Why you should love statistics | Alan Smith

翻译人员: Chen Zou 校对人员: Ivy Sun

Back in 2003,

早在2003年

the UK government carried out a survey.

英国政府进行了一项调查

And it was a survey that measured levels of numeracy

目的是了解国民的

in the population.

算术能力

And they were shocked to find out

结果非常让人吃惊

that for every 100 working age adults in the country,

在英国，每100个正值 工作年纪的成人中

47 of them lacked Level 1 numeracy skills.

47个缺乏一级的算术能力

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

一级算术能力 是GSCE考试的低端分数

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

它是运算分数 百分数和小数的能力

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

这个数据使英国行政部门愈发的担忧

Policies were changed,

（他们）改变了政策

investments were made,

进行了投资

and then they ran the survey again in 2011.

然后到了2011年 他们再次进行了普查

So can you guess what happened to this number?

你们能猜到这一次的数字吗？

It went up to 49.

这次，上升到了49

(Laughter)

（观众笑声）

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

事实上，当我在金融时报 报道这一数据时

one of our readers joked and said,

有个读者开玩笑地说

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

“这个数据只震惊了51%的人口”

(Laughter)

（观众笑声）

But I preferred, actually, the reaction of a schoolchild

但我实际上更喜欢一个学生的反应

when I presented at a school this information,

有一次我在学校展示这一信息时

这个孩子举手说道

who raised their hand and said,

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

“我们怎么知道得出这一数据的人

不是49%中的一个呢？”

isn't one of the 49 percent either?"

(Laughter)

（观众笑声）

So clearly, there's a numeracy issue,

很明显，算术能力成了一个问题

because these are important skills for life,

毕竟这是生活中的重要技能

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

更何况我们还想为这个 世纪带来许多的改变

involve us becoming more comfortable with numbers.

这需要我们对数字越来越应用自如

实际上，不仅英国存在这样的的问题

Now, it's not just an English problem.

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

OECD今年发布了一些 关于青少年计算能力的数据

and leading the way, the USA --

名单里领先的是美国

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

大约40%的美国青少年 算术能力低下

Now, England is there too,

英国也名列其中

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

但是有七个OECD国家的 数据在20%以上

这就有问题了 因为情况本不必如此

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

在图的最右端

If you look at the far end of this graph,

可以看到荷兰，韩国都是个位数

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

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

所以，这里绝对有一个算术 问题需要我们解决

Now, as useful as studies like these are,

和这些研究同样有用的是，

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

我认为我们无意间轻率地 将人群分成了两个类别

that there are two kinds of people:

也就是这么两种人

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

对数字可以应用自如 能够把玩数字的人

and the people who can't.

和做不到这一点的人

And what I'm trying to talk about here today

今天，我想要探讨的是

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

我认为这是个错误的二分法

It's not an immutable pairing.

这并不是一成不变的组合

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

我认为，你不需要高超的算术能力

to be inspired by numbers,

才能被数字所启发

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

这应该成为前路的起点

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

对于我来说，这条路的起始点之一

is looking at statistics.

是着眼于统计学

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

这里，我要首先承认 统计是有那么一点儿

of an image problem.

画面方面的问题的

(Laughter)

（观众笑声）

It's the part of mathematics

统计是数学的一部分

that even mathematicians don't particularly like,

但是它是连数学家 都不怎么喜欢的那一部分

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

因为与其它讲究精确 与确定性的数学领域不同

statistics is almost the reverse of that.

统计学几乎是反其道而行之

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

事实上，我自己也是 后来才转向统计学的

If you'd asked my undergraduate professors

如果你们去问问我本科时的教授

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

我大学毕业后最不可能 有卓越成就的两个领域是什么

they'd have told you statistics and computer programming,

他们会告诉你是统计和电脑编程

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

然而现在，我要用我编的程序

that I programmed.

给你们展示统计图表

So what inspired that change in me?

是什么激发我有了这样的转变呢？

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

是什么让我对统计产生了兴趣？

It's really because statistics are about us.

