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Standard Deviation vs. RMSE

I came across the concept of Root Mean Square Error (RMSE) two days ago at work, while investigating 3-D localization using Google Cartographer . I was familiar with the difference between RMSE and standard deviation previously, but at work I seemed to have gotten them mixed up (again). Like various other concepts that I frequently learned to forget, I figured I should write it down somewhere in case I need a quick refresher, hence this post. To get started, let's begin with their similarities. The standard deviation, generally represented by the Greek lowercase sigma letter $\sigma$, and the RMSE are similar mathematically: they are both metrics to measure the variance of a variable from a reference . Put simply, they tell you how much a variable you are measuring/estimating 1 vary from a reference. For example, if you get a high value in $\sigma$ or RMSE, you know that the variable that you are measuring/esti