Atomic Weight: The average mass of isotopes

What is the average weight of chlorine if 75.78% of chlorine is chlorine-35 and 24.22% is chlorine-37? Chlorine-35 has a mass of 34.969 amu and chlorine-37 has a mass of 36.966 amu.

Assume there are 100 chlorine atoms in a sample.

Then 75.78 are chlorine-35 with a total mass of 75.78 x 34.969 amu = 2649.95 amu

And 24.22 are chlorine-37 with a total mass of 24.22 x 36.966 amu= 895.316 amu

The total weight of the atoms divided by the number of atoms gives the average:

$$\frac{3545\,amu}{100}= 35.45 \,amu$$

How are these masses and % abundances known?