So, are the averages that you had listed in your above chart meant to be for the whole month? taking an average what the price would have been for each of the days of the month? Or is it calculated in a different way? I see that the CSV download (the one that I did) had given the BTC price each hour for the past 30 days (something like that or maybe it was 31 days?).. I suppose that you could average all of those prices that are in that hourly chart and then arrive at an approximation of monthly average that is close, but does not quite account for the trade volume variance.
I don't take volume into account at all. I understand how it might seem to be "less accurate" at first glance. But it's fine, really.
Using volume as weight will not change the end result all that much, obviously. It just makes calculations more complex, for very little benefit.
On that bitcoinity site you can switch from hourly to daily. I tested, and it's just a sum of their hourly data divided by 24.
So they are doing the same thing.
P.S.