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Standard Deviation

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by engg.manik » Thu Oct 08, 2009 2:38 am
Q.A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
A. 16%
B. 32%
C. 48%
D. 84%
E. 92%
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by rohan_vus » Thu Oct 08, 2009 3:25 am
Not sure , i am taking a hit .

If 68 % fall within one standard deviation means 32 % are outside this . Since its symmetric around mean , so 32/2 = 16 % would be outside m + d .
Last edited by rohan_vus on Thu Oct 08, 2009 6:20 am, edited 2 times in total.
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by sanjana » Thu Oct 08, 2009 6:07 am
Where did u get the 6 from?
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by rohan_vus » Thu Oct 08, 2009 6:14 am
Sorry for the typo . I meant 2 instead of 6 . Have corrected it .
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by tinmn8 » Thu Oct 08, 2009 6:45 am
I see it as this. Say 100 people take the test and the mean is 50 (m=50). 34 (d) people had more than 50, 34 had less than 50 (symmetrical 34 and 34 = 68). What percent of people would be less than m+d or 34+50. I think D 84%
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by srivas » Thu Oct 08, 2009 7:35 am
it is 50+34 = 84%

In normal distributoin 50% below the mean and 50% above.
m+d = 34%, m+2d = 14% m+3d = 2%

m-d = 34%, m-2d = 14% m-3d = 2%

here above m+d is 14+2 = 16%
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by sanjana » Sun Oct 11, 2009 8:15 pm
it is 50+34 = 84%

In normal distributoin 50% below the mean and 50% above.
m+d = 34%, m+2d = 14% m+3d = 2%

m-d = 34%, m-2d = 14% m-3d = 2%

"here above m+d is 14+2 = 16%"

Where did u get m+d=14+2?
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by CrackGMAC » Mon Oct 12, 2009 6:33 am
rohan_vus wrote:Not sure , i am taking a hit .

If 68 % fall within one standard deviation means 32 % are outside this . Since its symmetric around mean , so 32/2 = 16 % would be outside m + d .
It is B - 32%. You don't need to divide by 2. m+d is on both sides.
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by stufigol » Sat Feb 06, 2010 2:18 pm
so is it 16 or 32?
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by vscid » Sat Feb 06, 2010 8:17 pm
engg.manik wrote:Q.A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
A. 16%
B. 32%
C. 48%
D. 84%
E. 92%
Apparently the OA is D.
The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
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by Stuart@KaplanGMAT » Sat Feb 06, 2010 8:27 pm
engg.manik wrote:Q.A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
A. 16%
B. 32%
C. 48%
D. 84%
E. 92%
We can use common sense to almost immediately eliminate A, B and C, even if we understand only a bit of the question.

We want to know what percent of the distribution is less than m+d.

Well, since we have a symmetric distribution, roughly 50% of the distribution is less than m (I say roughly 50% because some of the distribution could be right on m); accordingly, more than 50% of the distribution is less than m+d, which is more than m. So, the answer must be either D or E.

To actually solve, we see that 68% of the data lie within 1 SD of the mean. So, 1 SD runs from 34% below the mean to 34% above the mean. 34% above the mean puts us at 84, so choose D.

If we want to be super picky, none of the answers are correct, since they're actually in the wrong format; the question says "what percent of...", so the right answer shouldn't have the percent sign included. Percent is a unit, just like miles or kilograms; if a question asked "how many miles did Bob travel", the answer would never be in the form of "50 miles" - it would simply be "50".
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