Saturday, November 22, 2014


I need someone a lot smarter than I am to help me with some simple research.

I have been thinking lately about how the "median income" - a dollar amount representing a point at which the number of people earning above that amount equals the number of people earning below it- may not really be as representative of levels of wealth and poverty as would be the "average" income- the amount that is reached by adding up all the incomes and dividing the result by the number of people "earning" that income.

So I started by Googleing "average income in Hawai`i" and the results, only showed "median income." At first I thought of Googleing "no you idiot, I said AVERAGE" until I came across an article that reminded me that the "average" anything is also called the "mean."

Fair enough- I'm the idiot. So I Googled "mean income in Hawai`i" and without exception, I got a page of listings for "median" income.

Now I did get an occasional reference to "per capita income." But that isn't the mean income. Per capita would denote the total of all income made divided by the total number of all residents, including people like children, the unemployed or others with zero income.

The problem with "median income," which, according to Wikipedia, was $68,020 in 2013 in Hawai`i, is that the dollar amounts above the median could conceivably, for argument sake, "average," $300,000 per year while the mean for those below it could average only $25,000 a year.

Meaning that the rich are a lot richer and the poor are a lot poorer than the $68,020 median- which seems pretty high to begin with- would seem to indicate to statistically-challenged idiots like me.

Based on nothing but noting the poverty of the regular working people I know who make $8-12 an hour and the relative apparent opulence of those who live in million dollar homes or half-million dollar Honolulu high rise condos I get the feeling that - surprise surprise- "median income" statistics are either lies or damnable lies.

Even at the $12 an hour rate, for a 40 hour work week that comes out to just a smidgeon under $25,000 a year. At $10/hr it's just under $21,000.

Is there a research/data/ statistical genius out there who can figure out the "mean" income for those above and below the median income. I have gone to the US Census and they don't even have "mean" just "per capita" and "median."

I started a math major in college but I never claimed to be any good at arithmetic. I remain your humble numerical idiot.


Andrew Cooper said...

The formulae for mean and median are in any statistics book, or on Wikipedia. They will come out fairly close to the same unless there is a really bad skew to the data. What you are looking for?

What you need is the raw data or something close. Then you can calculate mean, median, or better yet create some sort of distribution plot. Raw data from several decades would allow you to see how the distribution is changing, even more interesting. Finding the raw data is the job of a journalist;)

SMelman said...

Andy, I think median income is more revealing than mean income. Andrew Cooper, there IS a "really bad skew to the data," but most people assume the two averages would be close. I am in rush this morning, so cannot provide you folks with the numbers.

I think you know Bill Boyd, the economist, from FB? Despite his sometimes very wrongheaded ideas, like fanatical support for the Mufi Train and uncritical support for GMOs, he is actually very smart and well-informed, within certain narrow parameters.


He is very knowledgable with the Hawaii income data. Dept of Labor often relies upon his data, but you might be able to find the data on their website as well.

The US compares fairly well with other OECD countries when you look at mean income. But not when you look at median income. This is because mean income hides the growing inequality, wherein the rich are getting richer, the middle and working class are getting poorer. So overall income is climbing slightly on a per capita (or mean) basis. But because 90 of those increases have gone to the richest people at the top, it is perfectly possible for "per capita" income to rise while a majority of people have experienced a decline. Median income reveals that. Mean income conceals it.

Andy Parx said...

Thanks- I got a hold of the Hawaii info from DBEDT. Someone tagged Bill on FB discussion. I rather think it's the median that skews the gap- being lower the mean is closer to being realistic. Neither is good indicator but I have thee feeling that dividing the it into two groups of means, one below and one above the median it would show wheree the discrepancies are.

Loren said...

Hi Andy, I found this data broken down by state at Census web site; it does take configuring what you want to get the data.

For 2013 Household Income in Hawaii, there are 459K households: mean is $79,046 and median is $60,866.
The top bracket is most interesting - $100,000 and over - with 131K households: mean $165,051, median $144,055.

You can see a copy of the full dataset at or play with the link above.
Is this the data you wanted? (If not let me know what you want to see.)

A few comments … the US Census should not cut off brackets at $100, that's way too low as over one quarter of households get lumped up in it.
We know that "the top 1%" will always be way way above everyone else so they always pull up the mean much faster than they (counting as one data point) do the median.
For privacy reasons the government will not publish the raw individual income amounts, but that is what you need to accurately compute mean and median. From these brackets one can estimate and come close but not exactly deduce it.

I would say that a distribution chart of income brackets (with more brackets going higher) is really the best way to visualize the data.