We often rely on averages to simplify complex realities. They’re an easy tool for communicating a sense of normalcy or expectation in a messy and unpredictable world. But what happens when extremes skew the average? What happens when a few outliers distort the picture entirely? This concept, although straightforward, has far-reaching implications. Averages can mislead, mask critical information, and render essential nuances meaningless. Let’s dive into why averages can be problematic and what they mean for us as we navigate the increasingly irregular distributions of modern life.
The Bill Gates Example
The power of a single outlier in altering the perceived “average” is best illustrated by the example of Bill Gates stepping onto a bus filled with 50 random individuals. Each of these 50 individuals has a modest wealth of $54,000 in this case. This is not an extreme number by any means—it’s an average wealth figure for a middle-income person in many parts of the world. However, everything changes when Bill Gates, with his staggering fortune of around $59 billion, enters the mix. The average wealth of this group now jumps to an astronomical $1.15 billion.
This transformation is not because anyone else’s wealth has changed—it’s because one individual, Bill Gates, has wealth that is so far outside the norm that it completely distorts the “average” of the group. The shift isn’t just incremental; it’s explosive. A single data point, in this case, Gates’ wealth, has changed the average wealth of the entire group to an unrealistic, out-of-touch figure. This example highlights how averages can be misleading when outliers such as extreme wealth, income, or other metrics skew the result.
What this shows is the importance of not only calculating averages but also understanding their context. Averages, in some situations, can give us a general sense of a group, but they fail to convey the underlying disparities or extremes that may exist. In this case, the presence of an outlier like Bill Gates shifts the entire distribution of wealth within the group, making the “average” figure essentially meaningless in representing the wealth of the typical person. The moral here: averages can sometimes be a poor substitute for deeper insights into data distribution.
The River Analogy: Averages Can Be Dangerous
Nassim Taleb’s river analogy is a powerful cautionary tale about the risks of relying on averages in contexts where the underlying distribution may have significant extremes. Taleb uses the example of crossing a river that is, on average, four feet deep. At first glance, this may seem safe enough. After all, four feet is a manageable depth, and we might assume the river’s depth is uniform. However, Taleb points out that the average depth of a river doesn’t reflect the full reality—it might be shallow for most of its length but suddenly drop to twenty feet in certain areas. This extreme variation would have disastrous consequences for someone crossing based solely on the average depth.
This metaphor goes beyond rivers, applying to many real-world situations. For instance, the average temperature during the summer in a city might suggest a moderate, comfortable climate, but this ignores the potential for heat waves that could cause extreme discomfort or even health risks. Similarly, an average return on an investment might suggest a reasonable profit, but it could mask the volatility and risk of large swings in value. In other words, the average doesn’t reflect the unpredictability or dangerous extremes in the system. It’s like taking the average of a river’s depth and thinking that crossing it is safe without considering the hidden danger beneath.
By ignoring these variations, averages can hide the true risk involved. Just as crossing a river based on its average depth might put someone in serious danger, so too can relying on averages in other domains—whether in finance, health, or any complex systems. The key takeaway here is that averages are too simplistic and, when extreme values exist, can lead to decisions that are not just flawed but potentially harmful.
Averages Don’t Account for Distribution
Averages only tell part of the story. They provide a “middle ground” that can help us understand a dataset’s central tendency, but they completely miss the distribution—the spread of values from the low end to the high end. This is crucial because the extremes (the outliers) in any dataset often carry more weight and meaning than the average. Averages smooth out the differences and give us a general sense of “normal,” but they obscure the full picture.
Take the example of UV radiation exposure. On average, a person who spends the summer outdoors and gets moderate sun exposure each day is likely to stay within a safe limit for UV exposure. But now imagine someone who works in a dark office for months and then suddenly takes a trip to a tropical destination, where they lie in the sun for a week without sunscreen. Despite having an “average” amount of sun exposure over the summer, this individual is now at serious risk because they’ve accumulated an intense, concentrated dose of UV radiation in a short time. The “average” exposure over the summer doesn’t reflect the extreme spike in exposure at the end, which poses a real danger.
