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The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average
Average

In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "Expected value" value of the data set....
 values of both sets. It is based on the following quote, attributed to comedian Will Rogers
Will Rogers

William Penn Adair ?Will? Rogers was a Cherokee-United States cowboy, comedian, humorist, social commentary, vaudeville performer and actor. He was the father of U.S....
:
When the Okie
Okie

Okie is a term, dating from as early as 1907, originally denoting a resident or native of Oklahoma. It is derived from the name of the state, similar to Texan or Tex for someone from Texas, or Arkie or Arkansawyer for a native of Arkansas....
s left Oklahoma
Oklahoma

Oklahoma is a U.S. state and a sovereignty located in the South Central United States and Southern United States of the United States of America ....
 and moved to California
California

California is a U.S. state on the West Coast of the United States of the United States, along the Pacific Ocean. It is bordered by Oregon to the north, Nevada to the east, Arizona to the southeast, and to the south the Mexico state of Baja California....
, they raised the average intelligence level in both states.


The effect will occur when both of these conditions are met:

All of this of course also works the other way around.

>

The arithmetic mean
Arithmetic mean

In mathematics and statistics, the arithmetic mean of a list of numbers is the sum of all of the list divided by the number of items in the list....
 of R is 2.5, and the arithmetic mean of S is 7.

However, if 5 is moved from S to R, producing

R=
S=


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=
S=


with arithmetic means 1.5 and 10033. Moving 99 from S to R gives means 34 and 15000.






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The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average
Average

In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "Expected value" value of the data set....
 values of both sets. It is based on the following quote, attributed to comedian Will Rogers
Will Rogers

William Penn Adair ?Will? Rogers was a Cherokee-United States cowboy, comedian, humorist, social commentary, vaudeville performer and actor. He was the father of U.S....
:
When the Okie
Okie

Okie is a term, dating from as early as 1907, originally denoting a resident or native of Oklahoma. It is derived from the name of the state, similar to Texan or Tex for someone from Texas, or Arkie or Arkansawyer for a native of Arkansas....
s left Oklahoma
Oklahoma

Oklahoma is a U.S. state and a sovereignty located in the South Central United States and Southern United States of the United States of America ....
 and moved to California
California

California is a U.S. state on the West Coast of the United States of the United States, along the Pacific Ocean. It is bordered by Oregon to the north, Nevada to the east, Arizona to the southeast, and to the south the Mexico state of Baja California....
, they raised the average intelligence level in both states.


The effect will occur when both of these conditions are met:
  • The element being moved is below average for its current set. Removing it will, by definition, raise the average of the remaining elements.
  • The element being moved is above the current average of the set it is entering. Adding it to the new set will, by definition, raise the average.


All of this of course also works the other way around.

Numerical examples


Consider the sets R and S

R=
S=


The arithmetic mean
Arithmetic mean

In mathematics and statistics, the arithmetic mean of a list of numbers is the sum of all of the list divided by the number of items in the list....
 of R is 2.5, and the arithmetic mean of S is 7.

However, if 5 is moved from S to R, producing

R=
S=


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=
S=


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=
S=


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.

Stage migration

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.

Because these people are not healthy, removing them from the set of healthy people increases the average lifespan of the healthy group. Likewise, the migrated people are more healthy than the people already in the unhealthy set, so adding them raises the average lifespan of that group as well.

External links

  • by Paul Niquette
  • – A quote by Sir Robert Muldoon
    Robert Muldoon

    Sir Robert David Muldoon, Order of St Michael and St George, Order of the Companions of Honour served as Prime Minister of New Zealand from 1975 in New Zealand to 1984 in New Zealand, as leader of the governing New Zealand National party....