Information vs Choices
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The following data set shows that as the number of choices increases, then so does the amount of information that can be produced.
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Each row represents occurrence of ID in 100 samples per number of choices. E.g. 24 in column F means out of 100 samples with 6 possible choices, 24 met the ID criteria.
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Number of Choices12345678910
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Experiment 100010132113332318
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Experiment 20003162319222719
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Experiment 30008172118171728
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Experiment 40006161620212527
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Experiment 500010162222262222
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Experiment 600010121822192326
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Experiment 70009131621251222
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Experiment 80000191220292012
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Experiment 90007142421282729
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Experiment 1000014162426262521
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Standard Deviation0003.9735234852.14993544.0290610983.3266599874.8808013914.7010637095.274677452
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1 std above avg0007.715.219.720.224.622.122.4
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Average00011.6735234917.349935423.729061123.5266599929.4808013926.8010637127.67467745
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1 std below avg0003.72647651513.050064615.670938916.8733400119.7191986117.3989362917.12532255
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 Information vs ChoicesID example