The Median Isn't the Message
by Stephen Jay Gould
My life has recently intersected, in a most personal way, two of Mark Twain's
famous quips. One I shall defer to the end of this essay. The other (sometimes
attributed to Disraeli), identifies three species of mendacity, each worse than the
one before - lies, damned lies, and statistics.
Consider the standard example of stretching the truth with numbers - a case quite
relevant to my story. Statistics recognizes different measures of an "average," or
central tendency. The mean is our usual concept of an overall average - add up the
items and divide them by the number of sharers (100 candy bars collected for five
kids next Halloween will yield 20 for each in a just world). The median, a different
measure of central tendency, is the half-way point. If I line up five kids by height,
the median child is shorter than two and taller than the other two (who might have
trouble getting their mean share of the candy). A politician in power might say with
pride, "The mean income of our citizens is $15,000 per year." The leader of the
opposition might retort, "But half our citizens make less than $10,000 per year."
Both are right, but neither cites a statistic with impassive objectivity. The first
invokes a mean, the second a median. (Means are higher than medians in such
cases because one millionaire may outweigh hundreds of poor people in setting a
mean; but he can balance only one mendicant in calculating a median).
The larger issue that creates a common distrust or contempt for statistics is more
troubling. Many people make an unfortunate and invalid separation between heart
and mind, or feeling and intellect. In some contemporary traditions, abetted by
attitudes stereotypically centered on Southern California, feelings are exalted as
more "real" and the only proper basis for action - if it feels good, do it - while
intellect gets short shrift as a hang-up of outmoded elitism. Statistics, in this
absurd dichotomy, often become the symbol of the enemy. As Hilaire Belloc wrote,
"Statistics are the triumph of the quantitative method, and the quantitative method
is the victory of sterility and death."
This is a personal story of statistics, properly interpreted, as profoundly nurturant
and life-giving. It declares holy war on the downgrading of intellect by telling a
small story about the utility of dry, academic knowledge about science. Heart and
head are focal points of one body, one personality.
In July 1982, I learned that I was suffering from abdominal mesothelioma, a rare
and serious cancer usually associated with exposure to asbestos. When I revived
after surgery, I asked my first question of my doctor and chemotherapist: "What is