A survey by the Royal Statistical Society has today revealed the vast disparity between what the British public believes to be the state of the nation, and the actual reality reflected by sober official statistics.

It may not be surprising that people are sometimes rather skewiff in their assessments of some issues, but the gulf between perceptions and reality are quite staggeringly wide. The implications for politics and governance are profound.

To pick out just some of the survey findings, on average we think teenage pregnancy rates are 25 times higher than they are. A large majority of the public believe crime is constant or rising, when official surveys show there were 53 per cent fewer incidents in 2012 than in 1995. People overestimate the amount of benefit fraud 34 times over, believing the rate to be 24 per cent of the total benefits bill. The true figure is 0.7 per cent. When people were asked to select from a list which government policy would save most money, a third selected capping benefits at £26k, more than twice as many as selected raising the pension age to 66 for both men and women. The actual savings from a benefit cap would be £290m. Savings from raising the pension age would be £5bn, or about 20 times greater.

Download the new Independent Premium app Sharing the full story, not just the headlines

More than a quarter of people believe foreign aid is one of the top two or three items of government spending - indeed more people pick this as the top item of government expenditure than pick pensions or education, despite those being 74 times and 51 times larger respectively. The average member of the public believes 24 per cent of the British population is Muslim. It is actually five per cent. Average estimates of the total immigrant population are two to three times higher than reality.

It is tempting to attribute this to the straightforward mendacity of politicians and the media, in the memorable phrase of US writer-turned-Senator Al Franken, lies and the lying liars who tell them. There is certainly no shortage of examples. Ministers like Iain Duncan Smith and Jeremy Hunt – not to mention Harriet Harman before them – have been repeatedly rebuked by their own statistics watchdog for issuing false or misleading statistical claims. Meanwhile the manifold failings of print and broadcast journalists keep fact-checking sites like the essential Full Fact busy on a daily basis.

This, however, is only a small part of the problem. Apart from anything else, the public have long since given up on believing a single word spilling from the lips of a politician. Indeed, this may be one important root of the problem. Cynicism over economic figures or crime statistics is endemic, and for good reason. However the poison has spread so far that even dependable, meaningful research findings are assumed to come straight from the office of Walter Mitty.

The real issue is not the sin of dishonesty but the sin of omission. News reporters will relay incidents of violent crime or benefit fraud without any attempt at providing context or evaluation of scale, and it is not just the right wing tabloids that are responsible. The liberal and centre-left media will, for example, report frighteningly high numbers of domestic violence incidents without ever mentioning that, horrific though they remain, the numbers fallen by 69 per cent over the past two decades.

Being statisticians, the RSS have inevitably called for better public education on statistics, particularly in schools. Though this would certainly be welcome on its own terms, I’m not sure it gets to the heart of the problem. It is not that the public do not understand the difference between a median and a mean or think that a confidence interval is something Andy Murray takes between games. It is not that the public doesn’t understand the statistics, it is that they are virtually never told the statistics in the first place. Consequently, our impressions of society are formed by looking at individual factoids and scare stories as if through a long thin tube, only ever seeing a snapshot rather than the full panorama. We then depend upon cognitive biases and heuristics to fill in the gaping blank spaces.

What is lacking here is not education in statistics, but an education in media studies and political science. Politicians and media figures regularly bemoan the cynicism of the public, and widespread disengagement from the issues. Today’s research is a reminder that the public, in truth, are nowhere near cynical enough. It is public credulity that is the problem, not scepticism. If the political classes truly wish the British public to re-engage with democracy, their first step is obvious. Start telling us the truth, and the whole truth.