5.1.1 Index overview: definition and classification 指数概览：定义与分类在线视频

你是我的小呀小苹果
（A man humming a song)

怎么爱你都不嫌多
（A man humming a song)

夫妻离婚协议中写入CPI
CPI is written into the divorce agreement

与时俱进
Wow, keep pace with the times

哎 妞妞爸
Hey, my dear

你过来看看这个新闻
come over and read this news

我要是早一点看到
If I read it earlier

说不定对小艾有用呢
it might be useful to Xiao Ai

妞妞爸 CPI 我好像听说过
My dear, I seem to have heard of CPI

不过不记得在哪里听说过了
But I can't remember where I’ve heard about it

有了它
With it

就可以让抚养费增加
you can increase the maintenance cost

CPI呀 我很熟悉
CPI, I am very familiar with it

要不要我给你上一课
Do you want me to give you a lesson

不过要报酬
but with pay

啊 报酬
Ah with pay

你不会要把吸尘器给我吧
Don't give me the vacuum cleaner and let me do the cleaning

等我打扫完 陪我去理发
No, just go with me to get a haircut after I finish cleaning

这个可以有吧
Okay

这个可以有
Okay

成交 耶
Great! Yeah

同学们 大家好
Hello everyone

欢迎回到轻松学统计的课堂
Welcome back to the Easy Learning Statistics Class

我是李老师
I am Teacher Li

从现在开始
From now on

我们就要和妞妞妈一起学习
we will learn about index

有关指数的知识
together with Niuniu’s mom

指数这个词
Are we familiar with

我们是不是觉得很熟悉呢
the term Index

那么大家能不能很快说几个
So can you tell some

熟悉的指数
common indexes quickly

居民消费价格指数
Consumer price index

对
yes

这是一个最常用的指数
this is the most commonly used index

股票价格指数
Stock price index

对的
yes

这是证券市场里边常用的
this is often used in the stock market

还有幸福指数
There is also the happiness index

空气污染指数
air pollution index

对
yes

这些都是我们在日常生活里边
all of these are the indexes

随处可见的指数
that we can see everywhere in our daily lives

还有口红指数
There is also lipstick index

榨菜指数
and mustard index

对
Yes

看来大家的知识面也挺宽的
It seems that everyone has a wide range of knowledge

这些都是在我们生活里边
These are the indexes that

可能会接触到的指数
might affect our daily lives

如果我说我们现在就处在一个
If I say that we are

指数的世界
in a world of indexes

大家是不是觉得有点夸张呢
Would you think I am exaggerating

让我们先动手
Now let's start

来做一个小小的调查吧
with a brief survey

和大家分享一下
To share with you

我国统计学界著名的学者
a well-known scholar in the statistical field in China

邱东教授在2009年3月的时候
Professor Qiu Dong，in March 2009

也曾经在百度里边进行过
also conducted an index search

指数的搜索
In Baidu

当时他搜索到4730万条指数
At that time his search result showed 47.3 million entries

有关的条目
related to the term index

当时邱老师形容
Professor Qiu said

感觉自己像被指数包围了一般
he felt like surrounded by indexes then

和指数有关的条目
Since then, the entries related to indexes

翻了一番都不止
have more than doubled

可见指数在我们日常生活中
We can see that index

应用之广
is widely used in our daily lives

那我们继续打开网页
Now we go to the search engine

往下搜索
and make a search on index

看看到底有哪一些指数呢
to see which indexes are there

各种听过的
Wow, all kinds of indexes

没听过的指数铺天盖地般
we've never heard of

向我们袭来
are presented overwhelmingly before us

有百度指数 搜狗指数
There are Baidu Index, Sogou Index

居民消费价格指数
Consumer Price Index

南昌空气质量指数
Air Quality Index in Nanchang

淘宝指数 微指数等等等等
Taobao Index, Micro Index and so on

同学们
Are not the indexes

这一阵指数雨
like raindrops pouring down

是不是淋的酣�淋漓呢
Quite a lot, right

这么多指数汇聚起来
With so many indexes

是不是若海若洋
an ocean of indexes can be formed

它们不但数目全 品种多
They are all kinds of indexes

林林总总 五花八门
so rich in variety

基本上覆盖了我们生活中的
covering almost all aspects

方方面面
of our lives

可见指数在我们现代社会中的
It can be seen that the index is quite widely used

应用是非常广泛的
in modern society

把它称之为指数化时代
It is not an exaggeration

也不为过
to call it an index era

所以在这个指数化的时代
So in this era of index

来学一点有关指数的基本理论知识
isn't it very necessary

是不是很有必要呢
to acquire some basic theoretical knowledge on index

接下来我们就来学习第一讲
