Is there a place that displays statistics in such a manner that I can rely on? e.g. Google/Microsoft homepage screen size statistics? An international statistics organization that checks multiple websites to come up with a more accurate number?
Google previously had a tool at browsersize.googlelabs.com which is now shut down. Not sure that Microsoft currently shares this type of data either.
Here are a couple popular website statistics plugins used on a large number of websites that publish aggregated statistics which might be helpful:
http://www.w3counter.com/globalstats.php
http://gs.statcounter.com/#resolution-ww-monthly-201412-201505
From these charts you can see that no screen resolution individually makes up a majority of users as it might have in the past. Even the resolution with the highest share (1366x768) does not break the 30% mark in either of these statistics websites. Statistics from websites that I work on support these results as well.
I assume you are looking into browser sizes for the purpose of web design/development. In recent years the focus has turned towards responsive web design (RWD) due to the ever increasing usage of smartphones and tablets to access the web. Designing for just one particular resolution is not as viable as it was in the past because of this.