I was reading Simon S. Haykin's Digital Communications in order to understand the concept of quantization. However, on SQNR, I got stuck over the point where the author mentioned:
With the input $M$ having zero mean and the quantizer assumed to be symmetric, it follows that the quantizer output $V$ and, therefore, the quantization error $Q$ will also have zero mean. Thus, for a partial statistical characterization of the quantizer in terms of output signal-to-(quantization) noise ratio, we need only find the mean-square value of the quantization error $Q$.
where $M$ is the random variable of the sampled analog inputs, $V$ is the random variable of digitalized outputs and $Q$ is the random variable of the error.
$\star$ Can someone kindly elaborate this line like how does zero mean of $M$, $V$ and $Q$ implicates that we need to find the mean-square value?
I searched for the meaning of zero mean and partial statistical characterization and got them as follows:
Mean and correlation provide a partial statistical characterization of a random process in terms of its averages and moments. They are useful as they offer tractable mathematical analysis, they are amenable to experimental evaluation and they are well suited to the characterization of linear operations on random processes.
I just don't know how these concepts come together to imply that we need to find mean square value. Please help!