Now, let's start the first lecture

指数的概念与分类
the concept and classification of index

首先我们来了解一下
First let's take a look at

指数的起源
the origin of index

指数是英国经济学家
Index is a statistical analysis method

沃恒首创的一种统计分析方法
originally created by Voughan, a British economist

在十六 十七世纪
In the 16th and 17th centuries

英国在争霸的过程中
Britain was confronted with many competitors

面临着许多强敌
In its competition to be the world leader

如拥有欧洲最强大陆军的法国
Its competitors include countries such as France, which had the strongest continental army in Europe

海上马车夫的荷兰
the Netherlands, which was called the coachman on the sea

和拥有无敌舰队的西班牙等等国家
and Spain, which had invincible fleets

这些国家中
Many of these countries

许多都比英国的块头要大
appeared to be stronger than Britain

实力看似很强
with seemingly very powerful national strength

因此英国人在争霸过程中
So in the competition to be the world leader

心中无底
the British people were not very confident

此时威廉・配第
At this time, Sir William Petty

写了一本政治算术
wrote a book named Political Arithmetick

首次系统地用数据来说明
which for the first time used data to illustrate

比较英国与其他国家的实力
the comparison of national strength between Britain and other countries

证明英国虽小却实力强劲
which proved that although Britain was small, it was strong

就像是浓雾笼罩中的一颗核桃
like a walnut in the thick fog

非常坚硬
it was still very hard

这一分析极大地提高了
His analysis greatly improved

英国王室和人民的士气
the morale of the British royal family and the people

认清了自己的实力
they recognized the country's strength

并先后取得了对法国
and won the wars against France

西班牙和荷兰的战争的胜利
Spain and the Netherlands

那么英国的实力体现在哪些方面呢
So what were the strengths of Britain

根据文献
According to literatures

关键的有以下两点
there are two key points

第一 英国非常重视教育
First, Britain attached great importance to education

人民受教育水平很高
People had high levels of education

为国家实力的增强和经济发展
which laid a good foundation for enhancing national strength

科技创新
economic development

奠定了良好的基础
and technological innovation

第二 科技水平非常发达
Second, Britain had advanced science and technology

生产力水平也比较高
and relatively high productivity

英国号称当时的世界工厂
Britain claimed to be the world's factory at that time

再加上广大的殖民地
plus a large number of colonies

因此在对外贸易中
so it always took a favorable position

始终处于有利的地位
in foreign trade

及出现顺差的机会大
that is, the country had more chances of surplus than deficit

而出现逆差的机会少
in its trading with other countries

这就导致某一时间内
This accelerated the speed

流入英国的黄金和白银的增长速度
of gold and silver flowing into Britain over a certain period of time

超过工农业生产的增长速度
and this speed increase exceeded the growth rate of industrial and agricultural production

由于黄金和白银
Because gold and silver

主要用于通货
were mainly used as currency

当时迫切需要一种方法
a method was urgently needed

来反映英国的物价变动
to reflect the price changes in Britain

1675年英国经济学家提出
In 1675, British economist Voughan put forward

指数的计算方法
the calculation method of index

他在铸货币和货币铸造论中
In his book Currency Casting and Theories of Currency Casting

为了测定当时劳资双方
in order to determine the ratio of currency exchange

对于货币交换的比例
between workers and capitalists at that time

以谷物 家畜 鱼类 布帛
he used grain, livestock, fish, cloth

皮革等作为重要的样本商品
leather and so on as important referential commodities

将1650年的价格
He compared

和1352年的价格
the prices in 1650

进行比较
with the prices in 1352

这就是物价指数计算的开端
This is the beginning of the price index calculation

了解完指数的起源
Now we know the origin of index

接下来我们了解一下
let's proceed to

指数的定义
the definition of index

从广义上讲
Broadly speaking

指数是反映现象数量变动的相对数
index is a relative number that reflects changes in the quantity of a phenomena

