Renowned physicist Enrico Fermi’s name is synonymous with a type of estimation problem often illustrated by the classic question, “How many piano tuners are there in Chicago?” Finding a “Fermi estimate” of this number would typically involve multiplying a series of rough estimates, such as the population of Chicago, an approximate number of households owning pianos, the frequency with which a typical piano might be tuned, and so on. It’s unlikely that anyone would arrive at a precise, correct answer through this method, but a Fermi estimate should at least be able to generate an answer that is approximately the right order of magnitude.

A Fermi estimate usually seeks to measure a quantity that would be extremely difficult, if not impossible, to actually measure. “Piano tuners in Chicago” may have fallen into that category several decades ago, but as Wolfram|Alpha can now demonstrate, things have changed:

We recently overhauled our data on jobs and salaries in the United States, adding Bureau of Labor Statistics (BLS) data on more than 800 detailed occupations at the national, state, and metropolitan area levels. Which means Wolfram|Alpha can’t quite get you to an exact measurement of the number of piano tuners in Chicago (and presumably, many of them must at least dabble in other instruments), but it can come surprisingly close.

Wolfram|Alpha can also compute a number of interesting statistics that aren’t obvious from the source data, such as the fact that Chicago has quite a high density of musical instrument tuners and repairers—roughly 2.3 times the national average workforce fraction for this occupation—and that their median wage is roughly 1.3 times the national average. And it can also provide helpful context for any occupation, computing employment and wage information for related jobs and sub-specialties, according to BLS classifications.

You can also perform all kinds of interesting comparisons, of course: try asking Wolfram|Alpha to “compare producers and actors employment in California”, for example, or “garbage collectors vs waiters salaries in New York City”. Or if you’re contemplating a cross-country move, you might be interested to see a comparison between “computer programmers salaries in Seattle vs Philadelphia”.

And if you need to access salary and job-related data often, you can create your own Wolfram|Alpha Widgets tailored for specific jobs and regions. You can easily customize widgets, like the one below, and embed them in your website and share with your social networks.

Wolfram|Alpha couldn’t do your taxes for you this year, but we did just wrap up a quick project to add some interesting historical tax statistics. Now that all of our U.S. users have filed their taxes (we hope), they can explore IRS data about individual income taxes, broken down by adjusted gross income (AGI), from 1996 to 2007—the latest year for which the IRS has released statistics broken down by AGI. Users can also investigate less-detailed data about sources of individual taxable income from 1916 to 2007.

The basic input for this new dataset is simply an income, such as “AGI $35000”—type it in, and Wolfram|Alpha matches that input to a specific AGI bracket (in this case, $30,000–$40,000) and calculates a broad range of statistics.

First, the average effective federal tax rate, which is calculated by dividing total tax receipts in this bracket by total adjusted gross income:

Next, the average tax paid in the input’s bracket—which in this case dropped by nearly 50% over the decade covered by this dataset. You’ll also note that nearly a quarter of all tax returns in this AGI bracket had no tax due:

Third, average exemptions and deductions for all taxpayers in the input’s bracket. In this case, those increased by nearly $4,000 over this period, and in 2007 accounted for an average of 48% of AGI:

For some particularly interesting numbers, try asking about high income brackets (average tax on AGI $400k, average exemptions and deductions on $5 million) and very low brackets (average tax on AGI $500). More »

Since Wolfram|Alpha‘s launch in May 2009, one of its most talked-about features has been its ability to compute specific answers to questions about math, chemistry, economics, demographics, and much more. But as its knowledge base continues to grow, it’s also able to highlight interesting and useful connections between data sets, and to reveal information that you might not think to ask for on your own.

One of the coolest examples of this is our recently enhanced relocation calculator. For several months, we’ve been able to answer simple questions about the relative cost of living in various United States cities and metropolitan areas. If you told Wolfram|Alpha that you were relocating from Seattle to Miami with a salary of $35000, you’d get a comparison of the relative cost of groceries, housing, and other expenses in each city, plus an estimate of the salary required to maintain a comparable standard of living in your destination city. On its own, this is a useful little calculator—but it’s also something that dozens of other websites could do.

But because Wolfram|Alpha knows tons of other details about any given city, our relocation calculator can now do things that no other site can. In addition to salary and cost-of-living comparisons, you now get comparisons of each city’s population, median home sale prices, unemployment rates, crime rates, sales taxes, traffic congestion, and climate—a useful sampling of current and historical comparative data for anyone contemplating a move.

We’ll highlight similar enhancements as they are released. And as always, we welcome your suggestions for new data, or new ways of looking at existing data, in any domain covered by Wolfram|Alpha.

When we launched Wolfram|Alpha in May 2009, it already contained trillions of pieces of information—the result of nearly five years of sustained data-gathering, on top of more than two decades of formula and algorithm development in Mathematica. Since then, we’ve successfully released a new build of Wolfram|Alpha’s codebase each week, incorporating not only hundreds of minor behind-the-scenes enhancements and bug fixes, but also a steady stream of major new features and datasets.

We’ve highlighted some of these new additions in this blog, but many more have entered the system with little fanfare. As we near the end of 2009, we wanted to look back at seven months of new Wolfram|Alpha features and functionality.

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We have been highlighting ways that Wolfram|Alpha can be a useful tool in your everyday life, and we believe you will find our salary and wage data helpful in navigating your decisions in today’s job market. A lot of people are searching for full-time employment, relocating, exploring going back to school to change professions, or considering taking on multiple jobs. Many factors play into these decisions, and Wolfram|Alpha’s U.S. occupational salary data, and salary computations for local currencies, help you make informed choices.

Perhaps you are considering changing professions. In addition to supplying data on specific occupations, Wolfram|Alpha can compare U.S. occupational information for multiple jobs, including the median salary, the number of people employed at those jobs, and more. For example, here is the comparative information for a registered nurse, an elementary school teacher, and an accountant: More »