# Tag Archives: Central Tendency

## HOW OLD ARE THE MEDIAN, MODE, & ARITHMETIC MEAN?

According to one source, the word “mode” was first used (by Karl Pearson) in 1895. The concept of the “median” is a bit older; it was used for the first time by the Frenchman Antoine Cournot in 1843. The notion of the “arithmetic mean” is even older.

QUESTION: When do you think the concept of the “arithmetic mean” was born?

ANSWER: A long, long, LONG time ago. The Pythagoreans studied it in the 5th century B.C.

Filed under History of Statistical Terms

## DO YOU KNOW SOMEONE WITH CANCER

Dr. Stephen Jay Gould, a world-famous scientist who taught at Harvard, was 40 when diagnosed with cancer. He discovered that people with his kind of cancer live for a median of 8 months. Gould’s down-to-earth essay, “The Median Isn’t the Message,” deals with his “survival expectancy.” It’s considered by some to be “the wisest, most humane thing ever written about cancer and statistics.”

In his thoughtful commentary, Gould offered some important advice to those who hear (for themselves or a loved one) grim diagnoses based on median survival rates. As Gould so correctly pointed out,

What does “median mortality of eight months” signify in our vernacular? I suspect that most people, without training in statistics, would read such a statement as “I will probably be dead in eight months”––the very conclusion that must be avoided, since it isn’t so….

Dr. Gould’s essay contains important food-for-thought not just for those concerned about cancer or other life-ending diseases, but also for those who produce or receive statistically-based research claims in any disciple. In a nutshell, his admonition says: Don’t focus so heavily on means and medians that the important underlying variability is totally overlooked. As Gould put it,

We still carry the historical baggage of a Platonic heritage that seeks sharp essences and definite boundaries. … This Platonic heritage, with its emphasis in clear distinctions and separated immutable entities, leads us to view statistical measures of central tendency wrongly, indeed opposite to the appropriate interpretation in our actual world of variation, shadings, and continua. In short, we view means and medians as the hard “realities,” and the variation that permits their calculation as a set of transient and imperfect measurements of this hidden essence.

If the median is the reality and variation around the median just a device for its calculation, the “I will probably be dead in eight months” may pass as a reasonable interpretation. … But all evolutionary biologists know that variation itself is nature’s only irreducible essence. Variation is the hard reality, not a set of imperfect measures for a central tendency. Means and medians are the abstractions.

If you’d like to hear Gould’s essay read while you see a series of photos of him at work and play, click this link: http://www.youtube.com/watch?v=cH6XuiOBbkc

If you’d prefer to read Gould’s essay yourself, or print it, go here: http://cancerguide.org/median_not_msg.html