|Persons Below poverty level (2008-2012):||
|Persons per household (2008-2012):||
|Median Household Income (2008-2012):||
Ignoring savings, lifestyle differences, and region of the country. Purely based on income, what does a family have to make to be considered "Middle Class"? Go ahead, think of your answer, I'll wait...
Ok, got it? Let's try to figure this one out.
If you ask a handful of people what the income level of the middle class is you will probably get wildly varying answers. Surprisingly enough, almost everyone you ask will also tell you that they are in the middle class too. During the last election cycle both Romney and Obama said that the cutoff for the middle class was an income above $250,000. I don't know about you but I think that the majority of Americans will probably disagree and say that if you have an income of over $200,000 you are part of the upper class, not the middle. What's funny is that US Senators make $174,000 per year so I guess that means that they think that they're middle class. If their spouse works or they have investment income, they probably get pushed over the $250,000 limit anyways.
Common Middle Class Definitions
After my own research I found wildly varying definitions of what the middle class might be, some people say that "the middle class is a state of mind." I think that's a total cop out answer because everyone can't be in the middle class. We aren't passing out Ms. America prizes here, so trying to appease everyone is not an option.
Some other definitions are based off of your net worth, or if you can save X% of your income or that X% of your income was discretionary income.
Crap, crap, and more crap. Doctors and Lawyers can be making over $200,000 per year but start out with a negative net worth because of student loans. They also might not be able to save because they are paying down debt. Then there's millions of people that are bad at budgeting or just don't know how to control their spending. Peoples spending/saving habits shouldn't dictate if you are a middle class earner or not. All that tells you is how good of a saver or spender they are.
Side Note: The census says they have no official definition of the "middle class" 
Because of these reasons I want to focus on what a middle class income is. Without savings, lifestyle differences, and region, I want to just look at income levels and try to find an answer that makes sense.
My first step was to look at income data, so I turned to the census data for 2012. This seemed like the most unbiased data that I could readily get a hold of. Using the 2012 household income distribution data  I was able to graph out what the distribution of household incomes were. Please keep in mind that this data is per household, not per individual. I also added other pieces of data which I think will help us visualize the data better.
|(click to view larger version)|
You can see that I added the red line on the left to show the poverty threshold for an average household. I think that we can all agree that anything below this line is not middle class because even the government has decided that they do not make enough money to get by on.
I have also added a green line to show where two workers making the federal minimum wage ($7.25/hr) would fall within the data. Also, I believe that it's called a minimum wage for a reason, I don't think that minimum really qualifies as "average", and the middle class should encompass the "average person" not the minimum.
But why is the green line beyond the peak of the graph? Shouldn't two people earning minimum wage be where the majority of people fall under?
Well, to answer that we need to define the number of workers in the average household. I know that there are a lot of households that are a single worker with no children. A good portion of my friends actually fall under this category. Then there are households with children that do not work, I seem to have a lot of friends that fall under this too.
Since the peak of the graph is to the left of the green line, I would guess that this is due to the large number of single person households. In fact, the poverty line is almost exactly where a single person making minimum wage would be. Coincidence? Probably not.
Now this is where we have to start taking some educated guesses. I'm going to use the spherical cow method  to estimate this.
What?! Spherical cow? Now you're just making things up.
No. I'm not actually, the spherical cow is a real thing. (But I may have chosen to use it because of the name.) It's basically a way of simplifying the data to a point where we can make some easier calculations and our guess should get us into the relative ballpark for the answer that we are looking for.
For example, what if we shoot a cow from a cannon into the grand canyon, how far would it go before it hit the bottom? Some things to consider might be:
How does the cow rotate in the air?
Is there any wind to consider?
Is there any wind to consider?
Is the cow going to flail in the air or do we have a frozen cow that was donated to science?
As you can see, the problem gets complicated very quickly so we can simplify the model we are using to get us a close answer that will satisfy our needs. So, we assume the cow is a sphere since the shape of the cow probably won't matter that much. Then if we know the initial trajectory and force the problem gets simpler to a point where we can solve it.
But back to our problem, after some digging I found that from between 1960 to 2000 the number of workers per household has wavered between 1.2 and 1.25 workers per household.  Since we know that the average number of workers in a household is about 1.2, and the middle class should be making more than minimum wage let's just round the number of workers in a household up to two and keep the wage at the minimum wage where it is since we are adding slightly more workers. Now we can use the green line as our minimum threshold for a household in the middle class.
Now the upper bound for the middle class might be harder to guess. Normally I would think to try to mirror the lower bound onto the upper end and call it a day. But it's obvious that the data in this graph is skewed to the left, showing us that more people earn lower incomes than higher incomes. So an equal distribution on the bounds won't really work either.
So lets go back to the spherical cow method again, I can guess and say that if you make more money then 9 out of every 10 people you meet, you probably make an above average income. To me this sounds like a reasonable assumption so I have displayed the top 10% of income earners in purple. Let's use this for our upper bound for middle class income.
So for the average household we know the middle class income! (Approx. $30,160 to $147,500) How close were you? I personally thought it might be a little more narrow, especially on the upper end of the spectrum, but I stand by my conclusion unless someone can convince me otherwise.
Interesting note: Romney and Obama didn't even come close to this answer, according to them if the cutoff is $250,000 then they chose the top 2.37% of the population to be in the "upper class". Do you think they were right?
I could not find the same detailed data for California, so that we could get more of a regional comparison. But I did find some data on California that you can use to try to come to your own regional conclusion:
California persons per household: 2.93 
California median household income: $61,400 
California persons below poverty level: 15.3% 
California minimum wage 2012: $8.00
If you want to look up some of these details on your individual state you can go here.
The Origin of the Spherical Cow
The spherical cow is a theoretical physics joke about modeling a complicated problem into a simple format to get an answer that is close enough to what you need. Here is the joke (so laugh)
That's a joke.... You're supposed to laugh now.There is a dairy farm with cows, and the farmer wants to increase his production of milk. So the farmer hires three consultants – an engineer, a psychologist, and a physicist.
After a week, the engineer comes back and says: “If you want to increase production, get bigger milk pumps and bigger tubes to suck the milk through. This should improve production by 5%”
Next came the psychologist. He said: “You need to make the cows happy to produce more milk. You should paint the milking stalls green. This will make the cows think of grass fields. They will be happier and produce more milk.”
Finally, the physicist came to present his idea. He said: “First, assume the cow is a sphere….”
 - http://quickfacts.census.gov/qfd/states/00000.html
 - https://www.census.gov/hhes/www/income/data/inequality/middleclass.html
 - http://www.census.gov/hhes/www/cpstables/032013/hhinc/toc.htm
 - http://www.fhwa.dot.gov/planning/census_issues/ctpp/data_products/journey_to_work/jtw1.cfm
 - http://en.wikipedia.org/wiki/Spherical_cow
 - http://quickfacts.census.gov/qfd/states/06000.html
Spherical Cow image created by the author Zee