How to plot BER Vs SNR of a received signal
If you were to increase the dispersion about 3X, you'd no longer have a robust system, in that outliers of your 4 points would have moved into neighboring boxes, and your system would make Bit Errors.

Consider adding 10dB Noise Power to your datalink, and examine the 4 regions again.

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Your 4 points are of course not points at all. If these spreads are due to non-linearities and InterSymbolInterference, then as show, your SNR is infinite.

Add noise power that is 1% of the signal power. And think about the new points.

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for any set of data, you can compute the mean and standard_deviation/sigma/rms

I'd view the mean as signal power, and the sigma as noise power.