如2015年和2014年相比
For example, compared 2014 to 2015，we find that

我国棉花总产量的发展速度
the growth rate of China's total cotton output

为90.7%
is 90.7%

可以称棉花总产量指数为90.7%
We can say that the total cotton output index is 90.7% in 2015

狭义上来讲
In a narrow sense

指数是表明复杂现象总体
index is a relative number that indicates the comprehensive change

数量综合变动的相对数
in the quantity of a complex phenomenon population

这个定义比上面的定义
This definition sets more limitations

就多了一些限定
than the first definition

第一个限定是复杂现象总体
The first limitation is in "complex phenomenon population"

首先我们解释一下
Firstly, let me explain what is

什么是复杂现象总体
“complex phenomenon population”

所谓复杂现象总体
The so-called “complex phenomenon population”

是指那些由于各个部分
refers to those populations

性质不同而在研究其数量特征时
that cannot be directly summed or directly compared

不能直接进行加总
when studying their quantitative characteristics

或直接对比的总体
due to the different nature of each part

例如不同的产品或商品构成的总体
Take the populations of different products or commodities as an example

由于不同的使用价值
Due to different values in use

和不同的计量单位
and different units of measurement

因而在统计其实物产量
when calculating the actual production volume

销售量单位产品原材料消耗
sales, unit products, raw material consumption

单位成本 价格等数量方面的时候
unit costs, prices and so on

是不能直接进行加总的
they cannot be summed up directly

举一个小例子
Here is an example

我想大家都有在网上购物的经验
everyone has purchased online, right

打开某个网上商城
When log onto an online store

我们所看到的商品林林总总
we see a lot of commodities

有服装 有家用电器
There is clothing, household appliances

有化妆品有数码产品
cosmetics, digital products

有医疗保健品等等
health care products and so on

那这些商品
The value of use

它们的使用价值
and unit of measurement

以及它们的计量单位都不尽相同
of these commodities are different

它们所构成的总体
The population they constitute

就是一个复杂现象总体
Is a complex phenomenon population

离我们更近一点的例子是
Here is another example

财大购物广场中所销售的商品
The commodities sold in the Caida Shopping Plaza include

有毛巾 有牙膏
towels, toothpaste

还有衣服 包包以及文具等等
clothing, bags and stationery

这些商品所构成的
All these commodities

也是一个复杂现象总体
constitute a complex phenomenon

所以狭义的指数
So the narrow definition of index

对于现象总体做了一个界定
defined the phenomenon population

第二一个
Secondly

所谓的数量变动
the so-called quantity change

在狭义指数里边
in narrow index

主要是指
mainly refers to

不能直接相加的数量特征
the quantitative characteristics that cannot be added directly

比如销售量
such as sales volume

比如销售价格
and sales price

第三一个要注意的是
Thirdly, it should be noted that

我们在狭义的指数里边
the changes mentioned

所提到的变动
in narrow index

通常是指从基期到报告期
usually refer to changes during the time

反映时间的变动
from the base period to the given period

而广义的指数中
While for the broad index

既可以包括时间的变动
can include both changes

也可以包括空间的变动
in time and space

第四一个
Fourthly

这里的相对数
the relative number here

也就是仅仅指动态相对数了
only refers to the dynamic relative number

了解完指数的定义
Now we know definition of index

接下来我们来看一下
Next, let's take a look at

指数的分类
the classification of index

指数的分类有很多种
There are many ways to classify index

我们按不同的标准
According to different criteria

可以形成不同的分类
we can have different classifications

首先我们来看
First of all, let's take a look at

按照指数
the classification according to the range

所反映的范围不同
reflected by index

一般按照指数反映的范围不同
Generally, according to the range reflected by indexes

可以将指数分为
indexes can be divided into

个体指数和总指数
individual index and total index

个体指数是反映单一经济现象
Individual index is a relative number that reflects

数量变动的相对数
the quantity change of a single economic phenomenon

我们就拿天猫上面所销售的服装
Take the clothing sold on Tmall

来做一个例子
as an example

那服装是我们要了解的总体
Clothing is the population we need to know

服装打开以后
After getting searching results for clothing

我们还有接下来的分类
we see categories

比如有女装有男装
such as women's clothing and men's clothing

女装里边又分上装 下装
Women's clothing is further divided into tops and bottoms

上装里边又分春夏秋冬
Then tops are further divided into clothing for spring, summer, autumn and winter

对应的
Then

那么在冬装里边
in winter wear

我们又可以找到
there are woolen coats

毛呢大衣 羊毛衫等等
cardigans, etc.

