Evaluating Pref Gem Count

The Gem counts for prif gem rocks were evaluated. The given percentages add up to 99.98%, so I decided to figure out exactly what the gem distribution was and where the rounding error occurred. I took the Given % and multiplied it by the given N to get a gem count estimate. The number obtained was rounded to the nearest digit and then divided by 11771 to get a percentage. The gem count estimate was then manually increased and decreased by 1, while keep the denominator 11771 to see where rounding error occurred. One gem could be explained by increased the Onyx count by 1. The other was not found. Based on the percentages provided and the stated count, I don't see how the stated count is possible. The data should either be re-evaluated wherever it is stored or removed.

Given N = 11771	Given %	Given N*Given%	Rounded	Manual Change	True %		Rounded %	Should Match Given %
Uncut Sapphire	48.42%	5699.5182	5700	5700		48.42409%	48.42%		TRUE
Uncut Emerald	28.27%	3327.6617	3328	3328		28.27287%	28.27%		TRUE
Uncut Ruby	8.97%	1055.8587	1056	1056		8.97120%	8.97%		TRUE
Uncut Diamond	3.79%	446.1209	446	446		3.78897%	3.79%		TRUE
Uncut Onyx	0.08%	9.4168		9	10		0.084955%	0.08%		TRUE
Spirit Sapphire	5.78%	680.3638	680	680		5.77691%	5.78%		TRUE
Spirit Emerald	2.93%	344.8903	345	345		2.93093%	2.93%		TRUE
Spirit Ruby	1.24%	145.9604	146	146		1.24034%	1.24%		TRUE
Spirit Diamond	0.39%	45.9069		46	46		0.39079%	0.39%		TRUE
Spirit D-Stone	0.11%	12.9481		13	13		0.11044%	0.11%		TRUE
Total of Column	99.98%	11768.6458	11769	11771*		99.99150%**	99.98%
								Should be 100% for true and 99.98% for rounded

**Was obtained by summing the column but can also be seen as 11770/11771 which is the number of gems accounted for divided by Given N.

*This 11771 was inputed as the true value, as this column SHOULD add up to 11770. The sum of the column above is 11770 as 1 gem could not be accounted for. The True% is given by "Changing Rounded"/11771. This is fair to do because the given value of N is 11771 and there is no interaction between other numbers this way, since we are trying to get total count to 11771 anyway. It is also fair to do this because in the tests where +1 was added to each gem count, the column would have summed to 11771.

By inputting 11771 I could also lower each of the numbers by 1 to see if the rounded % stayed the same while the True% did not. This also did not change things.

The only gem count which could be increased without changing its rounded value to 4 decimal places was a Spirit Onyx.

Based on the percentages provided and the stated count, I don't see how the stated count is possible. The data should either be re-evaluated wherever it is stored or removed.