Last Night's TV - The Joy of Stats, BBC4; Natural World Special: Panda Makers, BBC2; True Stories: I Was Osama bin Laden's Bodyguard / More 4

Plus signs from the stat pack

Almost everyone in Sweden has more than the average number of legs. That's a statistic, and understanding why it's true delivers a crash course in how averages can sometimes divert from common sense, and how an understanding of the importance of distribution can bring them back in line again (essentially you need to remember that not one of Sweden's amputees is offset by a Swede with three legs, to keep the figures balanced). It also offers a good example of Professor Hans Rosling's eye for the kind of quirky oddity that will make a general audience sit up and pay attention. Professor Rosling is a Swedish epidemiologist whose stated ambition is to "make the data sing", and who has already done an exceptional job of making it dance through the development of graphics software that makes long-term trends instantly apprehensible to anyone. We saw him here, in a TED talk lecture, commentating on a thrilling 100-metre race between historic child mortality rates in Sweden and Singapore, in which Singapore took gold a millisecond before they hit the tape.

I don't know whether the BBC pays someone to sit through all the TED talks (it's a kind of YouTube for the brainy) and pick out the presenters that might have a television programme in them, but if The Joy of Stats is the sort of thing that results it would certainly make sense. When Professor Rosling bounced Tiggerishly up to the camera at the beginning and said, "I kid you not, statistics is now the sexiest subject around", you figured that the joke might turn out to be on him – a kind of Swedish chef of mass data collection. An hour later and the probability of you accepting his statement as true had risen by at least 98.6 per cent, after a programme that was smart, witty and unselfconsciously exhilarated by its own intellectual content. We get far too much ersatz enthusiasm on television, but Professor Rosling's is the real thing. He bubbles with technological optimism, talking of forthcoming developments in statistical science with the same eager expectation of a 13-year-old waiting for a much-hyped movie release.

Statistics, it turns out, were a Swedish thing, with an Office of Statistics (the Tabellverket) first being set up in 1749 to collate parish registry entries. This allowed the authorities to administer the country more effectively, but one of Rosling's main points here was that a science initially developed to enhance state control has now become a tool for citizen empowerment, giving voters the hard facts with which they can call politicians to account. For Florence Nightingale (something of a statistical heroine, and a pioneer of graphics that made the essential conclusions inescapable), statistics were "a measure of [God's] purpose". For her contemporaries, they were an endless source of fascination. But for us, Rosling suggested, they could also introduce a scientific revolution, since the combination of massive data recording and the kind of computing power that can penetrate the fog of raw numbers enables us to understand the world better than ever before. "And det's preddy exciting, izzent it!" he concluded, so possessed by excitement that he spasmed as if he'd been electrocuted. It izz, Professor, it really izz.

I don't know whether statistical science could help us understand the irresistible appeal of the panda, a conundrum whose solution must lie in the field of evolutionary psychology and probably overlaps in some weird way with the universal appeal of dark eye shadow. But it was fairly clear from Natural World Special: Panda Makers that no one is immune to it. Even the jobbing scientists of the Chengdu Research Base in China, which breeds pandas for eventual release into the wild, croon at their charges helplessly. I'm afraid that some sections of David Attenborough's narration were inaudible to me because of the high-pitched squeals of adoration from my wife and daughter, others because of their synchronised groans at the close-up footage of artificial insemination. But I suspect the words weren't really the point here.

Laura Poitras's I Was Osama bin Laden's Bodyguard was a slow-burn affair, and not quite as explosive as its title suggested. But it was genuinely intriguing, interleaving interviews with a Yemeni taxi-driver who called himself Abu Jandal with the story of what happened to his brother-in-law Salim Hamdan, who was employed as a driver by "the Sheikh" and ended up in Guantanamo. Having passed through a de-radicalisation process called "The Dialogue", Jandal now lives a curious afterlife, trading on his history as a jihadi and downplaying the fact that when the Americans interrogated him he spilled every bean in his possession, including his brother-in-law's name. His sense of guilt was half the story. The other half concerned the military trial of Hamdan – a strange mixture of Kafkaesque legal nightmare and unexpected due process (Hamdan's military counsel, for instance, appeared genuinely committed to his client's defence). Hamdan was eventually acquitted on the charge of conspiracy to commit terrorism but found guilty of "material support for terrorism", an offence specifically invented (after he'd successfully challenged his detention in the US Supreme Court) to avoid the embarrassment of letting him off scot-free. Donald Rumsfeld is still at large.