So the question is why do we have mean root square deviation (standard deviation)?
Isn't it enough just to use only such characteristic as dispersion?
Why is root square deviation (standard deviation) used if we already have dispersion?
I'd be very happy to discuss this topic with you, guys!
Thank you in advance!
Best Answer
The correct term is "root mean square", not "mean root square". "Dispersion" is a broad term: standard deviation is one measure of dispersion; mean absolute deviation is another; interquartile range is another, and so on. The main reason for using root-mean-square deviation is this: \begin{align} & \text{If } X_1,\ldots,X_n \text{ are independent} \\[6pt] & \text{then } \operatorname{var}(X_1+\cdots+X_n) = \operatorname{var}(X_1) + \cdots+\operatorname{var}(X_n). \end{align}