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within 1 standard deviation

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by sanju09 » Fri Mar 02, 2012 5:04 am
There are these 8 numbers in a set 9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, and 10.5. The mean and standard deviation of the 8 numbers are 10.0 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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by krusta80 » Fri Mar 02, 2012 5:09 am
sanju09 wrote:There are these 8 numbers in a set 9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, and 10.5. The mean and standard deviation of the 8 numbers are 10.0 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%
The range is 9.7 through 10.3 (mean +/- std dev), so we just count up how many fall within the range and divide it by 8...

6/8 = 75%

Answer is D
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by Anurag@Gurome » Fri Mar 02, 2012 5:23 am
sanju09 wrote:There are these 8 numbers in a set 9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, and 10.5. The mean and standard deviation of the 8 numbers are 10.0 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 and Standard Deviation, S.D = 0.3
1 S.D. of the mean = 1 * 0.3 = 0.3
Mean - S.D = 10 - 0.3 = 9.7, which is the lower limit
Mean + S.D. = 10 + 0.3 = 10.3, which is upper limit
We can see that only 6 out of the 8 given numbers, lie between 9.7 and 10.3.
So, percent of the 8 numbers that are within 1 standard deviation of the mean = (6/8) * 100 = [spoiler]75%[/spoiler]

The correct answer is D.
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by hjafferi » Fri Nov 02, 2012 2:14 am
Answer: D
mean = 10
sd = 0.3
"one standard deviation" = 1*(sd) = 0.3.
1 stdev range would be mean plus/ minus std Dev
Lower range:10 - 0.3 = 9.7
Higher range:10 + 0.3 = 10.3
6 numbers out of 8 fall within the range
Then 6/8 or 3/4 are within range
3/4 = 75%
Hence answer is D
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