一路往下面点击
We select the subcategories all the way down

最后我看中了某一件
and finally pick a fancy one

太平鸟女羊毛大衣
the Peacebird Bird wool coat

点击以后
By clicking the item name

我们来搜索有关它的信息
we search all items about it

假如我找到了基期的销售量
Suppose we found that the sales volume in the base period

q{\fs8}0{\r}是462件
q{\fs8}0{\r} is 462 pieces

报告期的销售量q{\fs8}1{\r}是154件
sales volume in the given period q{\fs8}1{\r} is 154 pieces

基期的销售价格是779元
sales price in the base period is CNY 779

报告期的价格
and price in the given period is

P{\fs8}1{\r}是789元
p{\fs8}1{\r} is CNY 789

对 这里我们说明一下
Here, please take a note

通常用小写的q代表数量
we usually use the lowercase q to represent quantity

小写的p代表价格
and the lowercase p to represent price

下标0代表基期
The subscript 0 corresponds to base period

下标1代表报告期
and subscript 1 corresponds to given period

那有了这些信息
With this information

我们就可以来了解
we now know

这一款女羊毛大衣
the fluctuations in the sales volume

它的销售量的波动情况
of this female wool coat

我们可以计算一个
We can figure out

个体的销售量指数
the individual sales volume index

（公式如上）
(formula as the above)

我们通常用小写的K（下标q）来代表
We usually use the lowercase k (subscript q)

个体的销售量指数
to represent individual sales volume index

它只要用报告期的销量
It is equal to sales volume in the given period

除以基期的销量
divided by the sales volume in the base period

把具体的数字
After plugging the specific values

代入进来
into the formula

我发现这一款女装
we found that for this women's dress

在报告期和基期相比是33.33%
the ratio of sales volume in given period to that of base period is 33.33%

说明它的销售量下降了
which indicates the sales volume has declined

再来看它的价格
Now let's take a look at the price

我们也同样可以采用个体销售
We can also use the method of

价格指数的方法
individual sales price index

来反映它的销售价格的变动
to reflect the changes in sales price

我们可以用（公式如上）
We can use (formula as the above)

来反映这一款女装
to reflect the fluctuations

在报告期和基期
of the sales price of this women's clothing

它的销售价格的波动情况
during the given period and the base period

小写的k{\fs8}p{\r}通常作为
The lowercase k{\fs8}p{\r} is often used to

个体销售价格指数的代表
represent individual sales price index

当然我们每一次的资料收集
Collection of data

都是从个体开始的
starts from individual data

最后我们需要把个体的指标
Finally, the individual indicators

汇聚成服装这一大类商品的
are aggregated into changes

价格或者是销售量的变动
in the price or sales volume of the major category of clothing

如果我们反映的是服装这一大类
If to reflect changes

商品的数量特征的变动
in the quantitative features of the major category of clothing

这个时候
then

计算的指数
the index calculated at this time

就可以被称之为总指数
can be called the total index

如销售量总指数
such as total sales volume index

如销售价格总指数
and total sales price index

我们通常用大写的（字符如上）
We usually use the uppercase (characters as the above)

作为销售量总指数的符号
as the symbol of the total sales volume index

通常用（字符如上）
and often use (characters as the above)

作为销售价格总指数的代表
to represent the total sales price index

这里大家可以先想一想
Here let's think about it first

刚才我们在计算
When we were calculating

个体销售量指数时候
the individual sales volume index just now

可以用（公式如上）来实现
we can use (formula as the above)

那这里我要计算（公式如上）
Here we are to calculate (formula as the above)

