Numerical Examples
Consider the sets R and S
- R={1, 2, 3, 4}
- S={5, 6, 7, 8, 9}
The arithmetic mean of R is 2.5, and the arithmetic mean of S is 7.
However, if 5 is moved from S to R, producing
- R={1, 2, 3, 4, 5}
- S={6, 7, 8, 9}
then the arithmetic mean of R increases to 3, and the arithmetic mean of S increases to 7.5.
Consider this more illustrative example:
- R={1,2}
- S={99,10000,20000}
with arithmetic means 1.5 and 10033. Moving 99 from S to R gives means 34 and 15000. 99 is orders of magnitude above 1 and 2, and orders of magnitude below 10000 and 20000. 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. Consider this example:
- R={1, 3, 5, 7, 9, 11, 13}
- S={6, 8, 10, 12, 14, 16, 18}
Moving 10 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.
Read more about this topic: Will Rogers Phenomenon
Famous quotes containing the words numerical and/or examples:
“The terrible tabulation of the French statists brings every piece of whim and humor to be reducible also to exact numerical ratios. If one man in twenty thousand, or in thirty thousand, eats shoes, or marries his grandmother, then, in every twenty thousand, or thirty thousand, is found one man who eats shoes, or marries his grandmother.”
—Ralph Waldo Emerson (1803–1882)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)