the UK government carried out a survey.

在2003年，

And it was a survey that measured levels of numeracy

英國政府進行了一項調查。

in the population.

主要是調查

And they were shocked to find out

國民的算數能力。

that for every 100 working age adults in the country,

他們驚訝地發現，

47 of them lacked Level 1 numeracy skills.

該國的成年就業者當中，

Now, Level 1 numeracy skills -- that's low-end GCSE score.

平均100個裡面有47個 缺乏等級一的算數能力。

It's the ability to deal with fractions, percentages and decimals.

等級一算數能力， 相當於低階的國中數學能力。

So this figure prompted a lot of hand-wringing in Whitehall.

這個等級代表你會計算 分數、百分比、小數點。

Policies were changed,

這個數據讓英國政府緊張地手心冒汗。

investments were made,

不但改變了政策、

and then they ran the survey again in 2011.

也編訂了預算，

So can you guess what happened to this number?

然後，在2011年他們再調查一遍。

It went up to 49.

各位猜猜，數字變到多少？

(Laughter)

上升到49。

And in fact, when I reported this figure in the FT,

（笑聲）

one of our readers joked and said,

事實上，當我把這數據 刊登在金融時報後，

"This figure is only shocking to 51 percent of the population."

我們其中一位讀者開玩笑地說，

(Laughter)

「這個數據只嚇到 51% 的人。」

But I preferred, actually, the reaction of a schoolchild

（笑聲）

when I presented at a school this information,

但我實際上更喜歡一個小學生的反應，

who raised their hand and said,

當我在他的學校演講提到這件事情時，

"How do we know that the person who made that number

他舉手問說，

isn't one of the 49 percent either?"

「我們如何知道，算出這個數據的人

(Laughter)

會不會也是在 49% 裡面的人？」

So clearly, there's a numeracy issue,

（笑聲）

because these are important skills for life,

所以很明顯的，算術能力不足問題相當嚴重，

and a lot of the changes that we want to introduce in this century

因為在我們人生中， 這些都是很重要的技能，

involve us becoming more comfortable with numbers.

而且，我們想要介紹的這個世紀的許多變化

Now, it's not just an English problem.

需要我們能夠更自在地面對數字。

OECD this year released some figures looking at numeracy in young people,

這不僅是英國的問題。

and leading the way, the USA --

OECD（經濟合作與發展組織） 今年也發佈了一些年輕人的算數能力數據，

nearly 40 percent of young people in the US have low numeracy.

美國第一名，

Now, England is there too,

他們將近有40%的年輕人算數能力有問題。

but there are seven OECD countries with figures above 20 percent.

英國也差不多，

That is a problem, because it doesn't have to be that way.

總共有七個OECD的會員國， 他們的數據都高於 20% 。

If you look at the far end of this graph,

這問題很嚴重，因為不該如此。

you can see the Netherlands and Korea are in single figures.

如果你仔細看這張圖表的末端，

So there's definitely a numeracy problem that we want to address.

你可以看到荷蘭跟韓國的數據只有個位數。

Now, as useful as studies like these are,

所以我們必須解決這個有關數學程度的問題。

I think we risk herding people inadvertently into one of two categories;

然而，就算這些報告很有用，

that there are two kinds of people:

我認為我們把人類分成這兩類是有風險的；

those people that are comfortable with numbers, that can do numbers,

就只是這兩類：

and the people who can't.

一類是能自在地面對數字的人，會算數的人，

And what I'm trying to talk about here today

另一類是不會算數的人。

is to say that I believe that is a false dichotomy.

而我今天要談的是，

It's not an immutable pairing.

我認為這樣的兩分法是錯誤的。

I think you don't have to have tremendously high levels of numeracy

這兩類人不會永遠都如此。

to be inspired by numbers,

我認為你不需要懂高階數學，

and that should be the starting point to the journey ahead.

也能被數字所啟發，

And one of the ways in which we can begin that journey, for me,

而且，這應該是未來旅程的起點。

is looking at statistics.

開啟這趟旅程的其中一個方法， 對我而言，

Now, I am the first to acknowledge that statistics has got somewhat

就是觀察統計數據。

of an image problem.

我應該是第一個說

(Laughter)

統計比較像是個圖像問題的人。

It's the part of mathematics

（笑聲）

that even mathematicians don't particularly like,

它是數學的一部分，

because whereas the rest of maths is all about precision and certainty,

但是數學家並不特別喜歡統計，

statistics is almost the reverse of that.

因為其它的數學講究的是 精準性及確定性，

But actually, I was a late convert to the world of statistics myself.

