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The average slave owner did not own 8 - 15 slaves. I'm not sure I understand your numbers...38,645 slave owners in Kentucky compared to 22,033 in Louisiana.
Well, let’s just take Kentucky and Louisiana since you already provided the numbers of slave owners. According to the 1860 census there were 225,483 and 331,726 slaves in each state respectively. That means that in Kentucky the average number of slaves per owner was 225,483/38,645 = 5.83. In Louisiana the average was 331,726/22,033 = 15.