Transcription
The math of this meme is wrong. And not just by a little bit. The numbers are not even close, and it isn't just this meme. A lot of posts on social media mess up the math, either on accident because they don't know any better, or on purpose to make a point. Either way, consumers of media should be prepared to engage such posts as skeptics and practice good quantitative literacy.
QL, or sometimes called Numeracy, is the math and statistics skills needed to successfully navigate everyday life. Reposting a problematic meme like this, even if you agree with the sentiment, is just bad and contributes to the social media misinformation epidemic. So let's go through and find out all of the ways this meme is wrong.
A foundational skill in QL is to release your inner skeptic. So many individuals, groups, institutions, governments, and businesses, are trying to pull the wool over your eyes to make you believe something that isn't true, or only partially true. So let's release our inner skeptic on this post.
The first red flag is that there is no citation given to know what data they used or even what year the data refers to. That should raise your suspicions right away since readers can't check up on the values or the process used to get the numbers.
The second red flag is that they don't clarify which average they are using. Is this the mean or the median? Or something else? An average can refer to various measures of central tendency.
The third red flag was that it doesn't pass the sniff test. According to the meme, the top 10 highest income individuals earn 12.67 percent of all US income. That is a crazy amount of money. I looked up the total US income in 2022 and calculated 12.67 percent of that amount. It was over 1.7 trillion dollars. That is an average of 170 billion dollars for each of the top 10 earners in one year. A quick internet search showed that no one in the US has ever got close to that with their increase in wealth, let alone in yearly income. (More on the difference between those two later). So there is no way that 10 people have averaged that in income.
The fourth red flag is that there are no specifications as to the unit of analysis. Are these values averages across all US individuals? Or across US households? There is a big difference between the two. For example, if we are averaging over all individuals in the US that includes about 40% of the population 16 and older that are not employed and will significantly lower the average income value. It would lower the average income even more if it was distributed across all individuals including those younger than 16.
I did some research and found that the Census did estimate the 2022 median household income to be $74,580. The years around that were not as close to the value on the meme of $74,500. So it looks like that has answered some of our questions: median not mean; and household not individual.
Well, this leads to the first egregious error of the meme. If they are using household median income as the measure, then there is no way they used the median for these other values below. Because medians are robust against outliers and that is what the top earning households are. Dropping 10 individuals at the top would hardly change the median income at all, maybe a penny but I doubt even that much. Dropping the top 50, maybe a few cents. The top 1000, probably not even a dollar. I don't have access to the Census data so I can't find the exact median value, but we could estimate it.
I found the distribution of US household income for 2023, one year later, and it shows that it takes about 3.5 percent of the households around the median to change a value of $5,000 dollars. There were about 131.4 million households in the 2022 US Census. 3.5 percent of 131.4 million is 0.4599, or 0.46 million, or 460,000 households. That means there is an approximate mean change in household income around the median of $5000/460,000, or 0.01086956522, or barely more than a penny. Dropping the top 10 individuals would lower the median income by about a dime (more than my guess of a penny), 50 about cents 55, and 1000 about 11 dollars. "So we could update the numbers to be the following: $74,500, $74,500, $74,499, $74,489. Not much change."
Those numbers are so far off of the values in the meme I am thinking the meme had to be a joke. "Seriously! How do they go from dropping the income by a dime to almost 10 grand! This is egregious!"
So now I was on a new quest. I had to try to find out how the creators of the meme actually got their numbers. My first thought was that they had to be doing calculations assuming the average was a mean rather than the median. That is the only way I could see them getting large drops in the median. Somehow they must have estimated the total income of the US, subtracted the income of the top 10 (or 50 or 1000) then redistributed the rest across the rest of the US population. It took a lot of experimentation, but I finally found out how they got their numbers with two more blatantly egregious errors.
What did they do? First, they estimated the total US income by multiplying the median US income by the number of US households. This is a huge error. Medians are not connected to the total amount like means are. If we had the mean US household income then we could find the total US income. The mean income value is the value each would get if we evenly distributed the total across all households. So we can recover the total by multiplying the mean by the number of households. But you can't do the same with the median unless the distribution is symmetric, and income is largely skewed. Their calculation, median times households, gets a total US income of $9,789,300,000,000.00, or under 10 trillion dollars. But the actual total income for 2022 was $13,980,960,000,000.00 (that is with the 2022 mean income of $106,400 and 131.4 million households), or just under $14 trillion dollars, which I estimated by multiplying the mean 2022 US income of $106,400 times the 131.4 million households. So right away the meme creators lost more than 4 trillion dollars of income in their calculations, almost 30% of the total US income. That is going to make things look much worse than they actually are.
The second egregious error I found is the value the creators used for the income of the top individuals. I spent a lot of time trying to track down the income of the richest Americans in 2022. I eventually was able to find published estimates of the income of the top 5 richest people. This process alone raised a red flag. Where did the meme creators get their values for the income of the top 1000, and 50, and 10 Americans? Reported income to the US government is not publicly available, and it took some research by journalists to find values to report for the income of the richest 5 individuals. So my guess is that the meme creators are not actually using income.
