# How are low/middle/high classes defined mathematicaly?

I am only looking for mathematical references. I think this belongs to econometrics but am not sure nor where to look at it specifically. I suspect the definition is given with some kind of weighted average where income and number of people with similar income are computed.

“Pew Research defines middle-income Americans as those whose annual household income is two-thirds to double the national median. For a family of three, that ranges from \$42,000 to \$126,000 in 2014 dollars. The lowest-income group earned \$31,000 or less for a family of three while the lower-middle group earned between \$31,000 and \$42,000 in 2014, according to Pew Research. At the most affluent levels, upper-middle-income, three-person households earned between \$126,000 and \$188,000, with the highest-income households topping \$188,000 in 2014 earnings.”