Liberal Arts Blog — The Pareto Distribution and the Pareto Chart — Life is Not Fair

Liberal Arts Blog — Monday is the Joy of Math, Statistics, and Numbers Day

Today’s topic — The Pareto Distribution and the Pareto Chart — Life is Not Fair

Today, in the capitalist world, wealth is unevenly distributed primarily because talent is unevenly distributed. Think musicians. Think the share of earnings garnered by the likes of the Beatles and Beyonce relative to the average musician. Or think athletes. Think the share of Grand Slam titles hogged by Nadal, Federer, Djokovic, Venus and Serena Williams. The technology and finance worlds are no different — think Warren Buffett, Bill Gates, or Elon Musk. In mathematics, this type of distribution is described as a Pareto distribution. A Pareto Chart graphically represents the primary causes of a phenomenon from the most important to the least in a combination of a bar chart depicting each separately from left to right and a curve marking the cumulative effect of the bars. In this case the first bar on the Pareto chart of causes of wealth inequality would be differences in talent. That is for modern capitalist America. At other places and times that first cause might be different, for example, differences in physical force, political, or religious power. Think the Soviet Union, Maoist China, Venezuela. The assault on meritocracy today gives very little thought to the lessons of history with respect to the alternatives. But enough on politics.The principle use of the Pareto chart has been in engineering quality control. Perhaps not surprisingly Pareto was himself an engineer by training. Experts — please chime in. Correct, elaborate, elucidate.

THE PARETO DISTRIBUTION — all things are not distributed “normally”

1. Popularized as “the 80/20” rule — namely that 80% of outcomes are determined by 20% of causes.

2. Applied to software: “a small number of bugs account for most crashes” or business “the top few customers account for the bulk of profits’ or insurance: “a small number of claims account for the bulk of payments.”

3. Or languages: “the most frequent words account for the most words in books. Or human settlement: a small number of cities include the bulk of the population.”


1. “The purpose of the Pareto chart is to highlight the most important among a (typically large) set of factors. In quality control, it often represents the most common sources of defects, the highest occurring type of defect, or the most frequent reasons for customer complaints.”

2. The chart above depicts, for example, the causes of late arrival at work. The top five are traffic, child care, public transportation, weather, and oversight.

3. The seven tools of quality control also include the flow chart, the histogram, the scatter plot, and the fishbone diagram of cause and effect (aka the Ishikawa chart).

VILFREDO PARETO (1848–1923) — did he turn economics into a mathematical science? was he a “theoretician of totalitarianism”?

1. “His legacy as an economist was profound. Partly because of him, the field evolved from a branch of moral philosophy as practiced by Adam Smith into a data intensive field of scientific research and mathematical equations. His books look more like modern economics than most other texts of that day: tables of statistics from across the world and ages, rows of integral signs and equations, intricate charts and graphs.” (Mathematician Bernard Mandelbrot and Richard Holdin).

2. Pareto was the son of an exiled Italian engineer (and marquis) living in Paris and a French mother. He became a civil engineer himself — earning a doctorate from the Polytechnic University of Turin in 1869 at the age of 21and working in the field for twenty years before switching to economics at age 45 when he joined the faculty of the University of Lausanne in Switzerland, where he remained until his death in 1923.

3. Quote: “The assertion that men are objectively equal is so absurd that it does not even merit being refuted.”

NB: Karl Popper called Pareto “the theoretician of totalitarianism.” Some scholars have claimed that he was inspiration for Mussolini. Others have denied it. His greatest works include: “Manual of Political Economy” (1906), “Trattato di Sociologia Generate” (1916).

Pareto distribution

Pareto chart

Pareto principle

Vilfredo Pareto

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So what are your personal favorite magic numbers? What do they stand for? Please share the coolest thing you learned this week related to math, statistics, or numbers in general. Or, even better, the coolest or most important thing you learned in your life related to math.

This is your chance to make someone else’s day. And to consolidate in your memory something you might otherwise forget. Or to think more deeply than otherwise about something dear to your heart. Continuity is key to depth of thought.