那是因为统计学是 研究我们自身的科学

If you look at the etymology of the word statistics,

如果你看看统计 (statistics) 的词源

it's the science of dealing with data

它是处理数据的科学

about the state or the community that we live in.

围绕着我们所生活的国家或社区

So statistics are about us as a group,

所以，统计学是研究 作为一个群体的我们

not us as individuals.

不是作为个人的我们

And I think as social animals,

而且我认为作为一种群居动物

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

我们会分享对作为一个个体， 如何与所在的群体以及同辈之间

to our peers.

发生联系的那种痴迷

And statistics in this way are at their most powerful

统计最强大的时候

when they surprise us.

是当它让我们惊讶的时候

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

伊普索莫利（英国第二大市场调查组织） 在过去几年进行过

by Ipsos MORI in the last few years.

一些很有意义的调查

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

他们调查了超过1000个英国的成年人

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

提出的问题是在每一百个 英格兰和威尔士人当中

how many of them are Muslim?

有多少个穆斯林？

Now the average answer from this survey,

调查的平均答案

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

是24，这是具有国民代表性的答案

That's what people thought.

这是国民的想法

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

英国人认为，在自己国家 每100个人中，有24个信仰穆斯林

而官方数据显示这个数字大约是5

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

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

很明显，我们的感知 与被统计资料呈现的事实之间

and the reality as given by statistics.

有着巨大的差异

And I think that's interesting.

我觉得这很有趣

是什么原因引起 这样的感知差距呢？

What could possibly be causing that misperception?

And I was so thrilled with this study,

我对这个研究感到很兴奋

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

并开始在各种演讲中提出这个问题

我曾经在哈默史密斯的

Now, I did a presentation

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

圣保罗女子中学做过一个演讲

and I had an audience rather like this,

当时我有一群像现在这样的观众

except it was comprised entirely of sixth-form girls.

唯一的差别是观众都是 六年级的女学生

And I said, "Girls,

我说道，“姑娘们，

how many teenage girls do you think the British public think

你们觉得英国公众认为 每年有多少个

get pregnant every year?"

青春期女孩怀孕？”

And the girls were apoplectic when I said

当我说出答案，女孩们是非常生气的

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

我说英国公众认为 每一百个青春期女孩中

get pregnant in the year.

每年有15个怀孕

And they had every right to be angry,

当然她们有生气的缘由和权利

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

因为实际上根据官方数字，

before I could color one in,

（按比例）我必须要有近200个点

in terms of what the official figures tell us.

才能将一个空白圆圈涂满色

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

和计算能力一样 这同样不仅仅是英国的问题

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

伊普索莫利机构在最近几年 在世界范围内扩展了调查研究

And so, they asked Saudi Arabians,

他们问沙特阿拉伯人

for every 100 adults in your country,

在你们国家，每一百个成年人中

how many of them are overweight or obese?

有多少个超重或是有肥胖症？

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

平均答案是四分之一多一点

That's what they thought.

那是他们认为的

仅仅是四分之一多一点的 成年人超重或有肥胖症

Just over a quarter of adults are overweight or obese.

官方数据显示，实际上 这个数字接近四分之三

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

(Laughter)

（观众笑声）

So again, a big variation.

这又是一个巨大的差异

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

下面这个调查我很喜欢 他们问了日本人

for every 100 Japanese people,

每一百个日本人里面

how many of them live in rural areas?

有多少人住在乡下？

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

平均答案大概是一半， 稍高于50%

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

他们认为每100个日本人中 有56个居住在乡村地区

The official figure is seven.

而官方数字是7

So extraordinary variations, and surprising to some,

如此巨大的差异震惊了一些人

but not surprising to people who have read the work

但是对一些人来说并不惊讶

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

比如阅读过诺贝尔经济学奖获得者 丹尼尔·卡内曼的研究成果的人

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

他和他的同事，阿莫斯·特沃斯基 花费了数年的心血在这个

between what people perceive and the reality,

人们的见解与现实脱节的问题上

the fact that people are actually pretty poor intuitive statisticians.

实际上人们是直觉很差的统计学家

And there are many reasons for this.

