end Paper BY SAM GUTTERMAN
The Problem With Averages
THERE’S NOTHING SO REVEALING—or potentially misleading—
as a statistical average.
Although a key metric that captures
the essence of populations or things being measured, an average in isolation may
provide, at best, incomplete information.
But, you say, aren’t you an actuary?
Isn’t the expected value, the mean or
the first moment of any distribution,
a fundamental basis for prices, financial reporting values, and so on? Let me
explain my position by laying out two
basic complaints—an average doesn’t
convey anything about the composition
of most populations, and, at best, it conveys limited information about the risk
and uncertainty of what’s being assessed.
Information about the parts is often
more useful than information concerning
the whole, even though the use of a single
metric is both simple and tempting. This
was brought home to me in a decade over-
seeing marketing research for a multiline
insurer. For instance, although statisti-
cally there may be an average American, I
challenge you to find her/him. I wouldn’t
focus a marketing campaign at the average
person and assume it meets everyone’s
needs (or even an average set of needs)—
there’s way too much diversity among
us. At least one competitor would under-
cut my prices or provide more appealing
benefits to lower-cost customers, while I
would be stuck with the higher-cost rem-
nants—and average prices.
SAM GUTTERMAN, a member of the
Academy, is director and consulting
actuary with PricewaterhouseCoopers
LLP in Chicago.
76 CONTINGENCIES JUL | AUG. 12