On the right side of Islam SE, I see the statistic:
Are there really that many people who visit daily?
The statistics come from direct measurements of traffic on Islam—Stack Exchange. You can see a slightly different result via Quantcast. It's important to note that all visitor statistics are estimates. So you can assume there is some error in that number. But it's likely to be fairly close.
When you write your questions and answers you are potentially helping thousands of other people answer their questions about Islam.
In regard to your Inquiry, that you asked “Are there really that many people who visit daily? (7,637 visitors/day)”, according to my ordinary experience concerning the mentioned site and its statistics, it seems to be a correct statistics or at least this would be close to the factual statistics as Mr. Jon Ericson declared as well.
Since it (particularly its main site “stackexchange.com”) would be considered as a relatively a famous site which has pretty a high rank… Consequently showing such a statistic could be possible. For instance you’d better look at the rank of “stackexchange.com” based on www.alexa.com:
Global rank: 171
Rank in United States: 90