Mean vs median in income and age

It's a pretty open-ended question, and there are whole classes on the subject, but in short, there are two answers. "Average" is usually synonymous with mean. However, particularly with income, median tends to be used more often, as the mean is affected by outliers. The median income-earner, who's earning more than half the population and less than the other half, is earning much less than what is "average", as income is concentrated among the highest earners (I'm starting to sound like a different Bernie here, but this is just math). If you have a population of 100 and the 3 highest income earners quadruple their income over a decade, but the 97 lowest income earners don't increase their income at all, the average will go up, but the median will be unchanged, closer reflecting reality for most people.

This blog post might do a better job explaining (I just found it by googling mean vs median): fredblog.stlouisfed.org/.../

It's a pretty open-ended question, and there are whole classes on the subject, but in short, there are two answers. "Average" is usually synonymous with mean. However, particularly with income, median tends to be used more often, as the mean is affected by outliers. The median income-earner, who's earning more than half the population and less than the other half, is earning much less than what is "average", as income is concentrated among the highest earners (I'm starting to sound like a different Bernie here, but this is just math). If you have a population of 100 and the 3 highest income earners quadruple their income over a decade, but the 97 lowest income earners don't increase their income at all, the average will go up, but the median will be unchanged, closer reflecting reality for most people.

This blog post might do a better job explaining (I just found it by googling mean vs median): fredblog.stlouisfed.org/.../

Well said Bernie. All I would add is that sometimes it makes sense to use income per capita, a sort of average, if you want to know how much money is floating around compared to population. it an be a shorthand for how much financial support a government can expect compared to people who could need services. Very high in municipalities of empty-nest celebrity mansions -- one year Fisher Island FL off Miami was the highest in the nation, very low in modest neighborhoods with lots of children. .  

Thanks I see a lot of median for income, but little mean. But I think I'm going with mean. Or maybe both. Also Family gets complex (in general and in flavors in ACS) Household does not, so another variance from the standard for me.  I do remember Statistics, although it was 40 years ago.  As for income for capita a valid and interesting measure, but I was trying to keep my list to 20 measures and I'm already passed that, not sure its in ACS or easily calculated, so maybe next year.  S1901 has median, mean and % over 200,000 for income by county.

Dear Tom,

Tim is correct if you want to know "how much money is floating around in a community" use average (mean) and multiply by head count.  If you want to know what the  amount of money that a "typical" household or person has use median.  The income distribution is highly skewed to the high side so if there are a few "high" earners the arithmetic average  (mean) doesn't give a clear picture of the typical individual/household  Also note income is "top coded" , i.e. has a cut off value.  Values above the top value are set to a fixed value: (From PUMS handbook 2021 pdf page 22 of 26) https://www.census.gov/content/dam/Census/library/publications/2021/acs/acs_pums_handbook_2021.pdf)  If you use an ACS table like B19001 there is a cut off at $200,000.  You can use this table to get a median(or other percentile)  but you can't use it to get an arithmetic average (mean).

"Top-coding is the process of taking any response exceeding a particular value and replacing it with a
predetermined value. These predetermined values differ by state."  Typical top coded variables are  income and age

www2.census.gov/.../2020_pums_top_and_bottom_coded_values.csv

PS don't use the word average -- use mean or median there will be no confusion.

Good point on top coding