It turns out the income of the top 5 richest Americans, about $32.4 billion, was driven by Elon Musk. His income was reported by CNN to be about $29.3 billion, 11 billion of which went to taxes. Most of this was generated through exercising stock options that were worth $23.6 billion dollars. The income of the other 4 were quite modest, especially Warren Buffet ($401,589), and Jeff Bezos ($1,681,840). So there are certainly people that had higher incomes that year than Warren Buffet and Jeff Bezos, so maybe I shouldn't include them in the top 10, but by the life of me, I don't know how to find the 10 Americans with the highest income that year. But stay with me, because we will find that the meme creators did actually use values from all five of these richest men in their calculations.
So let's try out their math. We incorrectly multiply the median income by the number of households to get a total, then subtract out the total income of the top 10. Since I could only find the income of the top 5 richest Americans ($32,440,783,429), I will double that value as an estimate of the income of the top 10. After the subtraction, we divide the total by the number of households minus 10, and we get a meaningless average of $74,006.23. $32,440,783,429.00. Well, that did drop the average by about 500 dollars, so how in the world did they get a drop of almost 20 times that!?!? I am not even close to getting the value they did. So the creators must have subtracted a value off that was much larger than the estimate of my top 10 income.
I had a breakthrough when I thought that the creators must not have subtracted off income, but wealth. There is a big difference between income and wealth. Income is the amount of salary or pay realized in a year, which is the amount you put down on a tax form. vs wealth is the total value of all the assets you own minus debt. If your stock portfolio increases in value, or real estate, or other assets, that increase is not considered income. For a large percentage of US households, their wealth increases each year more than their income. This is certainly true of the top 10 richest Americans.
I found estimates of the wealth of the top 10 in 2021 and in 2022 from data sets on kaggle.com and calculated how much their wealth increased. As a group, their total wealth increased an estimated $194.2 billion dollars (see calculations on the bottom of sheet 2). Replacing income of the top 10 with the increase in wealth of the top 10 in the previous calculation gets us a value of: $73,022.08. Well, that is a little lower, but still not even close to the reported $65,000. We have to subtract a much larger amount.
The largest amount I could conceive of is the total lifetime accumulated wealth of the top 10 instead of change of wealth. Let me emphasize that this is a totally different value than one year's worth of income, or even one year's growth in wealth. This is really subtracting apples from oranges. Well, it isn't even that close. The total lifetime accumulated wealth of the top 10 in 2022 was $1264.7 billion dollars. That is about 20 times the estimate of income of the top 10. If we throw that value into the calculation as the quote-unquote income of the top 10, then we start to see the light. We get darn close to the $65,000 on the meme. $64,875.20.
So to get it to look as bad as possible, the creators of the meme reduced the total income of the US by 4 trillion dollars, and subtracted off a value about 20 times the income of the top 10. No wonder it looks so bad. So many bad things happening here.
What should the values be? Well, we already saw what the values should have been looking at the median values each time. But if we want to use the mean instead of the median so subtracting off the high incomes make a bigger effect, then the top 2 values would be these: $106,400, and $105,906.24. A drop of about 5 hundred dollars. Still a big drop, but a far cry from 10 grand. I didn't take time to try to estimate income of the top 50 or 1000.
But what if the creators really wanted to subtract off the total accumulated wealth of the richest Americans? Then we should compare that to the total accumulated wealth of all Americans so we are comparing apples to apples. The total US wealth in 2022 was estimated to be just under 200 trillion dollars. That is all real estate, vehicles, stocks, pensions, business equity etc. minus debt. Evenly distributed across all households, that is an average accumulated wealth of $1,522,070.02. That is quite a lot. Subtracting off the wealth of the top 10 and evenly distributing again drops the mean US wealth by the same value as the original meme about 9.5 grand, but now it is only a drop of $1,512,445.32. 0.006323424378, about two thirds of one percent (0.63%), not 12.75%. 0.1275167785.
Don't get me wrong. The top 10 richest people in the US do make a lot of money and have a crazy amount of wealth, but it isn't nearly as bad this meme (and many others) make it out to be.
Ok, so what is the point. You need to be very cautious about believing what you come across online. There is so much misinformation out there that it can lead you to believe things that simply aren't true, and aren't even close to true. If something looks suspect, do some research. I heard from different sources that billionaires in the US have a small effective tax rate. That didn't match up to the values reported by CNN about how much Elon Musk paid in taxes on his 2022 taxes, which was a rate of 37.5%. Well, after doing research, I found that those doing the calculation to estimate the billionaire tax rate did a similar mistake that our meme creators made. They didn't use realized income, they used an estimate of their wealth increase as their income to make it look like they did not pay much. It doesn't seem comparable to consider the change in wealth as income for some when calculating the tax rate and not in others. Tens of millions of households' wealth increases through real estate appreciation or stock market investments or business growth, but it isn't counted in their tax rate calculation. Again, I am not doing this to argue that there is not a dramatic inequity in our country, just that there is massive misinformation out there about so many aspects of our society that we must be careful in how we digest what we are exposed to.