Congratulations. The very fact that you can read these lines indicates that you are literate. But how sure are you that you are numerate? Even if mathematics and statistics were some of your favorite courses back in school, chances are that your mathematical and arithmetic skills are a bit rusty these days. Given the mountain of financial and statistical data we have to deal with and correctly interpret as modern-day businesspeople, risking being innumerate can’t be an option. In today’s article and in two weeks’ time, let’s humbly take eight basic lessons to better play the numbers game.

Counting is easy, is it? Imagine you want to count sheep in the field. You see three sheep, one of which is a lamb. Does it count as a full sheep? Moreover, one sheep is a pregnant ewe shortly giving birth to a single lamb or twins. So how many sheep are there? Depending on how you count, your result may be 2, 2.5, 3, 3.5, 4 or 5.

While counting (“One, two, three, …”) is easy, counting something is often less straightforward. You need to have a clear definition for when or not to count something. For example, when do you count someone as a customer in your business? When someone walks into the door? Once you have taken an order? Once you have sold something and delivered the value? Once someone has paid you? Or only once someone paid a certain minimum amount? Clearly, you need to define what “a customer” means to your business.

Lesson 1: Counting isn’t the same as counting something. Always check on how something has been counted. Did they count peas or mushy peas? And of course, make sure that you count the right things that really matter.

This is a really big number, is it? According to the six degrees of separation theory, it is likely that through a chain of personal contacts, you are just six steps away from getting a personal audience with US President Obama. But how likely is it that you really will get it? Clearly, six is a very small number, but in the real context here, it is a big one. 300 million, on the other hand, is a very big number. It’s the number of British pounds that a few years ago, the UK government announced it would spend over five years to create a million new childcare places. But translate this number into the weekly spending per childcare place (£1.15, or £60 per year per childcare place divided by 52 weeks); you conclude that in this case, 300,000,000 is a ridiculously small number.

Lesson 2: Understand that a large number with many zeros may impress or alarm, but on its own means nothing. View an absolute number in proportion to decide if it really is a “big” or a “small” number. Always innocently ask: “Now is that a big number?” And if you are not sure, check what this means for you by asking: “Is it still big if I look at my share of it?”

What’s the average? A man who cannot swim hears that a river rises, on average, only to his knees. He decides to cross it — and drowns. This little story brings home an important point for you to understand: averages make an uneven world smooth. They flatten hills and raise hollows and tell you one height of the land as if it were flat. But as we know, the world is not flat.

A popular joke goes that Bill Gates comes to a bar and joins a group of four people at their table. They applaud. “What’s up?” asks Bill Gates. “Don’t you know what you’ve just done to our average income?” You probably understand now that if you wanted to analyze the distribution of incomes in a country like Thailand, the average income is likely to give you a very limited description of the reality.

Lesson 3: Averages = middle = muddle. Check for the ups and downs and other variations aside from the average. For example, aside from the statistical mean, look also at the median, the minimum and maximum, the standard deviation, the upper and lower quartile, and so on. Ask: “What are the ups and downs aside from the flat average?”

Numbers always go up, do they? Understand a very simple, fundamental truth about life: Numbers go up and down, without anyone having to do anything special to the movement. This phenomenon is also known as regression to the mean: When a number has reached a trough or a peak recently, the next move is likely to be back toward the average. For example, GDP growth rates go up and down in line with the economic cycles around a mean growth rate. Or when a certain mutual fund has done exceptionally well during the past two years, it is likely to drop in performance in the following two years. Or if a top football striker has scored a new record of goals this season, he’s likely to score fewer in the next.

Lesson 4: Numbers go up and down, all by themselves. When a number goes up and someone attributes it as one’s own contribution, be wary that the person may have not much to do with it all. Look at the historic numbers, and check out what is the mean. Then ask: “Knowing that numbers go up and down around a mean, what movements can we realistically expect next here?”

Outlook: Come back in two weeks’ time to learn four more lessons on how to prevent being innumerate. And consider learning more and in greater depth on how to play the numbers game by reading these two excellent books on which this article is based, “The Tiger That Isn’t” by Michael Blastland and Andrew Dilnot, and “Innumeracy” by John Allen Paulos.

© Dr. Detlef Reis 2010. This article was published in parallel in the Bangkok Post under the title “Learning to play the numbers game” on 24 June 2010.