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/.../

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 

OK, it looks like there are zero? tables that have mean age, only median age. Is this true? If not give me a table name. Or a link to a good conspiracy website about why this is the case. Is Julia Roberts safe? What should we do?

Dear Tom,

You can get the mean age using B01001  Sex x Age.  To get an approximation of the mean age (you should do males and females separately). Multiply the number of people by the middle of the B01001 age category  and add them up across age categories.  The only issue is the "85 and over" age category.  For that you need to know the life expectancy for an 85 year old male (in the case of males)  For Massachusetts that is 5.3. So for the 85+ category use 90.3 to multiply by the number of 85+ year old males and add that in. After you add everything up divide by the total number of males (for the male calculation)  For 85 year old females in Massachusetts the life expectancy is 6.3 years  So use 91.3 as the "midpoint" for the 85+ year old females.   As you can see you need a computer package to do the calculation.  The state life tables where you look up the life expectancy of 85 year olds (by state and sex) is located here: https://ftp.cdc.gov/pub/Health_Statistics/NCHS/Publications/NVSR/71-02/ If you want to skip doing everything by state, use  the overall US life table for males and females.  https://www.cdc.gov/nchs/data/nvsr/nvsr71/nvsr71-01.pdf page 2.  The mean age is relevant for insurance payout calculations, for example the expected total social security payments for the current population.

Thanks for the info.

So truthfully (practically) you can't get the mean age. I think the same can be said about Life Expectancy and mean age at death etc. There is absolutely no valid reason for the Census not to include it and for the various websites that have it listed and are sometimes different, and some of them use a package they don't fully understand and are "not sure it's 100% correct" (I've had some interesting phone calls). 

Long story short, just stick with the median age, lesson learned. Other windmills to fight.

The calculation that I gave you assumes "static" population dynamics for the tail of the age distribution and that the 85+ population for the local area "looks the same" i.e. has the same  distribution as  the country (or state) overall. The reason that the census  tables for smaller areas  "cut off" at 85 years is disclosure avoidance.