are mean/standard deviation and usual range good measures of the unemployment rate in America?

Mean and standard deviation are good for deriving a parameter, such as the true unemployment rate, from a sampling of people. Your final results shouldn't really include a standard deviation because there's only one true population proportion. If anything, there should be a confidence interval.

I'm not sure what else you would use. perhaps a 'turn over' number would be interesting and possibly useful. e.g. an unemployment number of 5% pm with 90% turn over pm would likely be a better indicator than 3% pm with 0% turn over.

In the US it’s the lowest in recorded history , especially for black and Hispanic Americans . A very good thing .