Will Rogers phenomenon

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2021-06-23 10:30:06

The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average values of both sets. It is based on the following statement, sometimes attributed (without any evidence)[1] to comedian Will Rogers:

with arithmetic means 1.5 for R and 10,033 for S. Moving 99 from S to R gives means 34 and 15,000. 99 is orders of magnitude above 1 and 2, and orders of magnitude below 10,000 and 20,000. It should come as no surprise that the transfer of 99 increases the mean of both R and S.

The element which is moved does not have to be the very lowest of its set; it merely has to have a value that lies between the means of the two sets. Consider this example:

Moving 10, which is larger than R's mean of 7 and smaller than S's mean of 12, from S to R will raise the mean of R from 7 to 7.375, and the mean of S from 12 to 12.333. The effect still occurs, but less dramatically.

One real-world example of the Will Rogers phenomenon is seen in the medical concept of stage migration. In medical stage migration, improved detection of illness leads to the movement of people from the set of healthy people to the set of unhealthy people.

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