Tilbage i 2003, gennemførte den britiske regering en undersøgelse, der målte regnefærdigheden i befolkningen. Og de var rystet over at se, at for hver 100 erhvervsaktive voksne, manglede 47 af dem niveau 1-regnefærdigheder. Niveau 1-regnefærdighed -- det er en lav GCSE-score. Det er evnen til at regne med brøker, procenter og decimaler. Dette tal skabte en masse hændervridning i Whitehall. Politikker blev ændret, investeringer blev foretaget. Derefter udførte man undersøgelsen igen i 2011. Kan I gætte, hvad der skete med dette tal? Det gik op til 49.
Back in 2003, the UK government carried out a survey. And it was a survey that measured levels of numeracy in the population. And they were shocked to find out that for every 100 working age adults in the country, 47 of them lacked Level 1 numeracy skills. Now, Level 1 numeracy skills -- that's low-end GCSE score. It's the ability to deal with fractions, percentages and decimals. So this figure prompted a lot of hand-wringing in Whitehall. Policies were changed, investments were made, and then they ran the survey again in 2011. So can you guess what happened to this number? It went up to 49.
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(Laughter)
Og da jeg skrev om dette tal i Financial Times, spurgte en af vore læsere og sagde: "Dette tal er kun chokerende for 51 procent af befolkningen."
And in fact, when I reported this figure in the FT, one of our readers joked and said, "This figure is only shocking to 51 percent of the population."
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Men jeg foretrak reaktionen fra en skoleelev, da jeg præsenterede denne information på en skole. Han rejste sin hånd og spurgte: "Hvordan kan vi vide, at ham, der regnede tallet ud, ikke også var en af de 49 procent?"
But I preferred, actually, the reaction of a schoolchild when I presented at a school this information, who raised their hand and said, "How do we know that the person who made that number isn't one of the 49 percent either?"
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Det er klart, at der er et problem med regnefærdigheden, fordi dette er en vigtig færdighed i livet. Mange af de forandringer, som vi gerne vil gennemføre i dette århundrede involverer, at vi bliver mere komfortable med tal.
So clearly, there's a numeracy issue, because these are important skills for life, and a lot of the changes that we want to introduce in this century involve us becoming more comfortable with numbers.
Det er ikke bare et engelsk problem. OECD udgav i år nogle tal om regnefærdighed hos unge, og forrest lå USA med næsten 40 procent af unge, som har ringe regnefærdigheder. England er der også, men der er syv OECD-lande med værdier over 20 procent. Det er et problem, fordi det ikke behøver at være sådan. Ser man på den anden ende af denne graf, kan man se Holland og Korea med ét ciffer-størrelser. Der er et problem med regnefærdigheden, som der skal gøres noget ved.
Now, it's not just an English problem. OECD this year released some figures looking at numeracy in young people, and leading the way, the USA -- nearly 40 percent of young people in the US have low numeracy. Now, England is there too, but there are seven OECD countries with figures above 20 percent. That is a problem, because it doesn't have to be that way. If you look at the far end of this graph, you can see the Netherlands and Korea are in single figures. So there's definitely a numeracy problem that we want to address.
Selvom disse undersøgelser er nyttige, tror jeg, at vi risikerer uforvarende at putte folk i én af to kategorier; at der er to slags mennesker: de mennesker, der er komfortable med tal, som kan regne med tal, og de mennesker, der ikke kan. Og det, jeg forsøger at sige, er, at jeg tror, at det er en falsk modsætning. Det er ikke en uforanderlig parring. Jeg tror ikke, man behøver en voldsom god talforståelse for at interessere sig for tal, og det bør være udgangspunktet for, hvad vi gør fremover.
Now, as useful as studies like these are, I think we risk herding people inadvertently into one of two categories; that there are two kinds of people: those people that are comfortable with numbers, that can do numbers, and the people who can't. And what I'm trying to talk about here today is to say that I believe that is a false dichotomy. It's not an immutable pairing. I think you don't have to have tremendously high levels of numeracy to be inspired by numbers, and that should be the starting point to the journey ahead.
Og en af måderne, hvorpå vi kan gøre tal interessante, er, for mig, at se på statistikken. Nu er jeg den første til at erkende, at statistikken har lidt af et imageproblem.
