This types of estimate is sadly deeply flawed. Voices are affected not just by ethnicity but also language and culture. I know because I can feel slight noticeable differences in tones between communities just 30-50 miles apart, within same social classes and everything. Bilinguals also sound noticeably different to monolinguals even in their primary language.

I think people thinks others sound same not because they're similar from beginning, but because voices must homogenize under peer pressures. There's a proverb "nails that sticks out gets hammered". Most people probably has hammered flat voices intended to not stand out.