
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Re: standard deviation is so mean [#permalink] New post 04 Dec 2009, 08:48
Thank you boss!!!
it helped :-D :-D
kudos!
Re: standard deviation is so mean   [#permalink] 04 Dec 2009, 08:48
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