这背后有着很多原因

个人体验，当然可以影响我们的见解

Individual experiences, certainly, can influence our perceptions,

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

但也包括媒体带有偏见

rather than what's normal.

而非全面客观的报道

Kahneman had a nice way of referring to that.

卡内曼对此有一个很好的描述

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

他说，“我们对显而易见的 事情视而不见”——

so we've got the numbers wrong --

所以我们有了错误的数字——

“但是我们可以对我们视而不见 这个事实视而不见。”

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

And that has enormous repercussions for decision making.

而这对做决策来说有巨大的影响

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

那么在统计学办公室， 当这些事情在发生的时候

I thought this was really interesting.

我觉得很有趣

我认为显然这是一个全球性的问题

I said, this is clearly a global problem,

但也许与地域差异有关

but maybe geography is the issue here.

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

这里的一些问题都是关于 你对你的国家了解多少

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

在这个问题里，是在问关于 你对6400万人口了解多少？

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

结果是，我并不是很了解

So I had an idea,

所以我有了一个想法

which was to think about this same sort of approach

是用相同的方法

but to think about it in a very local sense.

但是以一种非常地方化的方式来思考

Is this a local?

这是因地制宜的吗？

If we reframe the questions and say,

如果我们重新思考问题然后说

你对你的当地状况了解多少？

how well do you know your local area,

would your answers be any more accurate?

你的答案会更准确吗？

So I devised a quiz:

对此我设计了一个测试

How well do you know your area?

你对你居住的地区了解多少？

It's a simple Web app.

是一个简单的网络应用

You put in a post code

输入邮编

and then it will ask you questions based on census data

它会根据你所在地区的普查数据

for your local area.

给你提出问题

And I was very conscious in designing this.

我在设计时有特别注意

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

想要让它适用于最广范围的人群

not just the 49 percent who can get the numbers.

不仅仅是49%的会把玩数字的人

I wanted everyone to engage with it.

我想要每个人都能参与

所以，针对测试的设计

So for the design of the quiz,

I was inspired by the isotypes

我的灵感是由19世纪20到30年代 奥图·纽拉特的

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

“同形像”所激发

Now, these are methods for representing numbers

这是使用重复图标

using repeating icons.

来代表数字的方法

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

那些数字仅仅是作为背景

So it's a great way of representing quantity

所以这是一个代表数量的绝佳方式

without resorting to using terms like "percentage,"

不需要使用“百分比”

"fractions" and "ratios."

“分数” 和“比率”

So here's the quiz.

这个就是测试界面

The layout of the quiz is,

界面的布局是

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

你左手边有重复出现的图标

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

然后这里有一张地图 展现我们问你问题的地区

on the right-hand side.

在右手边

There are seven questions.

一共有七个问题

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

对于每一个问题，这里有 一个从0到100的可能的答案

and at the end of the quiz,

在测试结尾

you get an overall score between zero and a hundred.

你会得到一个在0和100之间的总分

And so because this is TEDxExeter,

因为这是TEDx埃克塞特

I thought we would have a quick look at the quiz

我们可以快速看一下关于

埃克塞特的前几个问题

for the first few questions of Exeter.

And so the first question is:

第一个问题是

每一百人中 有多少个在十六岁以下？

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,

当然，我对于埃克塞特不那么了解 所以我随便猜了一下

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

主要是演示这个测试怎样进行

You drag the slider to highlight your icons,

你将滑块拖至你所认可的数据图标

and then just click "Submit" to answer,

然后点击“递交”

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

然后我们将你的答案和现实之间的 差异用动画的方式表现出来

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

结果是，我错得很离谱， 只得了五分

How about the next question?

那么下一个问题呢？

这是问关于年龄的中位数

This is asking about what the average age is,

so the age at which half the population are younger

也就是该地区大于和小于这个年龄的

人口数相等

and half the population are older.

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

我以为是35—— 那对我来说是中年

(Laughter)

（观众笑声）

Actually, in Exeter, it's incredibly young,

实际上，在埃克塞特 结果是惊人的年轻

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

是我低估了大学在这个区域的影响

The questions get harder as you go through.

