Standard Deviation vs. Proportional Error


I am retaking physics I, this time calculus based, and my professor did a horrendous job at explaining the material. I don’t fully understand what proportional error is and whether or not it is any different than the standard deviation?
I don’t speak variable so I have no idea what an equation means if I just see: Sum((delta(a)/a)^2+delta(b)/b^2.

Thanks for the help. I know this has NOTHING to do with CoG, but I don’t feel like subscribing to another forum. Hopefully there’s a high level math wizard that reads this.


Standard deviation is a measure of variance - of how much the values in a particular data set deviate from the mean of those values.
I’m not quite familiar with the term proportional error, but statistically, ‘error’ usually refers to the deviance of your sample from the overall population. So say you take 20 people from your neighbourhood and ask them their ages, the standard deviation would be looking at the variance of ages in your sample, but the standard error would be looking at how the mean age differs from the mean age of the whole neighbourhood, as a way of checking if there’s something fundamentally flawed in your methodology.