commoners not holding slaves doesn't matter.
population of 10 slaves. Average number of slaves per household of 1.
0,0,0,0,0,0,0,0,0,10 = 10 slaves in 10 households, average 1. Same as 1,1,1,1,1,1,1,1,1,1 Ten slaves, ten households.
Even if the Empress had all 21 Tn slaves, and no other household had any, for the average per household to be 2.3 then there'd be 11 Tn households more or less.
and with 11 Tn households, and 21 Tn people to fill those households, then that's a very low number of people per household. Too low.
too low by far.