随着测试的进行问题的难度会增加

So this one's now asking about homeownership:

这个问题有关房屋所有权

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

在一百个家庭中，有多少个 是有贷款或借债的？

And I hedged my bets here,

我没有直接选出脑海中的数字

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

因为我不想有超过五十个

(Laughter)

（观众笑声）

And actually, these get harder, these questions,

实际上，这些问题 变得越来越困难

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

因为当你在一个地区 在一个社区

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

人口是否老龄化或是年轻化 这样的事情，是很容易找到线索的

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

看看周围环境就知道了

Something like homeownership is much more difficult to see,

像房屋所有权这样的事 要观察起来就困难得多

so we revert to our own heuristics,

所以我们还原了我们的启发法

关于我们自认为有 多少人拥有房屋所有权的偏差

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

Now the truth is, when we published this quiz,

然而真相是 当我们发表这个测试时

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

我们所依据的普查数据 已经是好几年前的了

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

我们有一个在线应用 你可以输入邮编

and get statistics back for years.

然后得到过去几年的数据

So in some senses,

所以，在某种程度上

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

这是有点儿过时的数据

But I was interested to see what reaction we might get

但是我很感兴趣 会得到什么样的反应

by gamifying the data in the way that we have,

用我们已有的方式去使数据游戏化

by using animation

通过使用动画

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

以及利用人们会有先入之见这一事实

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

结果是，反应...

was more than I could have hoped for.

比我所期望的要好

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

对我来说运营数据网站 需要持久的雄心

due to public demand.

因为公众有着庞大的需求

(Laughter)

（观众笑声）

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

这个网址包含单词“统计“，"gov" 和"UK"

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

这三个是在网址中最不受欢迎的单词

And the amazing thing about this was that the website came down

惊人的是这个网站在晚上

at quarter to 10 at night,

9点45的时候瘫痪了

because people were actually engaging with this data

因为人们实际上在基于自愿的基础上

of their own free will,

很积极地利用他们的

using their own personal time.

个人时间为我们提供数据

I was very interested to see

我很兴奋的看到

有二十五万人在测试发起的

that we got something like a quarter of a million people

playing the quiz within the space of 48 hours of launching it.

48小时之内参与了测试

And it sparked an enormous discussion online, on social media,

并且在网络和社交媒体上 激发了巨大的讨论

which was largely dominated

这些讨论大部分被

by people having fun with their misconceptions,

在见解偏差中找到乐趣的人们所占据

which is something that I couldn't have hoped for any better,

对于我来说，在某种程度上没有比这

in some respects.

更令人欣慰的了

I also liked the fact that people started sending it to politicians.

我也愿意看到人们开始将它发送给政客

How well do you know the area you claim to represent?

你对你自己声称代表的区域了解多少？

(Laughter)

（观众笑声）

And then just to finish,

那么我的演讲要接近尾声了

going back to the two kinds of people,

回到那两类人

I thought it would be really interesting to see

我很好奇

擅长数字的人是如何完成这个测试的

how people who are good with numbers would do on this quiz.

The national statistician of England and Wales, John Pullinger,

英格兰和威尔士的国家统计学家， 约翰·普令吉尔

you would expect he would be pretty good.

你会觉得他应该做得非常好

He got 44 for his own area.

然而他在自己的区域得了44分

(Laughter)

（观众笑声）

Jeremy Paxman -- admittedly, after a glass of wine -- 36.

杰瑞米·拍客斯曼——我得声明 是在喝了一杯酒之后——得了36分

Even worse.

还不如前面那位

It just shows you that the numbers can inspire us all.

它展示给大家数字可以启示我们

They can surprise us all.

可以给我们带来惊讶

So very often, we talk about statistics

所以我们常常把统计学

as being the science of uncertainty.

作为一种不确定性的科学来谈论

My parting thought for today is:

我今天的想法是

actually, statistics is the science of us.

实际上，统计是关于我们自身的科学

And that's why we should be fascinated by numbers.

这是为什么我们应该为此感到着迷

Thank you very much.

非常感谢

(Applause)

（观众掌声）