而統計幾乎是相反的。

If you'd asked my undergraduate professors

但實際上，我自己是比較晚愛上統計的。

what two subjects would I be least likely to excel in after university,

如果你問我的大學教授

they'd have told you statistics and computer programming,

我畢業後兩個最不可能會 成為我日後強項的科目，

and yet here I am, about to show you some statistical graphics

他們會告訴你，是統計及電腦編程，

that I programmed.

但我今天來這邊，是要向各位展示一些

So what inspired that change in me?

我編程的統計資料圖表。

What made me think that statistics was actually an interesting thing?

那到底是什麼改變了我？

It's really because statistics are about us.

是什麼事讓我覺得統計真的很有趣？

If you look at the etymology of the word statistics,

那是因為統計跟我們有關。

it's the science of dealing with data

如果你有去查「統計」這個詞的詞源意義，

about the state or the community that we live in.

它是一門有關

So statistics are about us as a group,

我們生活周遭的數據科學。

not us as individuals.

所以統計是有關我們群體，

And I think as social animals,

而不是我們個人。

we share this fascination about how we as individuals relate to our groups,

我認為身為群居動物的我們，

to our peers.

我們每個人都很想知道，

And statistics in this way are at their most powerful

我們個人與團體、同儕之間 有什麼關聯性。

when they surprise us.

而這也是統計在這些方面最有力，

And there's been some really wonderful surveys carried out recently

那麼另人驚訝。

by Ipsos MORI in the last few years.

最近有一些很棒的調查，

They did a survey of over 1,000 adults in the UK,

是由 Ipsos MORI（英國的市場調查公司） 近幾年所進行的調查。

and said, for every 100 people in England and Wales,

他們對一千多位英國民眾進行了訪問，

how many of them are Muslim?

問他們說，「你認為住在英格蘭及威爾斯的

Now the average answer from this survey,

每一百個人中，平均有多少人是穆斯林（回教徒）？」

which was supposed to be representative of the total population, was 24.

在這次的調查中，

That's what people thought.

這些可以代表大多數人的受訪民眾， 他們認為應該有 24% 。

British people think 24 out of every 100 people in the country are Muslim.

這是人們的想法。

Now, official figures reveal that figure to be about five.

英國人認為每一百個人當中 有 24 個是穆斯林。

So there's this big variation between what we think, our perception,

但官方的統計數字大約只有 5 。

and the reality as given by statistics.

所以我們認為的觀念與

And I think that's interesting.

實際上的統計有著很大的差距。

What could possibly be causing that misperception?

所以我認為這很有趣，

And I was so thrilled with this study,

到底是什麼原因造成這樣的認知差距？

I started to take questions out in presentations. I was referring to it.

我對這樣的研究相當感興趣。

Now, I did a presentation

我在每次的演講中， 都會提出類似的相關問題。

at St. Paul's School for Girls in Hammersmith,

之前，我到阿姆斯特丹的聖保羅學校，

and I had an audience rather like this,

向學校的女同學做了一次演講，

except it was comprised entirely of sixth-form girls.

聽眾人數和在座的差不多，

And I said, "Girls,

除了他們都是六年級的女學生。

how many teenage girls do you think the British public think

我問她們，「女孩子們，

get pregnant every year?"

你們猜一下，英國大眾認為

And the girls were apoplectic when I said

英國的未成年女生每年懷孕的人數有多少？」

the British public think that 15 out of every 100 teenage girls

那些女孩子們聽到我的回答，幾乎要中風了，

get pregnant in the year.

我說，「英國大眾認為你們平均每年

And they had every right to be angry,

100 個人裡面有 15 個人會懷孕。」

because in fact, I'd have to have closer to 200 dots

她們的確有權力表達她們的憤怒，

before I could color one in,

因為事實上，

in terms of what the official figures tell us.

根據官方的數據，

And rather like numeracy, this is not just an English problem.

我必須有將近200個圓點

Ipsos MORI expanded the survey in recent years to go across the world.

[官方數據：每一百人中有0.6人] 才能在其中一個上色。

And so, they asked Saudi Arabians,

算術能力不是只有英國才有的問題。

for every 100 adults in your country,

MORI市場調查公司，最近這幾年， 也到全世界進行其它調查。

how many of them are overweight or obese?

他們去問沙烏地阿拉伯人：

And the average answer from the Saudis was just over a quarter.

在你們國家的成年人當中，

That's what they thought.

平均每100人有多少人是 體重過重或肥胖的？

Just over a quarter of adults are overweight or obese.