And one of the ways in which we can begin that journey, for me, is looking at statistics. Now, I am the first to acknowledge that statistics has got somewhat of an image problem.
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Det er den del af matematikken, som selv matematikere ikke holder ret meget af, fordi, mens resten af matematikken handler om præcision og sikkerhed, er statistik næsten det modsatte. Jeg var faktisk sen til at konvertere til statistikken. Hvis man havde spurgt mine professorer, om hvilke to emner jeg næppe ville udmærke mig i efter universitetet, ville de have sagt statistik og programmering af computere, og alligevel er jeg ved at vise jer statistiske grafikker, som jeg har programmeret.
It's the part of mathematics that even mathematicians don't particularly like, because whereas the rest of maths is all about precision and certainty, statistics is almost the reverse of that. But actually, I was a late convert to the world of statistics myself. If you'd asked my undergraduate professors what two subjects would I be least likely to excel in after university, they'd have told you statistics and computer programming, and yet here I am, about to show you some statistical graphics that I programmed.
Hvad fik mig til den forandring? Hvad fik mig til at tænke, at statistikken faktisk er interessant? Det var fordi statistik handler om os. Hvis man ser på etymologien for ordet statistik, er det videnskaben om data, om staten eller det samfund, som vi lever i. Så statistik drejer sig om os som en gruppe, ikke os som individer. Og jeg tror, som sociale dyr, vi deler denne interesse i, hvordan vi er, i forhold til vore grupper, til vore jævnaldrende. Og statistik er på denne måde mest kraftfuldt, når den overrasker os.
So what inspired that change in me? What made me think that statistics was actually an interesting thing? It's really because statistics are about us. If you look at the etymology of the word statistics, it's the science of dealing with data about the state or the community that we live in. So statistics are about us as a group, not us as individuals. And I think as social animals, we share this fascination about how we as individuals relate to our groups, to our peers. And statistics in this way are at their most powerful when they surprise us.
Der er blevet lavet nogle vidunderlige undersøgelser for nyligt af Ipsos MORI i de sidste par år. De undersøgte over 1.000 voksne i Storbritannien. Man spurgte, "For hver 100 mennesker i England og Wales, hvor mange af dem er muslimer?" Det gennemsnitlige svar fra denne undersøgelse, som skulle repræsentere den samlede befolkning, var 24. Det er, hvad folk tænker. Britter tror at 24 ud af 100 mennesker er muslimer. Det officielle tal viser, at tallet er omkring fem. Der er en stor forskel mellem, hvad vi tror, og den statistiske virkelighed. Jeg synes, det er interessant. Hvad kunne være årsagen til denne fejlopfattelse?
And there's been some really wonderful surveys carried out recently by Ipsos MORI in the last few years. They did a survey of over 1,000 adults in the UK, and said, for every 100 people in England and Wales, how many of them are Muslim? Now the average answer from this survey, which was supposed to be representative of the total population, was 24. That's what people thought. British people think 24 out of every 100 people in the country are Muslim. Now, official figures reveal that figure to be about five. So there's this big variation between what we think, our perception, and the reality as given by statistics. And I think that's interesting. What could possibly be causing that misperception?
Jeg var så begejstret over det, at jeg begyndte at stille spørgsmål ved mine foredrag. Jeg fortalte om det. Jeg gav et foredrag på St. Pauls School for Girls i Hammersmith, og jeg havde et publikum magen til jer, bortset fra, at det udelukkende bestod af piger i 10. klasse. Og jeg spurgte, "Piger, hvor mange teenagepiger tror I, at den britiske offentlighed mener bliver gravid hvert år?" Og pigerne blev rasende, da jeg sagde, den britiske offentlighed mener, at 15 ud af hver 100 teenagepiger bliver gravide hvert år. Og de havde god grund til at være vred, fordi jeg skulle bruge flere end 200 prikker, før jeg kunne farve én, til at vise, hvad de officielle tal siger.
And I was so thrilled with this study, I started to take questions out in presentations. I was referring to it. Now, I did a presentation at St. Paul's School for Girls in Hammersmith, and I had an audience rather like this, except it was comprised entirely of sixth-form girls. And I said, "Girls, how many teenage girls do you think the British public think get pregnant every year?" And the girls were apoplectic when I said the British public think that 15 out of every 100 teenage girls get pregnant in the year. And they had every right to be angry, because in fact, I'd have to have closer to 200 dots before I could color one in, in terms of what the official figures tell us.
