# How can percents not adding up to a hundred be possible?

I was reading this paper about aquaponics and some of the stats did not make any sense with regard to the percents listed. What method would allow these percents to exist?

The most commonly raised aquatic animals by percent were tilapia (69%), ornamental fish (43%), catfish (25%), other aquatic animals (18%), perch (16%), bluegill (15%), trout (10%), and bass (7%). ~ http://www.sciencedirect.com/science/article/pii/S0044848614004724

• Even when components are disjoint, and there is no silly calculation or reporting error, rounding error can still bite. A simple example is (1 + 1 + 1)/3 yielding as percentages 33, 33, 33 or 33.3, 33.3, 33.3 or .... Here more decimal places just means smaller rounding error, but it never becomes 0. An immensely deeper analysis is provided by Diaconis and Freedman in JASA 1979, accessible, perhaps illicitly, at statweb.stanford.edu/~cgates/PERSI/papers/freedman79.pdf – Nick Cox Mar 15 '17 at 18:01
• @NickCox If you take alook at the numbers again you can easily see that that is not the reason in this case. Rounding errors can never give you a sum of 203%. – Cleared Mar 16 '17 at 14:49
• consider this: "have you ever raised: a] a cat, b] a dog". Result could be something like a] 62% b] 74%. Because they are not mutually exclusive (and not even covering the whole spectrum) – njzk2 Mar 16 '17 at 18:45
• @Cleared Sure, and I took that to be both obvious and the answer in this specific case. My comment starts "Even when components are disjoint...". Sorry that was not clear to you, but I could and can do the mental arithmetic of 69 $+$ 43 and immediately see that rounding is not the issue. If you take a look again at the title of the thread, then you should see that there is more than one reason why people might visit it. – Nick Cox Mar 16 '17 at 19:32