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 Click here to return to the Mathematics Archives

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