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The mean and the standard deviation of the 8 numbers shown

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The mean and the standard deviation of the 8 numbers shown [#permalink]

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New post 29 Jul 2010, 23:39
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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 above is 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%
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Feb 2012, 22:19, edited 1 time in total.
Edited the question and added the OA

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Re: P.S [#permalink]

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New post 30 Jul 2010, 00:13
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Question should be:

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 above is 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%

"Within 1 standard deviation of the mean" - means in the range {mean-1*sd; mean+1*sd} = {10-*0.3; 10+0.3} = {9.7; 10.3}.

From the 8 listed numbers, 6 are within this range so 6/8=75%.

Answer: D.
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Re: The mean and the standard deviation of the 8 numbers shown [#permalink]

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New post 15 May 2016, 14:58
The phrase ' Within one standard deviation ' actually means the values which lie in the (10 - 0.3) and (10 + 0.3)
So we have see which values lie between 9.7 and 10.3
clearly 6 values from the given list lie within one standard deviation
percent of values which lie within one SD = \(\frac{6}{8}\) * 100 = 75%
correct answer - D

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Re: The mean and the standard deviation of the 8 numbers shown [#permalink]

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New post 23 Jul 2016, 06:17
xmagedo wrote:
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 above is 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%


Mean = 10; SD=0.3
Range of values below 1 SD = Mean - 1 SD
Range = 10-0.3 to 10+0.3 = 10.30 to 9.70

9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5

Outside the range = 9.4 and 10.5 ; total 2/8
Inside the range 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 ; total 6/8

6/8 = 0.75 or 75%
ANSWER IS D
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Re: The mean and the standard deviation of the 8 numbers shown [#permalink]

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New post 18 Nov 2017, 00:58
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Re: The mean and the standard deviation of the 8 numbers shown   [#permalink] 18 Nov 2017, 00:58
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