US election: Crunching the numbers

President Barack Obama and Mitt Romney

Just like in every US presidential election campaign, the two opponents have been using statistics to bolster their arguments. But do the numbers stand up?

Where's the middle?

Politicians - particularly wealthy ones like Mitt Romney - are often accused of being out of touch. Sometimes they do not help their case.

Speaking recently to ABC News, Mitt Romney said: "No-one can say my plan is going to raise taxes on middle-income people, because principle number one is to keep the burden down on middle-income taxpayers".

The interviewer, George Stephanopoulos, asked if $100,000 (£62,000) was middle income, to which Mr Romney replied "no, middle income is $200,000 [£123,000] to $250,000 [£154,000] and less."

But it's not just the Republicans. President Obama's been boasting about "middle-class" tax cuts - and in that he includes households whose income is under that magic number, $250,000.

"Median [household] income in the United States is just about $50,000," says Roberton Williams from America's Tax Policy Center, "so this is much, much higher than the median income. In fact, we estimate two or three per cent of Americans have incomes above those thresholds."

So for families on $250,000 dollars to be middle class, the "middle" would have to extend to the 97th percentile - in other words, most of America.

So why "median" income rather than a simple average, the mean? The reason is that the mean is skewed by very high earners. One could earn - at the extremes - billions, but it's hard to earn less than nothing. So average income will be a lot higher than the actual incomes most people take home.

Roberton Williams explains it with a joke. "If Bill Gates [the Microsoft billionaire] walks into a bar," he says, "everyone [in the bar] is on average a millionaire."

Obama's jobs

Here's one statistic which has been deployed regularly by Democrats throughout the campaign. In the words of Vice-President Joe Biden, speaking at the Democratic National Convention, "we've … created 4.5 million private-sector jobs in the last 29 months".

President Obama made the same statement earlier in the summer, referring to a period that began around February 2010.

Such a statement raises a question - why 29 months?

The answer is that the Democrats are guilty of cherry-picking the data, choosing when to start counting to make the numbers look as flattering as possible.

Another way of looking at the job numbers is from the point at which President Obama took office, in January 2009.

Brooks Jackson, founder of, is scathing. "They are measuring this from the absolute bottom of the job slump. The economy has not regained all the jobs that it has lost since the President took office."

He also points out that by concentrating on "private-sector jobs" Vice-President Biden neatly avoided including in his statistic government jobs. "Teachers and policemen are still being laid off," he says.

Romney's 47%

Mitt Romney, the Republican Presidential candidate, was secretly recorded at a fundraising event claiming that 47% of Americans pay no income tax. His point was that such people are reliant on state hand-outs, and so would never vote for him, because he believes in smaller government.

In a way, he's about right. Last year 46% of Americans paid no federal income tax. But in another more important way he's very wrong. The idea that all those people are living on hand-outs - or even paying no tax - is inaccurate.

Roberton Williams from the Tax Policy Center, which does the calculations that Mr Romney is referring to, thinks the candidate's remarks were unhelpful.

"Mitt Romney misinterpreted the meaning of this 46%," he says. "Sixty percent of those people who don't pay income tax work, and therefore pay payroll taxes, the taxes that support … social security and Medicare. Of the remainder, more than half are elderly, retirees who have worked."

So nearly two-thirds of the people Mitt Romney was talking about are actually in work and paying taxes - hardly the state-dependent scroungers he described.