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<blockquote data-quote="auburn2" data-source="post: 8228239" data-attributes="member: 6855259">This is absolutely not true.&nbsp; The sample variance changes with every measurement (roll).&nbsp; Even if the sample distribution exactly matches the expected distribution for a population, the sample variance will still be larger than the population variance because the denominator in the sample variance is based on the number of measurements (rolls) minus 1 while the population&nbsp; variance is based on the size of entire population (no minus 1)As the number of rolls in a sample approaches the total number of rolls in the entire population, the variance of the sample will approach the variance of the population.&nbsp; It will generally approach the population variance from above (i.e. getting smaller with more rolls).&nbsp; It is possible for the sample variance to be smaller than the population variance, but that is abnormal for a large sample and represents a bias in the sample. It would also call into question whether the sample is in fact part of&nbsp; the population (i.e. is the RNG or dice loaded)</blockquote>

[QUOTE="auburn2, post: 8228239, member: 6855259"] This is absolutely not true. The sample variance changes with every measurement (roll). Even if the sample distribution exactly matches the expected distribution for a population, the sample variance will still be larger than the population variance because the denominator in the sample variance is based on the number of measurements (rolls) minus 1 while the population variance is based on the size of entire population (no minus 1) As the number of rolls in a sample approaches the total number of rolls in the entire population, the variance of the sample will approach the variance of the population. It will generally approach the population variance from above (i.e. getting smaller with more rolls). It is possible for the sample variance to be smaller than the population variance, but that is abnormal for a large sample and represents a bias in the sample. It would also call into question whether the sample is in fact part of the population (i.e. is the RNG or dice loaded) [/QUOTE]

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