What is Problem with Averages?

A video explaining Problem with Averages Bias by Rolf Dobelli the author of The Art of Thinking Clearly on the IDFC Mutual Fund Youtube Channel.

WHAT IS THE PROBLEM WITH AVERAGES AND WHY THERE IS NO SUCH THING AS AN AVERAGE WAR 

Suppose you’re on a bus with forty-nine other people. At the next stop, the heaviest person in America gets on. Question: by how much has the average weight of the passengers increased? Four per cent? Five? Something like that. Suppose the bus stops again, and on gets Bill Gates. This time we are not concerned about weight. Question: by how much has the average wealth risen? Four per cent? Five? Far from it!

Let’s calculate the second example quickly. Suppose each of fifty randomly selected individuals has assets of $54,000. This is the statistical middle value, the median. Then Bill Gates is added to the mix, with his fortune of around $59 billion. The average wealth has just shot up to $1.15 billion, an increase of more than two million per cent. A single outlier has radically altered the picture, rendering the term ‘average’ completely meaningless.

‘Don’t cross a river if it is (on average) four feet deep,’ warns Nassim Taleb, from whom I have the above examples. The river can be very shallow – mere inches – for long stretches, but it might transform into a raging torrent that is twenty feet deep in the middle, in which case you could easily drown. Dealing in averages is a risky undertaking because they often mask the underlying distribution – the way the values stack up.

Another example: the average amount of UV rays you are exposed to on a June day is not harmful to your health. But if you were to spend the entire summer in a darkened office, then fly to Barbados and lie in the sun without sunscreen for a week solid, you would have a problem – even though, on average over the summer, you were not getting more UV light than someone who was outside regularly.

All this is quite straightforward and maybe you were aware of it already. For example, you drink one glass of red wine at dinner every evening. That’s not a health issue. Many doctors recommend it. But if you drink no alcohol the entire year and on Dec 31 you gulp 356 glasses, which is equivalent to sixty bottles, you will have a problem, although the average over the year is the same.

Here’s the update: in a complex world, distribution is becoming more and more irregular. In other words, we will observe the Bill Gates phenomenon in ever more domains. How many visits does an average website get? The answer is: there are no average websites. A handful of sites (such as the New York Times , Facebook or Google) garner the majority of visits, and countless other pages draw comparatively few. In such cases, mathematicians speak of the so-called power law. Take cities. There is one city on this planet with a population of more than 30 million: Tokyo. There are 11 cities with a population of between 20 and 30 million. There are 15 cities with a population of between 10 and 20 million. There are 48 cities with between 5 and 10 million inhabitants. And thousands (!) between 1 and 5 million. That’s a power law. A few extremes dominate the distribution, and the concept of average is rendered worthless.

What is the average size of a company? What is the average population of a city? What is an average war (in terms of deaths or duration)? What is the average daily fluctuation in the Dow Jones? What is the average cost overrun of construction projects? How many copies does an average book sell? What is the average amount of damage a hurricane wreaks? What is a banker’s average bonus? What is the average success of a marketing campaign? How many downloads does an average iPhone app get? How much money does an average actor earn? Of course you can calculate the answers, but it would be a waste of time. These seemingly routine scenarios are subject to the power law. 

To use just the final example: a handful of actors take home more than $10 million per year, while thousands and thousands live on the breadline. Would you advise your son or daughter to get into acting since the average wage is pretty decent? Hopefully not – wrong reason.

In conclusion: if someone uses the word ‘average’, think twice. Try to work out the underlying distribution. If a single anomaly has almost no influence on the set, the concept is still worthwhile. However, when extreme cases dominate (such as the Bill Gates phenomenon), we should discount the term ‘average’. We should all take stock from novelist William Gibson: ‘The future is already here – it’s just not very evenly distributed.’ 

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The above article is from the book The Art of Thinking Clearly by Rolf Dobelli. The article is only for educational and informative purposes to explain and understand cognitive biases. It is a great book, definitely worth a read!