Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Standard Deviations

Name: Frank L.
Status: educator
Grade: 12
Country: USA
Date: Winter 2011-2012

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.

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

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory