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The given statistics are from J.F. Epperson on his site here. It is listed as Selected Statistics on Slavery at this link.

Methodology was "The figures given here are the percentage of slave-owning families as a fraction of total free households in the state." This is much like measuring velocity in furlongs per fortnight.

The data was taken from a now-inactive census archive site at the University of Virginia, but equivalent data may be found here.

The new link is:

http://www.civil-war.net/pages/1860_census.html?fref=gc

which redirects to

https://thegunzone.com/gun-reviews/

For actual 1860 census statistics see:

https://www.census.gov/library/publications/1864/dec/1860a.html

At the link are available, each as a seperate publication:

1860 Census: Population of the United States

1860 Census: Agriculture of the United States

1860 Census: Manufactures of the United States

1860 Census: Statistics of the United States

In the 1860 Agriculture Report, Slave Statistics appears a section entitled Recapitulation.

In the 1860 Population Report, appears a section entiled Recapitulation of the Tables of Population, Nativity, and Occupation. No slave statistics.

SLAVEHOLDER STATISTICS - 1860 CENSUS DATA

STATE	TOTAL POPULATION	# SLAVEHOLDERS	Families	% SLAVEHOLDERS	Fam size
AL	964,201	33,730	96,603	3.50%	8.86
AR	435,450	11,481	57,244	2.64%	7.61
FL	140,424	5,152	15,090	3.67%	9.31
GA	1,057,286	41,084	109,919	3.89%	9.62
LA	708,002	22,003	74,725	3.11%	9.47
MS	791,305	30,943	63,015	3.91%	12.56
NC	992,622	34,658	125090	3.49%	7.94
SC	703,708	26,701	58,642	3.79%	12.00
TN	1,109,801	36,844	149,335	3.32%	7.43
TX	604,215	21,878	76,781	3.62%	7.92
VA	1,596,318	52,128	201,523	3.27%	7.92

TOTAL:	9,103,332	316,602	1,027,967	3.31%	8.86

STATE	TOTAL POPULATION	# SLAVEHOLDERS	Families	% SLAVEHOLDERS	Fam size
DE	112,216	587	18,966	0.52%	5.92
KY	1,155,684	38,645	166,321	3.34%	6.95
MD	687,049	13,783	110,278	2.01%	6.23
MO	1,182,012	24,320	192,073	2.06%	6.15

TOTAL:	3,136,961	77,335	487,638	2.47%	6.43

Please take me off any of these posts.

woodpusher: "Methodology was "The figures given here are the percentage of slave-owning families as a fraction of total free households in the state."
This is much like measuring velocity in furlongs per fortnight. "

Clearly we have a case here of "figures don't lie but liars can figure."
Your calculations are self-evidently bogus.
Here's what they should say:

SLAVEHOLDER STATISTICS - 1860 CENSUS DATA

STATE	FREE POPULATION	FREE FAMILIES	SLAVEHOLDERS	SLAVEHOLDER FAMILIES	SLAVES
Mississippi	354,674	63,015	30,943	49%	436,631
South Carolina	301,302	58,642	26,701	45%	402,406
Georgia	505,088	109,919	41,084	37%	462,198
Alabama	519,121	96,603	33,730	35%	435,080
Florida	78,679	15,090	5,152	34%	61,745
Louisiana	376,276	74,725	22,033	29%	331,726
Texas	421,649	76,781	21,878	28%	182,566
North Carolina	661,563	125,090	34,658	28%	331,099
Virginia	1,105,453	201,523	52,128	26%	490,865
Tennessee	834,082	149,335	36,844	25%	275,719
Kentucky	930,201	166,321	38,645	23%	225,483
Arkansas	324,335	57,244	11,481	20%	111,115
Missouri	1,067,081	192,073	24,320	13%	114,943
Maryland	599,860	110,278	13,783	12%	87,189
Delaware	110,418	18,966	587	3%	1,798
Total/Averages	8,189,782	1,515,605	393,967	26%	3,950,551

So, the argument we've seen is that, well, there might have been more than one slaveholder per family, and if there were two, that would reduce those percentages by half.
The answer is: maybe, probably not, but even if true, that could in no way get the averages down to the 3% claimed in woodpusher's bogus statistics.

The key takeaway is that, especially in the Deep South, virtually everyone had family or neighbors who were slaveholders, and everyone clearly understood the importance of slavery to their economic well being.

"Our position is thoroughly identified with the institution of slavery-- the greatest material interest of the world.
Its labor supplies the product which constitutes by far the largest and most important portions of commerce of the earth.
These products are peculiar to the climate verging on the tropical regions, and by an imperious law of nature, none but the black race can bear exposure to the tropical sun.
These products have become necessities of the world, and a blow at slavery is a blow at commerce and civilization.
That blow has been long aimed at the institution, and was at the point of reaching its consummation.
There was no choice left us but submission to the mandates of abolition, or a dissolution of the Union, whose principles had been subverted to work out our ruin."