You are eliding significant details. First, minimum wage earners do not need to live in average housing. If the average one bedroom apartment rents for $1,800 a month, then half of all one bedroom apartments rent for less than $1,800 a month; I would expect a person with below average income to live in cheaper than average housing. Second, a one bedroom apartment is too much housing for a low income single person. A bachelor suite or shared accommodation are cheaper.