“An imbalance between rich and poor is the oldest and most fatal ailment of all republics.”

— Plutarch

We are used to inequality. There is inequality of height, weight, shoe size, intelligence – in fact every human characteristic you can think of. But most of these characteristics follow what is called a normal distribution, which looks (at least roughly) like a bell-shaped curve. Here, for example, is the way that height is distributed.

Only about 4% of people are less than 163 cm tall, and only about 2% are more than 193 cm tall. The tallest man in the world was Robert Wadlow whose height was verified at 272 cm. Literally nobody is taller than that, and his height is far less than double the most frequent height of 178 cm. That is the kind of inequality we can get our minds around.

Statisticians also are used to this kind of distribution, in which the three principal kinds of average are all very close. In the case of height, these are:

• the mode – the most frequent value – which as you can see from the graph is 178 cm;
• the median – the value of the person in the middle of the distribution – which is 176.5cm; and
• the mean – the value you get if you add everybody’s height by the number of people – which is again 178cm.

If you could repeat this analysis with shoe size, you would almost certainly get the same kind of result. Nobody has feet which are 4 foot long.

But wealth is different. The distribution is so strange that it is hard for us to get our minds round it. Here are (excerpts from) the same data we presented last week on wealth inequality in the UK, but this time presented as a frequency distribution.

In this distribution, the three kinds of average are dramatically different:

• the mode is between zero and £50,000;
• the median is around £280,000;
• the mean is around £560,000.

The three kinds of average tell completely different stories. The mode tells us that it is far more common to have household wealth of £0-£50,000 than any other equivalent band. The median tells us that a household in the middle of the distribution has total wealth of a about £280,000 – six times more. And the mean tells us that there is so much wealth in the upper part of the distribution that if it were equally divided, everyone would have double what the median household has today.

To help us get our minds around this kind of inequality, two metaphors relating to height are very helpful. The first one is due to the Dutch economist Jan Pen and I think the second one is due to Nassim Nicholas Taleb. I have adapted them both to relate to the latest UK data.

Pen’s Parade

Let us imagine a world in which everyone’s height is proportional to their wealth. As in our world, the median height in this world is 178 cm. Next imagine lining up the population of the other world’s equivalent of the UK in order of wealth: poorest first, richest last. Now imagine this line of people passing your window at a rate of about 200,000 people per minute. The entire population of the other world’s UK would parade past your window in approximately five hours.

And this is what you would see. For the first three minutes, you would see some extraordinary creatures which actually had a negative height. They would be followed by tiny humans, less than 30 cm high who would take up the rest of the first quarter of an hour. Gradually the height would rise until, after a little over 2 ½ hours, there would come what we think of as the normal human being – 178 cm tall.

And the height would continue to increase: after three hours, we would be seeing people 230 cm tall; after four hours, they would be 456 cm tall; and after five hours, the people would be around 12m tall! Even if you were in an upstairs window, you would have to crane your neck to look at their faces.

But we still have not got to the exciting part of the parade. In the last three minutes, the people would average over 50 m in height. And the last 150 people – the UK’s billionaires – would all be over 6 km high. Finally, bringing up the rear of these gigantic creatures, would come Jim Ratcliffe, the UK’s richest man, who would be over 200 km tall. This makes him 22 times taller than Mount Everest.

Ratcliffe has been reported as moving to Monaco in order to avoid UK taxes. In our hypothetical world, if he stood up straight, he might still be visible from London.

Taleb’s Football Stadium

Wembley Stadium has a capacity of 90,000. If it were filled with a random selection of the UK’s population, their average height would be 178 cm and their average (mean) household wealth would be around £560,000.

If Robert Wadlow walked into the stadium, the average height would rise by much less than a millimetre. The change would be undetectable.

if Jim Ratcliffe walked into the stadium, the average wealth would rise by over £350,000 – an increase of 63%.

We are used to dealing with distributions in which it makes sense to ignore the outliers because, as with Robert Wadlow walking into the stadium, the impact is so small that we can safely ignore them. When it comes to wealth inequality, the disparities are so great that we cannot ignore them – not even singly. Both normal people and even professional policy-makers find it hard to get their minds around how extreme wealth inequality is, and ignore the top of the distribution as being outliers. As Taleb’s stadium shows, this is an error.

In the UK, the top 1% own roughly as much at the bottom 60%. A fairer distribution would improve tens of millions of lives.

If this matters to you, please do sign up and join the 99% Organisation.