Similarly, consider the impact of unhealthy habits. Suppose someone eats a reasonably balanced diet most of the year, with only occasional indulgences. The average diet might seem fairly healthy. But if they suddenly binge on junk food for an entire week, the cumulative impact of those extreme dietary choices can have serious long-term consequences. The average doesn’t account for the effects of the binge, which are far more significant than the daily average might suggest.
This is why averages often fail to provide meaningful insights in many situations. They flatten out the data, ignoring the extremes that can have far more significant effects. Whether you’re looking at health metrics, financial data, or behavior patterns, the distribution—how values are spread out—truly matters. And when these distributions are uneven or skewed, as they often are in modern society, averages can mislead us into thinking we’re safe or secure when we’re actually at risk.
The Growing Irregularity of Distribution
The world we live in today is increasingly governed by what is known as the “power law.” This refers to a distribution where a small number of entities—people, companies, websites, or cities—dominate the entire landscape, while the rest are much smaller or less impactful. In the case of websites, for instance, a handful of sites such as Google, Facebook, and YouTube attract the vast majority of online traffic. Meanwhile, millions of other websites receive little to no attention. This is a clear example of a power law in action, where a few outliers significantly distort the overall distribution.
The same phenomenon can be seen in cities. Tokyo is the only city in the world with a population of over 30 million. There are only 11 cities with populations between 20 and 30 million and 15 cities with populations between 10 and 20 million. However, the vast majority of cities have much smaller populations—often under 5 million. When looking at the “average” city population, the reality is heavily skewed by a few massive cities, making the concept of an average virtually meaningless.
As more fields move toward these power law distributions, the reliance on averages becomes less relevant. In the business world, for example, a few giant companies like Amazon, Apple, and Microsoft dominate their industries, while millions of smaller companies struggle for survival. The “average” company size, income, or success is increasingly irrelevant because the power law dictates that a small number of companies control the vast majority of wealth, influence, and attention.
Understanding this shift is key to navigating today’s world. The future is less about averages and more about extremes. A small number of people, companies, and cities are gaining more and more, while the rest are left with a diminishing share. In this context, averages don’t tell us anything meaningful. Instead, we need to focus on the distribution and understand how a few outliers have come to dominate.
The Myth of the Average in Other Domains
As we have seen, averages are fundamentally flawed when a few extreme values drive the distribution. But this problem extends to many other domains, from economics to entertainment, health to the environment. Take the entertainment industry, for example. The average salary for an actor might seem decent, but this figure is profoundly distorted by a few superstars earning millions of dollars per year. In reality, the vast majority of actors live much more modest lives, with many barely scraping by in between gigs. The “average” salary tells us nothing about the industry’s inequality and wealth distribution.
Similarly, a few bestsellers account for most book sales in the book publishing world. These blockbuster titles highly skew the “average” number of copies sold. Most books, however, sell a fraction of what the top sellers do. The same applies to the music industry, where a few chart-topping artists dominate while thousands of others make little to no money.
In construction, project cost overruns are often driven by a few large, complex projects that encounter significant challenges, while most projects stay on budget. These outliers dominate The average cost overrun, making it a poor reflection of the industry. The same pattern emerges in other fields, like banking, where the bonuses of a few top executives inflate the “average” figure, rendering it irrelevant to the typical employee.
Relying on averages in these contexts is not only misleading—it’s dangerous. Averages obscure the realities of how systems work. The extremes are the key players in many industries, and focusing on averages does not give us a realistic picture of success or failure. It’s important to understand that in these fields, as in others, the distribution—not the average—matters most.
Conclusion: Rethinking the Average
When someone mentions the word “average,” take a moment to pause and think critically. Averages can be useful in certain contexts but fail when extreme cases dominate the landscape. Understanding the underlying distribution is far more important. The average may still have value if a single anomaly has little effect on the set. However, when outliers like Bill Gates skew the numbers, the average loses its relevance.
As the novelist William Gibson wisely said, “The future is already here – it’s just not very evenly distributed.” In our complex world, extremes and outliers are becoming more common, and we would do well to focus less on the average and more on the distribution that shapes our world.
This article is part of The Art of Thinking Clearly Series based on Rolf Dobelli’s book.