5.4.1 Comprehensive Index System 综合指数体系在线视频

同学们大家好
Hello, everyone

接下来我们学习指数第三讲的内容
Now let's begin the third lesson about indexes

综合指数体系
-- Composite Index System

在这一讲里面我们会学习
In this lesson, we will learn

指数体系的定义
the definition of index system

以及综合指数体系的应用两大内容
and the application of composite index system

首先我们来看一下
First of all, let's take a look at

综合指数体系的定义
the definition of composite index system

一般来讲指数体系
Generally speaking, an index system

是指在经济上有联系
refers to the whole composed of

在数量上存在着对等关系的三个
three or more indexes

或者三个以上的指数
that are economically related

所构成的整体
and quantitatively equivalent

由于我们前面介绍的指数算法
For the exponentiation algorithm we introduced earlier

是用综合指数
is based on composite indexes

所以我们前面加了两个字
so we add a word to it

综合指数体系
-- Composite Index System

当然如果我们指数的算法变了
Of course, if our exponentiation algorithm changes

指数体系它仍然也还是成立的
The index system is still satisfied

比如经济上的联系
like the economic connection

通常可能在我们其它的课程
Usually, in our other courses

或者其它的原理里边
or other principles

比如我们现在所看到的
As we see now

销售额等于销售量乘以销售价格
Sales Amount = Sales Volume × Sales Price

这是一个最简单的
This is the simplest

这三个指标之间的联系
relationship among the three indexes

第二个例子
Take another example

工业总产值等于产品产量
Gross Industrial Output Value = Product Output

乘以出厂价格
× Ex-factory Price

这个我们在学工业方面的知识的时候
When we are learning about the industry

也经常会学到这个
we often meet that

还有比如农作物产量等于
In addition, for example, Crop Yield is equal to

播种面积乘以单位面积产量
Sown Area × Yield/Unit Area

这些式子都反映了这些指标之间
These formulas reflect

存在的经济上的联系
the economic connection among these indexes

第二 我们的指数体系
Second, our index system

还存在着数量上的对等关系
is also quantitatively equivalent

它有哪些数量上的对等关系呢
What are its quantitative equivalences

第一个 相对数上面的对等关系
The first one is the equivalence in relative quantity

这个式子里边的三个指数
Three indexes in this formula

我们能分得出来吗
can we tell them

对了 左边一个p和q的时间
By the way, P and Q on the left

同时都在变动
are changing simultaneously

这就是总变动指数了
This is a general change index

右边这两个指数
Then, the two indexes on the right

第一个是（公式如上）
The first one is (formula as above)

这是拉氏指数还是帕氏指数
Is it a Laspeyres index or a Paasche index

如果同学们立马就回答出来
If you answer right away

它是拉氏指数的话
that it's a Laspeyres index

说明我们上一讲的内容
it shows what I taught last time

学的还挺牢固
has been learned well

对了 这个是同度量因素
By the way, it is an isometric factor

被固定在基期对不对
It is fixed in the base period, isn't it

那它当然是一个拉氏指数
So, of course, it's a Laspeyres index

它是一个数量指标指数
A quantitative index

K{\fs8}q{\r}bar对不对
K{\fs8}q{\r}bar, right

那当然后面这个就是
Well, of course, the second one

帕氏的价格指数了
is a Paasche price index

从这个指数的构造上来看
From the structure of this index

我们很快也发现
we can find out soon

拉氏指数的分子∑q{\fs8}1{\r}p{\fs8}0{\r}
whether ∑q{\fs8}1{\r}p{\fs8}0{\r}, serving as molecule of Laspeyres index

和帕氏指数的分母∑p{\fs8}0{\r}q{\fs8}1{\r}
and ∑p{\fs8}0{\r}q{\fs8}1{\r}, serving as denominator of Paasche index

是不是完全相同
are identical

对了 它们不是可以约去嘛
By the way, they can be divided out

那右边这两个指数合并以后
After the two indexes on the right are combined

不就剩下（公式如上）
the rest (formula as above)

所以指数
So indexes

总变动指数和数量指标指数
That is, general change index, the quantity index

以及质量指标指数之间
and quality index

一定存在这个相对数上的对等关系
must be equivalent in relative quantity

而在绝对数上面
On the absolute number

同样地它也会存在一个对等关系
similarly, they will also be equivalent

也就是说（公式如上）
that is to say (formula as above)

报告期减去基期
Report Period － Base Period

（公式如上）
(Formula as above)

也是用报告期减去基期
also Report Period － Base Period

（公式如上）
(formula as above)

同样地拉氏指数里边的∑q{\fs8}1{\r}p{\fs8}0{\r}
Similarly, ∑q{\fs8}1{\r}p{\fs8}0{\r} of the Laspeyres index

和帕氏指数里边的∑p{\fs8}0{\r}q{\fs8}1{\r}
and ∑p{\fs8}0{\r}q{\fs8}1{\r} of the Paasche index

是同一个组合
are in the same combination

也是可以被约去的
So they can be divided out too

剩下的依然是（公式如上）
The rest is still (formula as above)

