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 familyMedian net worthAverage net worthLess than 35$13,900$76,30035-44$91,300$436,20045-54$168,600$833,20055-64$212,500$1,175,90065-74$266,400$1,217,70075+$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.
[This entry was cross-posted from https://canyonwalker.dreamwidth.org/36854.html. Please comment there using OpenID. That's where most of the action is!]
Household net worth by age
Age of head of familyMedian net worthAverage net worthLess than 35$13,900$76,30035-44$91,300$436,20045-54$168,600$833,20055-64$212,500$1,175,90065-74$266,400$1,217,70075+$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.
[This entry was cross-posted from https://canyonwalker.dreamwidth.org/36854.html. Please comment there using OpenID. That's where most of the action is!]