It has no diameter because it is a point particle (it has nothing inside it). It has mass because the mass has been measured experimentally. If this is hard to imagine, science has lots more concepts even harder.
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an electron is about 1/1836 amu.
Dunno, but the ratio of the mass of a proton to the mass of what prople think of as being an electron is approx 1980. I'd check that if I were you though. Probably OK to +- 5%.
it is usually the mass without the x10^-31
1/1836 the mass of a proton
Here's a guess... Without getting overly complicated.... The diameter of the atom isn't just the diameter of the atom's nucleus... it is the diameter of the whole atom including the electron cloud surrounding the nucleus. As the name implies, an electron cloud represents all the possible locations that the electron could be. This cloud has thickness and therefore the atom could be smaller if the electron is in a portion of the cloud closer to the nucleus or larger is the electron is in a portion of the cloud farther from the nucleus. The "known value" is probably just the average of the two. Therefore, an atom's diameter has a range rather than a fixed value.