An Average a Day

Speaking for a moment as a person who occasionally writes up summaries of surveys, studies, financial reports, market analyses, and other documents which purport to offer quantitative information about companies, topics, and trends, I have a pet peeve: the use of the word average. Most people—and most public relations and marketing people—use the word "average" in a cavalier fashion, assuming that everyone knows its definition. You've seen the sort of statements I'm thinking about:

Americans watched an average of 4 hours and 32 minutes of television a day during 2005.
(Nielsen Media Research, 29-Sep-2005; PDF format.)

By May 2006, the average person bought a new cell phone every 17.6 months.
(Businessweek, 21-Aug-2006 citing J.D. Power & Associates.)

The numbers in these statements aren't deeply problematic because their sources are relatively clear and sample sizes—the number of people surveyed—are large. I admit to paraphrasing for my purposes, but the statements aren't as cut-and-dry as they might seem.

The first suffers from a vague definition of "American." Does this term include people who don't own televisions? How about folks like prisoners, military personnel, children, or people in jobs or institutions which restrict or preclude television access? Or, given that Nielsen is a media metrics firm which rates viewership of television programming, does "Americans" only refer to folks who own and watch televisions in their homes? Or, just maybe, it refers to:

  • non-military
  • non-institutionalized
  • United States citizens
  • over the age of 18
  • in the contiguous 48 states
  • who own and watch television
  • who have landline phones:
    • on residential exchanges
    • with numbers listed in public directories or
  • answer unexpected calls from unrecognized callers and/or numbers
  • who are at home and available when Nielsen calls
  • speak English

(Maybe. I'm just speculating. Check into the notion, if you like. Could be fun.)

Similarly, the second statement uses "people" in an offhand manner. As I write, the estimated population of the planet Earth is pushing 6.6 billion people. Are we to assume, on "average," these people buy a new cell phone every 17.6 months? More likely, "people" here means "current mobile phone owners in the United States," which is a much smaller barrel of fish. As of February 2006, there were an estimated 207 million mobile phone subscribers in the U.S. (a number barely half the estimated number of mobile phone users in China). Suddenly we're discussing only about 70 percent of the estimated U.S. population, and just over 3 percent of all the "people" in the world. The "average person" in the Businessweek article is probably not the same as an "average person" in the world.

And then there's that word average. What does it mean?

There are three kinds of averages, called the mean, median, and mode. Most reporting, publicity, and advertising citing an "average" never specifies which type they're using, and the values for each other these can be very different depending on the data being described.

The sum of all the values in a set (or population) divided by the number of items in that set. This is the "average" many of us were taught in elementary school.
A value in a set which divides the members of a set such that half the values are above the median, and half the values are below the median. If some values are exactly equal to the median, then less than half the set will be above or below the median. (It is possible for some sets to have more than one median value.)
The single most common value in a set.
Describing wages is usually a fabulous way to demonstrate how wildly different these averages can be. Let's say you have a 25 person company where 10 entry-level employees earn $1500 per month (a wage of roughly $9.38 per hour). Salaried professionals, managers, supervisors, administrators, accountants, executives, and (of course) the owners earn more:
Description People Wage "Average"
Entry level • • • • • • • • • • $1500 mode (most common)
Shift supervisors • • $2000
Security $2300 median (half above, half below)
Asst Managers • • • $2500
Managers • • $3000
Buyer/Sales Rep • • $3500 mean (close; it's actually $3512)
Attorney (retainer) $5000
Accountant, Director • • $8000
President $10000
Owner $15000

One could legitimately describe this company as offering an average wage of $1500, $2300, or $3512 per month. Which do you think most accurately represents the company?

The answer, of course, is "it depends." If you were trying to play up the company's positive impact on the local economy (say, to a local journalist), you might use the mean. After all, saying a company has an "average" wage around $3500 a month conveys the impression it's offering a number of high wage jobs and a good standard of living to its employees.

If you were representing the company's payroll to a potential investor worried about labor costs, you might say the company had an average wage of only $1500 a month, conveying the impression that salary and wage expenditures were well under control…and neatly obscuring the owner's monthly take.

If you were hiring a new manager, you might say the company had an average salary of $2300, to bolster your negotiating position when your preferred candidate asked for a salary over $4000 a month.

Of course, a real company—especially one with an accountant worth $8000 a month— would be able to doctor these numbers in all sorts of interesting ways. For instance, salaries for high-end employees would probably, on paper, be quite a bit lower so salary "averages" seem more proportionate. Instead, management and upper-level executives would likely receive portions of their compensations through "bonuses" and "incentives" separate from their salaries.

But you get the idea: whenever you see the word "average," ask yourself what average is being used, and what is being represented by that number. If you can't tell, it's fair to suspect some chicanery.