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standard deviation question

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standard deviation question

by EddieU » Mon May 30, 2011 2:34 pm
one more question:

if a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

my approach was adding 2.5 sd from 20...23 (first sd from mean), 26 (second sd from mean) and 27.5 (the last half sd from mean)...however, 27.5 is not an answer choice and the correct answer is 12

why??

Thanks in advance again
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by g.shankaran » Mon May 30, 2011 5:48 pm
EddieU wrote:one more question:

if a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

my approach was adding 2.5 sd from 20...23 (first sd from mean), 26 (second sd from mean) and 27.5 (the last half sd from mean)...however, 27.5 is not an answer choice and the correct answer is 12

why??

Thanks in advance again
Mean = 20
SD = 3.0
Which of the following is more than 2.5 SD?

So, 2.5 SD = 2.5 x SD
= 2.5 x 3
= 7.5

The value more than 2.5 SD from mean would be either > (20 + 7.5) , which is >27.5 or <(20 - 7.5) which is <12.5.
You didn't provide the options available, I hope you don't have a value greater than 27.5 as you have pointed out that the answer is 12.
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by cans » Mon May 30, 2011 7:07 pm
EddieU wrote:if a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Notice the question - more than 2.5 s.d. away from mean.
It can be below mean or above mean.
2.5s.d. = 2.5*3 = 7.5
thus 20+-7.5 => 12.5 or 27.5
therefore value <12.5 or value >27.5 will satisfy the condition.
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by EddieU » Tue May 31, 2011 3:37 pm
Yes, you both are totally right!!! Thanks you two! The words more than irritated me...if I remember right, 26,5 was the highest answer choice...after reviewing this, I can actually say that this was an easy (but tricky) question :)
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