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# A question about the standard deviation

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Manager
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If you know how to solve this problem, please explain it to me. Thank you.

9.4 9.9 9.9 9.9 10.0 10.2 10.2 10.5
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?

a)90%
b)85%
c)80%
d)75%
e)70%
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Re: A question about the standard deviation [#permalink]  21 Apr 2007, 13:39
GMAT_700 wrote:
If you know how to solve this problem, please explain it to me. Thank you.

9.4 9.9 9.9 9.9 10.0 10.2 10.2 10.5
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?

a)90%
b)85%
c)80%
d)75%
e)70%

D. 75%

since 6 out of 8 are within the 1 SD from the mean, 6/8 is 75%.
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Re: A question about the standard deviation [#permalink]  21 Apr 2007, 14:49
GMAT_700 wrote:
If you know how to solve this problem, please explain it to me. Thank you.

9.4 9.9 9.9 9.9 10.0 10.2 10.2 10.5
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?

a)90%
b)85%
c)80%
d)75%
e)70%

Himalayan hit it right on the head with his explanation. I will offer something a bit more boilerplate.

We are given that the mean of this set of numbers is 10. We're also given that the standard deviation is 0.3. The range of numbers that is one standard deviation away from the mean (in this case 10) are any number that fall within the following range:

10 - 0.3 = 9.7: 1 standard deviation away from the mean on the negative side

10 + 0.3 = 10.3: 1 standard deviation away from the mean on the positive side.

So, you're looking to count the numbers that fall within this range. There are 6 number that fall in this range. 6 out of 8 numbers = 6/8 = 3/4.

I hope that helps.

Regards,
Alex
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Re: A question about the standard deviation [#permalink]  25 Apr 2007, 09:39
GMAT_700 wrote:
If you know how to solve this problem, please explain it to me. Thank you.

9.4 9.9 9.9 9.9 10.0 10.2 10.2 10.5
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?

a)90%
b)85%
c)80%
d)75%
e)70%

Standard deviation measures dispersion around the mean. 1 SD of the mean = 10 +/- 0.3 so it would go from 9.7 to 10.3. 6 out of the 8 numbers fall within that 9.7 to 10.3 range, hence the percentage = 6/8 or 75%.
Senior Manager
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Yes D.

When something is 1 standard deviation from the mean, you add and subtract the standard deviation from the mean. (i.e. 10-0.3 and 10+0.3).

When something is 2 standard deviation from the mean, you add and subtract 2*standard deviation from the mean. (i.e. 10-0.6 and 10+0.6)

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within 1 standard deviation of the mean = +/- 0.3 from 10 -> 9.7 and 10.3

So 6 numbers are within this range. % = 6/8 * 100% = 75%
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