Ligesom regnefærdighed, er dette ikke bare et engelsk problem. Ipsos MORI udvidede undersøgelsen med mange lande. De spurgte de saudiske arabere: "For hver 100 voksne i dit land, hvor mange af dem er overvægtige eller fede?" Det gennemsnitlige svar fra saudierne var lidt over en fjerdedel. Det er, hvad de troede. Lidt over en fjerdedel var overvægtige eller fede. De officielle tal viser faktisk, at det er tættere på tre fjerdedele.
And rather like numeracy, this is not just an English problem. Ipsos MORI expanded the survey in recent years to go across the world. And so, they asked Saudi Arabians, for every 100 adults in your country, how many of them are overweight or obese? And the average answer from the Saudis was just over a quarter. That's what they thought. Just over a quarter of adults are overweight or obese. The official figures show, actually, it's nearer to three-quarters.
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Så igen, en stor forskel.
So again, a big variation.
Jeg elsker denne her. De spurgte i Japan: "For hver 100 japanere, hvor mange af dem bor i landdistrikterne?" Den gennemsnitlige svar var omkring 50-50, lidt over halvvejs. De troede, at 56 ud af hver 100 japanere levede i landdistrikterne. Det officielle tal er syv.
And I love this one: they asked in Japan, they asked the Japanese, for every 100 Japanese people, how many of them live in rural areas? The average was about a 50-50 split, just over halfway. They thought 56 out of every 100 Japanese people lived in rural areas. The official figure is seven.
Ekstraordinære forskelle, og overraskende for nogle, men ikke overraskende for folk, som har læst Daniel Kahnemans arbejde: Nobel-prismodtager i økonomi. Han og hans kollega, Amos Tversky, brugte år på undersøgelser af denne uoverensstemmelse mellem, hvad folk oplever og virkelighededen. Det faktum, at folk faktisk er temmelig dårlige intuitive statistikere. Og der er mange grunde til dette. Individuelle erfaringer kan i hvert fald påvirke vore opfattelser. Men også det, at medierne skriver om det usædvanlige, snarere end hvad der er normalt. Kahneman udtrykte det på en pæn måde. Han sagde: "Vi kan være blinde overfor det indlysende" -- så vi tror på forkerte tal -- "men vi kan være blinde overfor vores blindhed." Det har enorme konsekvenser for beslutningstagning.
So extraordinary variations, and surprising to some, but not surprising to people who have read the work of Daniel Kahneman, for example, the Nobel-winning economist. He and his colleague, Amos Tversky, spent years researching this disjoint between what people perceive and the reality, the fact that people are actually pretty poor intuitive statisticians. And there are many reasons for this. Individual experiences, certainly, can influence our perceptions, but so, too, can things like the media reporting things by exception, rather than what's normal. Kahneman had a nice way of referring to that. He said, "We can be blind to the obvious" -- so we've got the numbers wrong -- "but we can be blind to our blindness about it." And that has enormous repercussions for decision making.
Dengang syntes jeg, at dette var virkeligt interessant. Jeg sagde, at dette er et globalt problem, men måske er det geografien, der er problemet her. Spørgsmålene drejede sig om, hvor godt kender du dit land? Sagt på en anden måde: Hvor godt kender du 64 millioner mennesker? Ikke særlig godt viste det sig. Jeg kunne ikke gøre det. Så jeg fik en idé, som var, at have samme slags tilgang, men at sætte det i en meget lokal sammenhæng. Er det om det lokale? Hvis vi omformulerer og spørger, hvor godt kender du dit lokalområde, ville svarene så blive mere præcise?
So at the statistics office while this was all going on, I thought this was really interesting. I said, this is clearly a global problem, but maybe geography is the issue here. These were questions that were all about, how well do you know your country? So in this case, it's how well do you know 64 million people? Not very well, it turns out. I can't do that. So I had an idea, which was to think about this same sort of approach but to think about it in a very local sense. Is this a local? If we reframe the questions and say, how well do you know your local area, would your answers be any more accurate?
