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The Bell inequality is derived under the assumption of three physical datasets, random or deterministic. The data sets represent a laboratory realizationof the three probability based variables used by Bell. For physical data as canbe written on paper, the derivation of the inequality results only fromprinciples of algebra and is independent of assumptions of locality, hiddenvariables and even randomness. Cross correlations of thee data sets carried outas Bell correlated three random variables results in the same inequality thatis identically satisfied even by deterministic data. However, to obtain threedata sets on two particles destroyed by measurement, two experimental runs arerequired, followed by data matching to reduce four data sets to three. Ifquantum mechanical probabilities are used to describe the data frequencies, theBell inequality is satisfied. The situation is analogous to performing two setsof coin flips to compare the effect of two different coin loadings on theprobabilities for heads and tails.

Unseen facts due to the statistical derivation of the Bell inequality and their logical consequences