Or take the number of Muslims living in countries that are historically non-Muslim.
The highest proportion of the population is in France, where 8 per cent are Muslims -- but the average guess of the French people polled was 31 per cent (and Fox News seems to believe it's nearly half).
Only 1 per cent of Americans are Muslim, but Americans believe it is 15 per cent.
These huge over-estimates are probably driven in part by the fear of Islamist terrorism, which in turn is driven by the media's fascination with the subject. It's quite striking, for example, that while Americans guess three times too high when asked about the proportion of immigrants in the country, they guess 15 times too high when asked about Muslims.
One could go on and on about how wrong people get things. Indians (urban, educated Indians) think that one-third of the country's population is non-religious. In fact, less than 1 per cent is. Saudi Arabians think that 28 per cent of the population are overweight or obese, when actually 71 per cent are (the highest proportion of all 35 countries polled).
But the more interesting question is: how much do these misperceptions affect politics and policy?
Not much, probably, when we're talking about religion or obesity. But it's pretty clear a huge popular over-estimate of the number of immigrants in Britain contributed to the "Leave" victory in June's UK referendum on membership of the European Union.
But the ignorance often gets a lot of help. London's population, for example, is more than a third foreign-born: almost 37 per cent. But Londoners are comfortable with this, and voted strongly for "Remain".
In fact, almost all of the big English cities voted "Remain" -- while in suburban and rural parts of England, where immigrants are rare or entirely absent, people were so panicked by immigration that they voted equally strongly for "Leave".
This was not just a coincidence. For many years a big chunk of the British media, including the country's three largest-circulation morning papers, the Sun, the Daily Mail and the Daily Telegraph, has constantly exaggerated the scale of the immigration and the problems it causes.
So in parts of England where immigrants are scarce, people don't believe the evidence of their own eyes; they believe the media instead.
The same phenomenon has played a big part in the rise of Donald Trump in the US.
When he talks about building a wall to stop hordes of Mexican rapists pouring across the border of the US, or promises to ban all Muslim immigration, the media-fed misconceptions of Americans about immigrant and particularly Muslim numbers make his lies easier to believe.
There is a chicken-and-egg question here, of course. Are the media just pandering to existing popular fears, or are they creating them? The inevitable answer is: a bit of both.
In the century and a half when there have been free mass media (and now social media), nobody has come up with a solution for this problem. "Free" includes free to make mistakes, and free to tell outright lies.
Gwynne Dyer is an independent journalist whose articles are published in 45 countries.