45-50% is my guess based on the analysis and statistic logics. The first keys are not representative due to higher dispersion, so it is better to exclude not 10 first keys but at least 15, of even 20.

The idea is that "the higher the bit --> the tighter dispersion". As the probability of 1 or 0 bit is always 50% for every bit, so the total quantity of "1"s (or "0"s) will tend to 50% in higher bits keys.


Such "wide" range could be applicable only for low bit keys. But for higher bit keys the dispersion will be narrow.
Try to flip a coin 100 times --> more likely you will have at least 45 Heads but not more than 55 (the same for tails).
You can not take the results from the "10-15 times" coin flips and apply them to the random number where you flip the coin 100 times. No, the "heads" probability (number of "1"s) will tend to 50% while you increase the quantity of flips (bit value of the key).

Of course, everthing is possible, even the key with only 10% of "1"s, BUT morelikely for high bit keys the quantity of "1"s is within 45-55% range. Moreover, for keys higher than 140-150bit, i beleive that the quantity of "1"s is 46-54% or even 47-53%.

PS. All these calcualtions could be proved mathematically with the certain level of assurance.