Så jeg udtænkte en quiz: Hvor godt kender du dit område? Det er en simpel web-app. Man skriver et postnummer, og så stiller den spørgsmål baseret på folketællingsdata for lokalområdet. Jeg var meget bevidst om designet. Jeg ønskede at gøre det åbent for det bredeste udvalg af befolkningen. Ikke bare de 49 procent, der kan regne. Jeg ønskede at alle deltog i det. Så til udformningen af quizzen, blev jeg inspireret af isotyperne af Otto Neurath fra 1920'erne og 30'erne. Det er metoder til repræsentere tal ved hjælp gentagne ikoner. Tallene er der, men de findes i baggrunden. Det er en fantastisk måde at repræsentere en mængde uden at ty til at bruge udtryk som "procent", "fraktioner" og "nøgletal".
So I devised a quiz: How well do you know your area? It's a simple Web app. You put in a post code and then it will ask you questions based on census data for your local area. And I was very conscious in designing this. I wanted to make it open to the widest possible range of people, not just the 49 percent who can get the numbers. I wanted everyone to engage with it. So for the design of the quiz, I was inspired by the isotypes of Otto Neurath from the 1920s and '30s. Now, these are methods for representing numbers using repeating icons. And the numbers are there, but they sit in the background. So it's a great way of representing quantity without resorting to using terms like "percentage," "fractions" and "ratios."
Her er quizzen. Layoutet af quizzen er, man har de gentage ikoner på venstre side, og et kort, der viser dig det område, vi stiller spørgsmål til på højre side. Der er syv spørgsmål. For hvert spørgsmål, er der et muligt svar mellem nul og hundrede, og i slutningen af quizzen får du en samlet score mellem nul og hundrede. Og så fordi dette er TEDxExeter, tænkte jeg, vi tager et hurtigt kig på quizzen for de første par spørgsmål af Exeter. Så det første spørgsmål er: "For hver 100 mennesker, hvor mange er under 16 år?" Nu kender jeg ikke Exeter ret godt, så jeg gættede, men det giver en idé om, hvordan denne quiz fungerer. Man trækker skyderen for at fremhæve ikonerne, og så bare klikke på "Send" for at svare, og vi animerer forskellen mellem dit svar og virkeligheden. Og det viste sig, at jeg havde et ret forfærdeligt gæt: fem.
So here's the quiz. The layout of the quiz is, you have your repeating icons on the left-hand side there, and a map showing you the area we're asking you questions about on the right-hand side. There are seven questions. Each question, there's a possible answer between zero and a hundred, and at the end of the quiz, you get an overall score between zero and a hundred. And so because this is TEDxExeter, I thought we would have a quick look at the quiz for the first few questions of Exeter. And so the first question is: For every 100 people, how many are aged under 16? Now, I don't know Exeter very well at all, so I had a guess at this, but it gives you an idea of how this quiz works. You drag the slider to highlight your icons, and then just click "Submit" to answer, and we animate away the difference between your answer and reality. And it turns out, I was a pretty terrible guess: five.
Hvad med det næste spørgsmål? Det spørger hvad den gennemsnitlige alder er, den alder, hvor halvdelen af befolkningen er yngre og halvdelen er ældre. Og jeg troede 35, det lød midaldrende for mig.
How about the next question? This is asking about what the average age is, so the age at which half the population are younger and half the population are older. And I thought 35 -- that sounds middle-aged to me.
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(Laughter)
Det er utroligt ungt i Exeter. Jeg havde undervurderet virkningen af universitetet her i området. Spørgsmålene bliver sværere efterhånden. Denne spørger om eget hus: "For hver 100 husstande, hvor mange har et banklån?" Jeg afdækkede mine gæt her, for jeg ikke ønskede, at have flere end 50 forkert.
Actually, in Exeter, it's incredibly young, and I had underestimated the impact of the university in this area. The questions get harder as you go through. So this one's now asking about homeownership: For every 100 households, how many are owned with a mortgage or loan? And I hedged my bets here, because I didn't want to be more than 50 out on the answer.
(Latter)
(Laughter)
Disse spørgsmål bliver sværere og sværere, for når du bor i et område, når du bor i et samfund, er der fingerpeg om, hvorvidt befolkningen er gammel eller ung. Bare ved at kigge rundt i området, kan man se det. Noget som det at eje hus er langt vanskeligere at se, så vi vender tilbage til vore egen heuristik, vore egne fordomme om, hvor mange vi tror ejer deres eget hjem.
