You can set enableTypeIgnoreComments: false in your pyright configuration (see here) to tell pyright to leave type: ignore comments to mypy. You would still be able to ignore pyright specific type violations with pyright: ignore comments.

As for the error itself, I believe it is caused by the type declaration of float.__pow__ in typeshed. A negative float raised to the power of another float would result in a complex number, example:

>>> (-1.0)**0.5
(6.123233995736766e-17+1j)

There is no way for typeshed to tell if the result would be float or complex because there is no way to distinguish negative and positive floats so it was decided to annotate the method as returning Any. See the typeshed change here python/typeshed#6287.

To add, you can make this type check without a # type: ignore by using math.sqrt instead of ** 0.5:

return math.sqrt(sum((x - mean) ** 2 for x in values) / n)

That also has the benefit of being slightly faster:

$ python3.13 -m timeit -n100 'for x in range(100000): x**0.5'        
100 loops, best of 5: 3.34 msec per loop

$ python3.13 -m timeit -n100 -s 'import math' 'for x in range(100000): math.sqrt(x)'
100 loops, best of 5: 2.25 msec per loop

Alternatively, you could use cast(float, (...) ** 0.5), or disable the no-any-return error code with --no-warn-return-any to match pyright's behavior.

If your actual use case is computing the (population) standard deviation, you might also consider using statistics.pstdev.

@hamdanal thank you for the explanation.
__pow__() indeed returns complex numbers for roots of negative values, so mypy was right.
It would have helped, if the method was annotated as returning float | complex, but that's not mypy's fault ;-)

I am aware of the global flags to disable checks.
As for the workarounds, I will go with math.sqrt(), thanks for the pointer, @brianschubert