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<blockquote data-quote="FrogReaver" data-source="post: 7542179" data-attributes="member: 6795602">Let me give a simple example:Suppose there are 2 distributions defined belowd1 =&nbsp; {3, 3, 3, 3, 6, 6}d2 = {0, 0, 6, 6, 6, 6}The Mean on both distributions is&nbsp; 4.&nbsp; With d1 you only have a 33% getting a result equal to the Mean or above.&nbsp; With d2 you have a 66% chance of getting a result equal to the mean or above.&nbsp; In other words, what you are demonstrating with the EB and firebolt example is a perfectly natural occurrence that has numerous other examples.&nbsp; The only issue is the commonly mistaken assumption that rolling some number or higher 50% of the time has anything to do with the Mean.&nbsp; It doesn't.&nbsp; Rolling some number or higher 50% of the time would be the Median, not the Mean.&nbsp; Now the Median is a great indicator of central tendency, maybe even better than the Mean is in many circumstances, but it's not the Mean.&nbsp; Expecting the Median to be the same as the Mean is actually extremely rare.&nbsp; It would actually be extraordinary if the mean and median were the same in either the firebolt or the eb example.</blockquote>

[QUOTE="FrogReaver, post: 7542179, member: 6795602"] Let me give a simple example: Suppose there are 2 distributions defined below d1 = {3, 3, 3, 3, 6, 6} d2 = {0, 0, 6, 6, 6, 6} The Mean on both distributions is 4. With d1 you only have a 33% getting a result equal to the Mean or above. With d2 you have a 66% chance of getting a result equal to the mean or above. In other words, what you are demonstrating with the EB and firebolt example is a perfectly natural occurrence that has numerous other examples. The only issue is the commonly mistaken assumption that rolling some number or higher 50% of the time has anything to do with the Mean. It doesn't. Rolling some number or higher 50% of the time would be the Median, not the Mean. Now the Median is a great indicator of central tendency, maybe even better than the Mean is in many circumstances, but it's not the Mean. Expecting the Median to be the same as the Mean is actually extremely rare. It would actually be extraordinary if the mean and median were the same in either the firebolt or the eb example. [/QUOTE]

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