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I have run many trials with random data (to compare with a real set) and found that about 90% of items occur within one-third of the mean which suggests that where the size of SD approaches the mean then randomness is less likely (even for a normal distribution!). Investigations with relative mean deviation (MD/Mean) on random data sets also show that it tends to 20+% as the number of items is increased. A distribution too regular or too clumped (even about the mean) is unlikely to be a result of chance. Is there a theoretical SD to mean formulation that can express probability of randomness? Stating 68% of values occur within 1 SD does not address this. Thanks.

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