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Standard Deviations
Name: Frank L.
Status: educator
Grade: 12
Country: USA
Date: Winter 2011-2012
Question:
An author of a well respected book wrote "one characteristic of standard deviations is that they are additive. In our example, if one standard deviation from the mean is 3, then two standard deviations is 6. Two standard deviation from the mean is 7.5 +/- 6 = 1.5 to 13.5" (range to represent 95.4% probability). Not to disrespect the author, but I believe this is not the case and that two standard deviations is the variance multiplied by 2, (in this 9 x 2 =18), squared ( to give 4.2). Therefore the range for 95.4 probability is 3.3 to 10.8. I'm usually tentative to question authors that should have this expertise and wonder if I am interpreting the author's assertion correctly. I would appreciate your validation.
Replies:
Using Google, I found the book from which this quote came, and I think
the author is not claiming that standard deviations are additive in the
sense you took him to mean. All he is saying, I think, is that two of
anything is twice as much as one of the same thing. It is confusing that
he calls this a characteristic of standard deviations. He is not talking
about how one might calculate the standard deviation of a distribution
that results from two random variables, which, I think, is what you are
talking about.
Tim Mooney
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Update: June 2012
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