The question is about the notion of variance in control theory, a college course I am taking.
Ever since I can remember, in every maths or physics class, whenever a professor started teaching something they just listed definitions from a textbook. For example: speed is equal to the ratio between distance and time. Thankfully, common sense tells me that speed just measures how fast I can go from x to y.
Keeping this in mind, variance, as my professor so dearly explained, is $$\frac1 {N+1} \sum_{t=-\frac N 2} ^ {\frac N 2} (u[t] - {\frac1 {N+1} \sum_{t=-\frac N 2} ^ {\frac N 2} (u[t])^2) }$$
Can someone be kind enough to tell me with English words what meaning this actually has? What is it that variance actually measures and how can I visualize it so I can actually understand it?