Why do you think surveys would be unaccurate for that reason? Everything varies from region to region. There is always a margin of error, but it doesn't mean polls don't work at all. Pollsters don't just survey people in a particular area, but everywhere in proportion. Some surveys are larger than others, but at least some are big enough to be statistically significant nation wide.
The numbers vary, depending on methodology, but they are all within a range, and that range is much less than 55 million. Thats why I didn't give 3 significant digits, but I gave a very broad range of "less than 7 million". That range covers most of the estimates. Many of them are in fact much less than 7 million, more in the range of 2-3 million. 55 million is off by an order of magnitude, its not even in the ballpark of any figures.
The numbers I used are from the LDS church itself, which tend to be higher than numbers from surveys. They are more tightly organized than some other more personal faiths you might be familiar with, so its feasible for them to have actual numbers on their membership. They may have different criteria for who they include in their numbers than others though. There are some small Mormon offshoot groups that don't fall in the official LDS, but certainly not 48 million of them.
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