Wealthy Americans? A Lesson on Median vs. Mean

A few days ago in a forum I follow an overseas member posted, "OMG, Americans are so wealthy!" with a link to this CNBC article (8 Mar 2021) about the average net worth in the US. In particular she focused on the figures in the far right column of this table:

Household net worth by age

Age of head of family	Median net worth	Average net worth
Less than 35	$13,900	$76,300
35-44	$91,300	$436,200
45-54	$168,600	$833,200
55-64	$212,500	$1,175,900
65-74	$266,400	$1,217,700
75+	$254,800	$977,600

This prompted a discussion by pretty much everyone else in the forum about the difference between median and mean.

What's the Average? Mean vs. Median

In mathematics there are several different ways to define "average". The one most people are familiar with from grade school math is the arithmetic mean. Add up all the numbers, then divide by the number of numbers in the set. For example, the arithmetic mean of 1, 1, 2, 6, 20 is 6. That's because 1+1+2+6+20 = 30; and 30÷5 = 6.

The mean is not the only definition of "average", though. In high school math you probably learned about two other terms, median and mode. The median is essentially the middle value in a set; the point at which half the numbers are above it and half are below it. In the set 1, 1, 2, 6, 20 I gave above the median is 2. Note that's a fairly different "average" value from the mean of 6. The mean is 3x higher than the median.

When it comes to talking about wealth, experts widely agree that median wealth is the figure that should be used. Even the article linked above acknowledges this, though begrudgingly and in passing in the middle of the story:

"Economists argue that it’s better to look at the median net worth to understand where most Americans fall on the spectrum, since it’s not skewed by mega-high-worth individuals or those deep in the red."

As it notes, the reason experts routinely use median instead of mean to talk about "average" wealth is that it's not skewed by the values at the extremes. In the US, the wealthiest people are extremely wealthy. A Forbes article from October reports data from the federal government that the top 1% of Americans hold more than 30% of the total wealth in the country. The bottom half of all Americans hold just 2%. Link: Federal Reserve report.

So, that example set of 5 numbers I suggest above? You might have thought that big 20 on the end was out of place, that it skewed the average. Indeed it did skew the average (mean), but it's less skewed than actual economics in the US.

Those figures in the table above showing that "average" households in their 50s, 60s, and 70s have over $1,000,000? That's not representative at all of reality in the middle class. Those mean figures are skewed way up by the tiny number of people who have billions, tens of billions, or even hundreds of billions, of dollars.

A Year of Pandemic. Light at the End of the Tunnel

Today is the one year anniversary of the Coronavirus pandemic. It was on March 11, 2020 that the World Health Organization (WHO) declared a global pandemic. I know that because— well, do you even read news? It's all over the media— and also because I wrote about it in my blog one year ago today.

Anniversaries are natural times for retrospective. There's so much I could write about how things are different now vs. then, even how what I think is different now vs. then. For example, on March 11, 2020 it wasn't clear that Coronavirus would become a pandemic in the U.S.

As I noted in a blog post six weeks earlier Covid-19 was following trajectories similar to SARS and MERS, two other Coronaviruses that reached pandemic stage earlier in the 21st century but never spread significantly into developed countries. But the spread had already begun; we just didn't know it. Through political leaders combining gross incompetence with flagrant dishonesty we didn't know how bad things were becoming until around mid-March. When their house of cards fell, it fell fast— at least for those of us open to science. Deniers kept on denying for months.

Now, at least, there's light at the end of the tunnel. Several vaccinations have been tested and approved. Millions have gotten shots. Although the rollout started three months ago the medicine is still in short supply. Locally I've seen a stop-start cycle with vaccination centers opening wide for appointments one day then having to close a few days later due to insufficient doses. A "vaccine tracker" at NPR (data as of 11 Mar 2021) shows that nationwide in the US just under 10% of the population are fully vaccinated and just under 20% have received one shot of the two-shot plan. I am among those who've not even been permitted to get a first dose yet. So, while the light is visible at the end of the tunnel, we're not out of the danger yet.