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Of all the mathematical concepts humanity has invented to help deal with reality — such as zero, infinity, numbers, etc. — surely the least useful and most toxic is the notion of “average.” Like empty calories — food that has no nutrition — the idea of an average something is without any real utility. In a heartbeat I can look up the average high temperature for today and it will not tell me what the actual high temperature will be, five or ten degrees above or below the average. So what use is it to know the average?
Meteorology uses a lot of averages. They rate the likelihood of storms of a certain size and destructiveness by labeling them, for example, storms that on average will occur once in 100 years, or once in 1,000 years. So far this year, the American Midwest has experienced four “once in 1,000 year” storms. In 2018, a single location, Ellicott City, Maryland, experienced two thousand-year storms in two years. Knowing the average chance of a serious storm where you live is content-free information.
I had a friend once who was an economist. He used to introduce himself by saying, “I’m an economist. Which means that if you forget your telephone number, I will estimate it for you.” Averages are precisely that useful.
Averages mislead in more dangerous ways. Right now, they are contributing to a dangerous misapprehension about this year’s “off-year” (meaning not a presidential election year) Congressional elections. Someone took an average of the results of decades of off-year elections, that is, the number of seats won and lost by the two parties, and concluded that, on average, the party that holds the White House will lose a substantial number of seats in any off-year election.
Look more closely at history and you will find that only a few recent midterm elections resulted in setbacks for the party holding the White House, but they were large setbacks. Many midterm elections see little or no change. But when you roll all the numbers together and average them, it looks like doomsday for the party in power. One statistician said this is as meaningful as putting Bill Gates in a room with four homeless personas and declaring that the average net worth of the people in that room is $20 billion.
An even more toxic use of averages is made by politicians who stand up in front of audiences and assure them that the economy is in wonderful shape; jobs are being “created” at a furious pace, unemployment is at historic lows, corporate profits are higher than ever.
The problem is that almost every individual I know has had one lousy job since Methusaleh was in diapers, has not had a raise in a coon’s age, could not begin to afford investing in the stock market, and is watching fearfully as the price of basic necessities skyrockets. When someone like that hears a politician or an economist insist that everything is fine, they doubt that speaker’s sanity and honesty. And they go looking for a political leader as angry and as pessimistic as they are. That never turns out well.
It’s the equivalent of being told that if you are standing with one foot immersed in ice water and the other in boiling water, on average you are perfectly comfortable. Mathematically defensible, perhaps, but those calories are completely empty.
“Numbers never lie” is perhaps the grandest lie of all. Just look at Trump’s reporting of assets, liabilities and income: one set of numbers is submitted to the IRS, a completely different accounting to the banks. Both sets can, I’m sure, be rationalized on one level or another…I guess, on average, Donald Trump is quite the regular fellow.
There are three measures of central tendency: mean (arithmetical average), median (the observation with half the remainder above, half the remainder below), and mode (most common observation).
The mean has good mathematical properties (i.e. easy to estimate, predict, and compare), under the assumption of a normally distributed population (i.e. follows the bell curve). It’s the source’s (the one asserting the statistic) responsibility to confirm that the data is normally distributed, because otherwise the results are misleading.
N-year events are a little different. They are based on another poor assumption, that the future will be like the past. But doing it right would require mathematical models and computer simulations, and who can bother with that?
Of course, relatively few producers of statistics ever bother with any of this, or even know to do it. Even worse than ‘average’ is the rating scale, in which ranks along many dimensions are added up to provide a ‘scientific’ or ‘mathematical’ result which is as bogus as a $11111 bill. IMO.
Attaching numbers to phenomena is perhaps the most difficult thing a human tries to do. Doing something with those numbers is almost as hard. Yet everyone from illiterate to Ph.D. thinks it is a trivial matter that he can do by virtue of some innate gift. The mathematician Holder proved otherwise, but who’s ever heard of him?
It’s even worse than logical inference, where everyone who has never heard of a fallacy believes in his soul that he can think like Einstein..
IMO. Obviously a hobby horse topic.
It was those statistical averages, or N-year events that convinced me not to invest in SW Ontario for long term residency. The Canada Climate Atlas is a great source of climate prediction if one knows how to interpret the information:
https://climateatlas.ca/map/canada/plus30_2030_85#
SW Ontario is the region from Detroit/Windsor up to the Toronto metropolitan area.
Fortunately, I had lived in the region in the late 80’s and got to experience what a prolonged heat wave looks like. The forecasts for the same region increased the likelihood and magnitude by multiples. It only takes one really bad one. Forget the averages over 5, 10, 50, or 100 years. One year is enough.
The outgassing of Arctic methane renders all previous calculations of warming ratios misleading. The End will be swift and uncomprehending.