那些沙烏地阿拉伯人回答： 平均應該比四分之一多一點，

The official figures show, actually, it's nearer to three-quarters.

這是他們自己認為的數字，

(Laughter)

只有 28% 的人是有體重過重或肥胖的問題。

So again, a big variation.

實際上，官方數據是將近四分之三，

And I love this one: they asked in Japan, they asked the Japanese,

（笑聲）

for every 100 Japanese people,

所以你看，差距很大。

how many of them live in rural areas?

我喜歡這一個，他們問日本人說：

The average was about a 50-50 split, just over halfway.

「每100個日本人中，

They thought 56 out of every 100 Japanese people lived in rural areas.

有多少人住在農村地區？」

The official figure is seven.

他們說大概 50-50 ，差不多剛過半。

So extraordinary variations, and surprising to some,

他們認為每 100 個人中， 有 56 個人住在農村地區。

but not surprising to people who have read the work

但官方數據只有 7 。

of Daniel Kahneman, for example, the Nobel-winning economist.

如此大的差距，讓有些人很驚訝，

He and his colleague, Amos Tversky, spent years researching this disjoint

但有些人看到這個數據時並會不感到驚訝，

between what people perceive and the reality,

像是，諾貝爾獎經濟得主，丹尼爾·卡尼曼。

the fact that people are actually pretty poor intuitive statisticians.

他和他的同事，阿姆斯·特爾斯基，

And there are many reasons for this.

花了好幾年的時間研究 人們的主觀與實際上的差距，

Individual experiences, certainly, can influence our perceptions,

他們發現， 人們在對統計方面的直覺度相當薄弱。

but so, too, can things like the media reporting things by exception,

這有很多原因。

rather than what's normal.

個人經歷，肯定會影響我們的觀念，

Kahneman had a nice way of referring to that.

同時，媒體對於例外事件的報導， 而不是平常的事，

He said, "We can be blind to the obvious" --

也會影響我們的觀念。

so we've got the numbers wrong --

關於這一點，卡尼曼有一個很好的比喻。

"but we can be blind to our blindness about it."

他說，「我們經常無視於明顯的事情——

And that has enormous repercussions for decision making.

所以，我們都猜錯了數字——

So at the statistics office while this was all going on,

但我們若對我們的無知也一無所知， 那就真的太瞎了。」

I thought this was really interesting.

而且這對你做決定，會有很大的影響。

I said, this is clearly a global problem,

所以，我在統計辦公室 面對這樣的事情時，

but maybe geography is the issue here.

我心想，這真的很有趣。

These were questions that were all about, how well do you know your country?

我是說，這是個全球性的問題，

So in this case, it's how well do you know 64 million people?

但也許只是因為地理性的問題。

Not very well, it turns out. I can't do that.

這些問題是不是 與你對國家的認知有關？

So I had an idea,

像是測驗你對6400萬人口的認識？

which was to think about this same sort of approach

很難，其實，我也辦不到。

but to think about it in a very local sense.

所以，我想到了一個辦法，

Is this a local?

跟這些問題的問法有點像，

If we reframe the questions and say,

但會要你去思考比較當地的問題。

how well do you know your local area,

會不會當地的問題就比較好回答？

would your answers be any more accurate?

如果我們把問題改成，比如說，

So I devised a quiz:

你對當地的認識有多深，

How well do you know your area?

你會不會回答地比較精準？

It's a simple Web app.

所以，我設計了這樣的測試：

You put in a post code

你對你所在的區域認識有多深？

and then it will ask you questions based on census data

這是一個很簡單的網路 App 應用程式。

for your local area.

你只要輸入郵遞區號，

And I was very conscious in designing this.

然後程式就會問你一些

I wanted to make it open to the widest possible range of people,

當地資料調查出來的問題。

not just the 49 percent who can get the numbers.

我很小心地設計這個應用程式。

I wanted everyone to engage with it.

我希望對吸引絕大部分人，

So for the design of the quiz,

而不是只有 49% 的人會回答而已。

I was inspired by the isotypes

我希望每個人都能參與回答。

of Otto Neurath from the 1920s and '30s.

所以，為了設計這個測試，

Now, these are methods for representing numbers

我被奧圖·紐拉特

using repeating icons.

在1920~1930年所用的圖像符號所啟發。

And the numbers are there, but they sit in the background.

他的方法是利用重複的圖像

So it's a great way of representing quantity

代表不同的數字。

without resorting to using terms like "percentage,"

數字就隱藏在圖像的背後，

"fractions" and "ratios."

