# Statistics

**URL:** <https://boards.straightdope.com/t/statistics/51330>\
**Category:** Factual Questions\
**Created:** [January 22, 2001, 11:48pm UTC](https://boards.straightdope.com/t/statistics/51330 "2001-01-22T23:48:25Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![rmorgan](https://avatars.discourse-cdn.com/v4/letter/r/958977/32.png) [@rmorgan](https://boards.straightdope.com/u/rmorgan)\
**Post date:** [January 22, 2001, 11:48pm UTC](https://boards.straightdope.com/t/statistics/51330/1 "2001-01-22T23:48:25Z")

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I have a statistical question that I know I should be able to answer myself, but I can’t. Here it is.

Let’s say I have several independent variables, each with a known normal distribution; i.e., I know the mean and standard deviation of each variable. How I calculate the standard deviation of the sum of the variables?

Let me use an example to illustrate. Suppose I am going to put three electrical resistors in series. The first resistor comes from a box of resistors that has a mean value of 10 ohms and a standard deviation of 1 ohm. The second resistor comes from a box that has a mean of 20 ohms and a standard deviation of 2 ohms. The third resistor comes from a box that has a mean of 30 ohms and a standard deviation of 3 ohms. By picking one resistor at random from each box and putting them in series I know that, if I do this many times, the mean value of the resistance I get will be 60 ohms (10+20+30), but will be the standard deviation around that mean?

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**Author:** ![\_Tim](https://avatars.discourse-cdn.com/v4/letter/_/e47c2d/32.png) [@\_Tim](https://boards.straightdope.com/u/_Tim)\
**Post date:** [January 23, 2001, 12:05am UTC](https://boards.straightdope.com/t/statistics/51330/2 "2001-01-23T00:05:32Z")

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It’s the square root of the sum of the squares. In your example, it’d be

sqrt(1^2 + 2^2 + 3^2)= sqrt(1+4+9) = sqrt(14) Ohms

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**Author:** ![rmorgan](https://avatars.discourse-cdn.com/v4/letter/r/958977/32.png) [@rmorgan](https://boards.straightdope.com/u/rmorgan)\
**Post date:** [January 23, 2001, 4:59am UTC](https://boards.straightdope.com/t/statistics/51330/3 "2001-01-23T04:59:52Z")

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Aha. THAT’s what it was. Thanks, Tim.