能不能通过（公式如上）来实现呢
Can this be achieved via (formula as the above)

按照我们刚才的分析
According to our analysis just now

销售量可以直接加总吗
can we add up the sales volume directly

我们知道它不能直接加总
No, they can't be added up directly

所以销售量总指数
So, the total sales volume index

思路上面是可以通过
can be ideally figured out via

报告期的总销售量
the total sales volume of the given period divided

除以基期的总销售量来实现
by the total sales volume of the base period

但是在计算上面
But actually

是不能通过（公式如上）来实现的
it cannot be figured out via (formula as the above)

因为它是一个复杂现象总体
Because it is a complex phenomenon population

那我们该怎么办呢
What should we do

稍候在指数的编制中
Later in the part of index compilation

会详细地向大家介绍
I will show you in detail on

如何来编制销售量总指数
how to compile the total sales volume index

和销售价格总指数
and the total sales price index

在总指数和个体指数之间
Between the total index and the individual index

还有若干的分类
there are many subcategories

比如男装女装 上装下装
such as men's clothing, women's clothing, tops, bottoms

春装秋装等等
spring wear, autumn wear and so on

那中间这些指数的分类
There is also a name for the classification

我们也有一个名称给它
of these indexes in the middle

通常把它们称之为类指数
which is usually called the class index

或者组指数
or group index

它们的性质和总指数类似
Their properties are similar to the total index

只不过范围比总指数来的更小
but their scope is smaller than the total index

这是指数的第一种分类方法
This is the first method to classify index

第二 按照指标性质的不同
Second, according to the nature of their indicators

我们通常会将指数分成
indexes are usually divided into

数量指标指数
quantitative indicator index

和质量指标指数
and quality indicator index

我们先来回忆一下
Let's first recall

前面学过的内容
what we have learned earlier

在第一章的时候
In the first chapter

就曾经向大家介绍过
we have discussed

指标的分类
the classification of indicators

我们知道指标可以分成
We know that indicators can be divided into

数量指标和质量指标
quantitative indicators and quality indicators

还记得数量指标是反映什么吗
Do you remember what quantitative indicators reflect

质量指标是反映什么吗
What about quality indicators

对
Yes

数量指标是反映总体的总规模
Quantitative indicators reflect such phenomena as the overall size

总量 总水平这一类现象的指标
total quantity and overall level of the population

而质量指标是反映总体的
while quality indicators reflect

相对水平 平均水平等
the overall relative level, average level

质量特征的指标
and other quality characteristics of the population

那如果我们计算的指数
If the index we are to calculate

是反映数量指标的变动
reflects the changes of a quantitative indicator

我们就把它称之为数量指标指数
we will then call it a quantitative index

如果我们计算的指数
If the index we are to calculate

是反映质量指标的数量的变动
reflects the quantitative changes of a quality indicator

我们就把它称之为
then we will call it

质量指标指数
a quality index

下面我来说一些指标的名称
Next, I am going to give the names of some indicators

请大家来判断
Please determine

它们哪些是数量指标
which are quantitative indicators

哪些是质量指标
and which are quality indicators

听好了
Listen

销售额
Sales revenue

总成本
total cost

收购额
purchase amount

总产值
total output value

产量
output volume

销售量
sales volume

收购量
and purchase volume

大家来想一想
Let's think about it

能不能把这些指标
Can you distinguish

哪些是数量指标
which of these indicators are quantitative indicators

和哪些是质量指标分清楚呢
and which are quality indicators

有的同学是不是已经看出来了
Some of you may have the answers

老师
Mrs. Li

你给我们的指标
all the indicators given

全部都是数量指标
are quantitative indicators

对的
Yes

说明我们对前面的指标的知识点
So you already have a solid knowledge

掌握的还挺牢固
on indicators

我给大家的指标
Actually, the indicators provided

其实全部都是数量指标
are all quantitative indicators

那这些数量指标
Are there any differences

有没有什么不同呢
between these quantitative indicators

有没有同学看出来呢
Does anyone know the answer

有观察仔细的同学
Some of you who have observed carefully

可能已经看出来了
may have found out

老师
Mrs. Li

你给我们的第一行的指标
the indicators in the first row

都是价值量计量的数量指标
