# Find standard deviation given standard deviation

How would I find the standard deviation of a value, V that is the average of other values, say heights of people, given that I have the standard deviation of the heights? I'm looking to improve my intuition and understanding of standard deviation.

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## 1 Answer

You need to know that:

• the variance of the sum of independent variables is the sum of the variances
• the standard deviation is the square root of the variance.
• sd$(\lambda X) = \vert \lambda \vert$sd$(X)$, for $\lambda \in \mathbb R$.

Hope this helps.

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What is the difference between the average of the variances i.e. (var(x)+var(y))/2 vs. var((x+y)/2)? Which one would I be looking for in the case above? – John Mar 19 '13 at 18:20
I think I'm looking for the second one. And arriving at (var(x)+var(y))/4. – John Mar 19 '13 at 18:23
Would the standard deviation of say z = (x+y)/2 with x and y st. deviations 50 and 70 be sqrt((2500+4900)/4)? – John Mar 19 '13 at 18:28
yes you've got it. – roger Mar 19 '13 at 22:55