所以用這樣的方式表達數量， 是一個很好的方式，

So here's the quiz.

不須要用「百分比」、

The layout of the quiz is,

「分數」、「比例」來表示。

you have your repeating icons on the left-hand side there,

這裡是這個測試，

and a map showing you the area we're asking you questions about

測試展現的方式是這樣的：

on the right-hand side.

你的左邊會有一些重複的圖像，

There are seven questions.

題目中地區的地圖

Each question, there's a possible answer between zero and a hundred,

顯示在你的右手邊。

and at the end of the quiz,

一共有七個問題。

you get an overall score between zero and a hundred.

每一個問題的答案是零到100

And so because this is TEDxExeter,

回答完題目後，

I thought we would have a quick look at the quiz

你會得到一個零到100的分數。

for the first few questions of Exeter.

因為我們這一場在埃克塞特舉辦的 TEDx演講，

And so the first question is:

我想，我們可以很快的看一下

For every 100 people, how many are aged under 16?

有關埃克塞特的一些問題。

Now, I don't know Exeter very well at all, so I had a guess at this,

第一題：

but it gives you an idea of how this quiz works.

每100人中，有多少人是未滿16歲的？

You drag the slider to highlight your icons,

我對埃克塞特也不是很了解， 所以我也只能用猜的，

and then just click "Submit" to answer,

但你可以透過這個考試來了解。

and we animate away the difference between your answer and reality.

你可以拖曳這個滑標來標示圖像，

And it turns out, I was a pretty terrible guess: five.

然後點選「提交」傳送答案，

How about the next question?

我們就會將你的答案與實際的差距 用動畫方式表示出來。

This is asking about what the average age is,

結果，我猜的答案（24）差很多， 答案是5。

so the age at which half the population are younger

下一問題呢？

and half the population are older.

這一題問平均年齡是多少，

And I thought 35 -- that sounds middle-aged to me.

哪一半的人口較年輕，

(Laughter)

另一半較老。

Actually, in Exeter, it's incredibly young,

我猜是35歲， 因為我覺得那是中年人的年紀。

and I had underestimated the impact of the university in this area.

（笑聲）

The questions get harder as you go through.

實際上，埃克塞特的人口相當年輕（20），

So this one's now asking about homeownership:

我低估了這個區域裡的大學的影響。

For every 100 households, how many are owned with a mortgage or loan?

接下來的題目越來越難。

And I hedged my bets here,

這一題是關於擁有房產的人口比例：

because I didn't want to be more than 50 out on the answer.

每100人中，有多少人有設定或揹貸款？

(Laughter)

保險起見，我猜高一點，

And actually, these get harder, these questions,

因為我不想一半的答案都是錯的。

because when you're in an area, when you're in a community,

（笑聲） [實際：25，你猜：50]

things like age -- there are clues to whether a population is old or young.

實際上，這些題目越來越難，

Just by looking around the area, you can see it.

因為如果你是在地的，你身處當地的社區，

Something like homeownership is much more difficult to see,

像年齡這種問題...人口的老、少 多少還有點線索可尋，

so we revert to our own heuristics,

只要稍微觀察一下你的生活周遭即可。

our own biases about how many people we think own their own homes.

但像是有多少人擁有房產， 這就很難看得出來，

Now the truth is, when we published this quiz,

所以我們會採用我們個人的「啟發法」，

the census data that it's based on was already a few years old.

也就是我們對「有多少人擁有房產」 這件事情上的個人偏見。

We've had online applications that allow you to put in a post code

事實上，當我們公佈這些問題後，

and get statistics back for years.

調查的結果是基於幾年前的資料。

So in some senses,

我們的線上應用程式 讓你可以在輸入郵遞區號後，

this was all a little bit old and not necessarily new.

取得數年之前的統計資料。

But I was interested to see what reaction we might get

所以在某些方面，

by gamifying the data in the way that we have,

有些資料已經有點老舊、還沒有更新。

by using animation

但我當時比較有興趣的是，

and playing on the fact that people have their own preconceptions.

如果把這些問題變得比較遊戲化， 大家會有什麼樣的反應，

It turns out, the reaction was, um ...

藉由動畫，

was more than I could have hoped for.

和娛樂方式來看看大家對自己偏見的反應。

It was a long-held ambition of mine to bring down a statistics website

結果，反應...相當...嗯...

due to public demand.

比我想像的還熱烈。

(Laughter)

長久以來的我的一個野心就是，

This URL contains the words "statistics," "gov" and "UK,"

因應大眾的要求， 設立一個統計網站。

which are three of people's least favorite words in a URL.