are all quantitative indicators measuring values

你给我们的第二行的指标
while the ones in the second row

都是实物量计量的数量指标
are all quantitative indicators measuring physical quantity

对的
Correct

我分了两行来给大家这些指标
I have put these indicators in two rows

这些指标确实有差异
there are indeed differences between them

那我问一个问题
Then here is a question

销售额 收购额 总成本
For indicators such as

这一些指标
sales revenue, purchase amount and total cost

它们能直接求和吗
can they be added up directly

对
Yes

它们当然可以直接求和
Yes, of course they can be added up directly

它们都是用价值量计量的指标
They are all indicators measuring value

因此
So

按照我们刚才前面
according to the definition of complex phenomenon population

关于复杂现象总体的描述
we have discussed previously

它应该是不具有可加性的
it should not be additive

那这些数量指标
but these quantitative indicators

它是直接具有可加性的
are additive

因此在计算指数的时候
when calculating the index

这些指标
these indexes

我们把它单独称为总变动指数
are particularly named as total change indexes

它并不属于数量指标指数的范畴
Total change index does not belong to the category of quantitative index

因此我们一般所指的数量指标指数
Therefore, what is generally referred to as the quantity index

仅仅是指以实物量计量的
is only the quantity index

数量指标指数
measuring physical quantities

所以这里特意给大家做一个区分
So let's make a distinction here

而常见的质量指标
The common quality indicators

一般有价格 平均工资
generally include price, average salary

单位成本等等
unit cost, etc.

相对来说比较容易区分
which are relatively easy to distinguish

当然数量指标和质量指标的划分
Of course, the division of quantitative indicators and quality indicators

也是具有相对性的
is a relative division

例如 在计算应纳税额的时候
For example, when calculating the taxable amount

应纳税额等于
the taxable amount

销售量乘以销售价格乘以税率
is equal to sales volume times sales price and then times tax rate

销售价格相对于产品的销售量来讲
Relative to sales volume of the product

它是质量指标
sales price is a quality indicator

但是相对于税率来讲
while relative to tax rate,

它又属于数量指标了
it is also a quantitative indicator

因此数量指标和质量指标的划分
So, the distinction of quantitative indicators and quality indicators

是要在整个系统里边
should be put

来考虑的
in the entire system

这是第二种分类
This is the second method to classify index

第三种分类则是在一个
Now let's proceed with the third method of index classification

指数数列里边
In the time series of indexes

按照指数计算的基期不同
According to the base period used in calculating an index

可以将指数分为定基指数
An index can be classified as a fixed-base index

和环比指数
or a chain index

数列我们上一章刚刚学过
We have learned time series in the last chapter

一般是指按时间的先后顺序
It is a group of data

所形成的
in chronological order

那指数它既然是一个指标
Since index is an indicator

它也可以形成数列
we can also have time series of indexes

那在形成指数数列的时候
When working out the indexes to form a time series

如果每一个指数
if the base period

它们计算的基期都相同的话
of each index is the same

那么我们就把它称之为定基指数
then it is called a fixed-base index

如果每一个指数计算的时间
If the base period of each index

都是以报告期的前一期为基期的话
is the previous period of the given period

那么我们通常把它称之为环比指数
then it is called a chain index

我们可以来看一个例子
Here is an example

比如打开中国统计年鉴
When we open the China Statistical Yearbook

我们可以翻到有关指数的内容
we can turn to the part of index

在指数的内容里边
In the part of index

有一个指数的内容
the fixed-base index

就是定基指数
is expounded

目前我们国内的定基指数
At present, the fixed-base index of China

是以1978年为基期的
is calculated based on 1978

往下翻
and you can further turn to

也可以翻到环比指数
the part on chain index

环比指数的位置就有一个说明
The base period of chain index is the previous period of the given period

上一年等于100
The index of the previous year is set as 100

那上一年等于100就说明
The base period is changing constantly

它计算的时期是在不停地轮换的
in the calculation of index of each period

那么它就属于环比指数
So it is called chain index

好 同学们
Okay, everyone

第一讲的知识就到这里
Here is the end of this lecture

第二讲 我们接着学习指数的编制
In Lecture 2, we'll discuss index compilation