This site is advertising that the average rate for assisted living is $3,000 per month?

Everywhere actually.

If you are looking in the core of a major city where rent for average people is off the charts then of course you will have to pay more for assistive living there too. And it really depends on what level of care you need as well, since each increase in care level also means an increase in fees.
If you are comfortable telling where you are looking Caregal some people here may have more specific advice.

Caregal, it's all about location, location, and location. And as cwillie points out, what perks are being offered at that price.

The $3k sounds very low in my opinion, thus there might be an added fees for meals, another for transportation, ever more for housekeeping, etc.

Certainly not in NYC. But in in the surrounding suburbs, yes.

$3000 is apparently a nationwide average. In my area, ( a suburb of NYC) Assisted living starts at about $5500/month. Each service is added on to that. Current costs for my MIL is $6600/month. Memory care AL for my Mom was $7200/month 3 years ago when she passed away! Caregal--- you will need to call the ALs in your area and ask about their charges and services. Depending upon what your loved one needs, you will then be able to choose what is best.

I see the statement from Agingcare.com saying: "The national average rate for assisted living is $3,000 per month, according to the AgingCare.com Assisted Living Cost data." I really think this needs some demographic stratification. Such as rural/urban/suburban and Northeast, Midwest, Pacific Coast, etc. In our flyover part of the country, costs are less than the big city but still a lot higher than $3000 per month. Curious.