Under the condition that comparison results are Gaussian distributed with a common mean, a chi-square statistics of arithmetic mean is proposed and investigated through the Monte Carlo simulation. Simulation results show that the arithmetic mean has its own (n – 1)th-order chi-square statistics under the condition that the uncertainties of participants are comparable. Furthermore, the density curve of the proposed statistics is confined between the (n - 1)th-order and first-order chi-square under the condition that the uncertainties of participants are incomparable. However, the expected value of this statistics equals n – 1, which is unaffected by the uncertainties. Based on these properties, the proposed statistics is applied to the consistence testing of arithmetic mean by examples.
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