The Weierstrass function is an example of a function that is continuous everywhere but differentiable nowhere.
My question is whether the mean $\bar{f}$ of the Weierstrass function $f(x)$ can be found. Where the mean of a function is defined as:
$$\bar{f}=\frac{1}{b-a}\int_a^bf(x)\,dx.$$
As a follow up question if the mean exists does the variance of this function exist?