The business world revolves around numbers. But what are they saying?

Over the last decade, the buzz word “metric” has gained significant currency. A more recent business phrase deals with the “dashboard,” a real-time display of an organization’s analytic data.

Of course, businesses must also keep a finger on the pulse of key data points relating to response time, sales, inventory, cash flow and other important gauges of their operations.

Numbers are often used during political debates to make (or prove) a point. But many times post-debate fact checking indicates the statistics cited were not accurate. Consider the famous adage popularized by Mark Twain, which first appeared in his "Chapters from My Autobiography in 1906”: “Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: 'There are three kinds of lies: lies, damned lies, and statistics.’”

We all know that numbers can be used selectively to make a situation appear better than it actually is. And nothing can be more mind-numbing than a discussion devolving into a litany of numbers that are not directly related to the topic at hand.

One oft-referenced statistic is the “average.” But the type of average used can make an enormous difference in the results. Most people are familiar with an arithmetic mean, which is the sum of a series of numbers divided by the count of that series of numbers.

If you were asked to find the arithmetic mean of the free throw percentage for a basketball team, you would simply add them up and then divide that sum by the number of players. For example, if their foul shooting percentage was 50%, 60%, 70%, 80% and 100%, the arithmetic team mean would be 72%, calculated as(0.5+0.6+0.7+0.8+1.0)/ 5 = .72.

The reason for using an arithmetic mean for calculating free throw percentage is that each shooter’s results are an independent event. One player’s results don’t impact those of the other players—they are independent of one another.  In some other examples, the events are not independent of each other, so using the arithmetic mean is not the right choice.

A great example is investment returns. Since negative years reduce the amount of money to invest for the following year, these do not constitute independent events. Consequently, to account for the impact, arriving at the actual return requires calculating the geometric mean by multiplying each year’s returns—not simply adding and dividing them.

The following example illustrates the difference:

• Portfolio A: +10%, -10%, +10%, -10%
• Portfolio B: +30%, -30%, +30%, -30%

The arithmetic mean yields an average return of 0% for both portfolios. But the geometric mean is as follows:

• Portfolio A: -2%
• Portfolio B: -17%

Whenever someone is spouting numbers, it’s important to know whether the results involve independent or dependent events—and whether the results are based on an arithmetic or geometric mean.

Dave Evans is a certified financial planner and an IA contributor.