Mean delay for a M tap harmonically weighted filter
The coefficients of this FIR filter do not posses any type of symmetry, hence it cannot be a linear phase filter. However, you can still compute its phase response either analytically (or numerically) as:

$$\phi(\omega) = \tan^{-1}( \frac{ \mathcal{Im} \{ H(e^{j\omega}) \} }{\mathcal{Re} \{ H(e^{j\omega}) \} } ) $$

Then you can compute its derivative (again either analytically or numerically) to obtain the group delay function

$$ \tau(\omega) = -\frac{d\phi(\omega)}{d\omega} $$

from which you can compute the mean delay according to its definition.