And actually, these get harder, these questions, because when you're in an area, when you're in a community, things like age -- there are clues to whether a population is old or young. Just by looking around the area, you can see it. Something like homeownership is much more difficult to see, so we revert to our own heuristics, our own biases about how many people we think own their own homes.
Nu er sandheden den, at da vi offentliggjorde denne quiz, var de data, som det er baseret på, allerede et par år gamle. Vi har haft online-applikationer, der tillader en at skrive et postnummer og få statistik fra årevis tilbage. Så på en måde, var dette altsammen lidt gammelt og ikke nødvendigvis nyt. Men jeg var interesseret i at se, hvilken reaktion man kan få ved at gamificere det ved hjælp af animation og lege med det faktum, at folk har deres egne fordomme.
Now the truth is, when we published this quiz, the census data that it's based on was already a few years old. We've had online applications that allow you to put in a post code and get statistics back for years. So in some senses, this was all a little bit old and not necessarily new. But I was interested to see what reaction we might get by gamifying the data in the way that we have, by using animation and playing on the fact that people have their own preconceptions.
Det viste sig, at reaktionen var mere end jeg kunne have håbet på. Det var en af mine ambitioner at bringe en statistik-hjemmeside i knæ grundet offentlig efterspørgsel.
It turns out, the reaction was, um ... was more than I could have hoped for. It was a long-held ambition of mine to bring down a statistics website due to public demand.
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Denne URL indeholder ordene "statistik", "gov" og "UK", som er tre af folks mindst foretrukne ord i en URL. Og det fantastiske ved dette var, at hjemmesiden gik i knæ kvarter i 10 om aftenen, fordi folk faktisk legede med disse data af egen fri vilje, og i deres egen tid. Jeg fandt det meget interessant, at vi fik noget i retning af en kvart million mennesker, der spillede quizzen gennem 48 timer efter den blev lanceret. Og det udløste en enorm diskussion online, på sociale medier, som i vid udstrækning var domineret af folk, der har det sjovt med deres misforståelser, hvilket er noget, jeg ikke har kunnet håbe på noget bedre på en måde. Jeg kunne godt lide, at folk begyndte at sende det til politikerne. Hvor godt kender du området, du hævder at repræsentere?
This URL contains the words "statistics," "gov" and "UK," which are three of people's least favorite words in a URL. And the amazing thing about this was that the website came down at quarter to 10 at night, because people were actually engaging with this data of their own free will, using their own personal time. I was very interested to see that we got something like a quarter of a million people playing the quiz within the space of 48 hours of launching it. And it sparked an enormous discussion online, on social media, which was largely dominated by people having fun with their misconceptions, which is something that I couldn't have hoped for any better, in some respects. I also liked the fact that people started sending it to politicians. How well do you know the area you claim to represent?
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Og så bare til afslutning, lad os gå tilbage til de to slags mennesker. Jeg syntes det kunne være interessant at se, hvordan mennesker, der er gode til tal ville klare quizzen. Den nationale statistiker i England og Wales, John Pullinger, skulle man tro ville klare sig ret godt. Han fik 44 for sit eget område.
And then just to finish, going back to the two kinds of people, I thought it would be really interesting to see how people who are good with numbers would do on this quiz. The national statistician of England and Wales, John Pullinger, you would expect he would be pretty good. He got 44 for his own area.
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Jeremy Paxman -- ganske vist efter et glas vin -- 36. Endnu værre. Det viser bare, at tallene kan inspirere os alle. De kan overraske os alle.
Jeremy Paxman -- admittedly, after a glass of wine -- 36. Even worse. It just shows you that the numbers can inspire us all. They can surprise us all.
Ofte taler vi om statistik, som værende videnskaben om usikkerhed. Mine afskedsord i dag er: I virkeligheden er statistik videnskaben om os. Og det er derfor, vi bør være fascineret af tal.
So very often, we talk about statistics as being the science of uncertainty. My parting thought for today is: actually, statistics is the science of us. And that's why we should be fascinated by numbers.
Mange tak.
Thank you very much.
(Bifald)
(Applause)