这个是从指数的构造上面
This is a relationship

直接可以看出来的关系
that can be seen directly from the structure of indexes

因此任意的三个指标
So for any three indexes

只要它们在经济上能形成
as long as they can form

像刚才那样的数据关系
the data connection economically like that

它们的指数一定具有这两个等量关系
they must have these two equivalences

这就是我们通常说的指数体系
This is the index system what we usually call

那有了这个指数体系
Then with this index system

它可以帮助我们做什么呢
what we can do

好 接下来我们就来看一下
Well, then let's take a look at

指数体系的应用
the application of index system

它第一个最重要的应用
Its first most important application

就是帮助我们对某一个总指标的变动
is to help us, for the change of a certain general index

来进行因素的分解
decompose factors

比如在前面一讲综合指数编制里边
For example, in the first lesson about composite index compilation

我们分析天猫商城双十二
when we were analyzing the changes in Tmall’s turnovers

和双十一的营业额的变动的时候
on November 11 and December 12

那么就可以利用指数体系
then we can use the index system

来帮助我们分别分析营业额的变动
to help us analyze the changes in turnovers separately

受销售量的变动
How are they effected

带来了多少影响
by the changes in sale volume

受销售价格的变动带来了多少影响
How are they affected by the changes in sales prices

那接下来我就给大家
Next, I'll make

详细地来介绍一下
a detailed introduction to you

因素分析的具体步骤
As for specific steps of factor analysis

一般我们可以按照先左后右
generally, we can follow the principle of "from left to right"

先相对数后绝对数的方法
from relative quantity to absolute quantity

来进行指数体系的运用
to use the index system

先左 那就意味着我们先要了解
Starting from left, it means that we must understand

总变动的情况
the general change first

我们还是使用上一节天猫双十二
We still take the comparison of Tmall’s turnovers

和双十一比较的例子
on November 11 and December 12 that I said last time for example

那先左就意味着我们先要计算
So it means we have to calculate

K{\fs8}pq{\r}bar
K{\fs8}pq{\r}bar first

K{\fs8}pq{\r}bar用报告期的营业额
K{\fs8}pq{\r}bar, Turnover in the Report Period

除以基期的营业额
÷ Turnover in the Base Period

（公式如上）
(formula as above)

上一次计算的结果是88.05%
The result of last calculation is 88.05%

那对应的（公式如上）
that corresponds to (formula as above)

代表的是绝对量的变动
or represents the change of absolute quantity

报告期的营业额减去基期的营业额
Turnover in the Report Period － Turnover in the Base Period

它的绝对量的变动是
Its absolute quantity is

减少了295718元
reduced by 295,718 yuan

那么它的营业额减少了295718元
and then its turnover is reduced by 295,718 yuan

是由销售量和销售价格
How is it separately affected

分别带来了多少呢
by the change in sales volume and the change in sales prices

我们接下来可以进一步地计算
Next, we can further calculate

销售量指数和销售价格指数
sales volume index and sales price index

首先我们来计算销售量总指数
First of all, let's calculate the general sales volume index

按照我们前面的学习
According to our previous study

销售量总指数
the general sales volume index

是采用拉氏指数的方法来计算
is calculated as a Laspeyres index

那我们就用（公式如上）的方式
Then by such method (formula as above)

计算的结果是91.38
the result of calculation is 91.38

91.38%

那销售量减少了8.62%
This shows a 8.62% decrease in sales volume

由于销售量下降
The decrease in sales volume

使得销售额减少了213268元
leads to a reduction of 213,268 yuan in sales amount

销售价格又发生了怎样的变化呢
Then how sales prices change

那销售价格我们采用的是
Sales prices are

帕氏价格指数
based on Paasche index

（公式如上）
(formula as above)

计算的结果是96.35%
The result of calculation is 96.35%

价格下跌了3.65%
Prices fall by 3.65%

那么由于价格下跌
Then prices falling

使得营业额减少了82450元
leads to a reduction of 82,450 yuan in turnover

这三个数字
These three numbers

如果我们不去验证的话
if we don't test them

一下子是发现不了
we can't find all of a sudden

它们存在的数量上的联系
the quantitative connection among them

同学们 如果你手边正好有计算器
Students, if you just have a calculator on hand

当然也可以打开Excel
of course, you can also open Excel

我们不妨把相对数用Excel去换算
we may as well use Excel to convert both relative quantities

把绝对数也放到Excel里边去运算
and absolute quantity

我们会发现刚才我们前面说的
We'll find

两个数量上的对等关系
the two quantitative equivalences that we said earlier

相对数上88.05%
In terms of relative quantity, 88.05%

恰好会等于91.38%×96.35%
= 91.38% × 96.35%

而从绝对数上面来看
In terms of absolute quantity

负的295718元
- 295,718 yuan

正好也会等于负的213268元
= 213,268 yuan

加上负的82450元
＋ - 82,450 yuan

这就形成了数量上的两个对等关系
This forms two quantitative equivalences

当然 有了这两个对等关系
Of course, with these two equivalences

我们就可以将营业额的变动
we can decompose the change in turnover

分解为销售量和销售价格
into the change brought about by sales volume

所带来的变动
and the change brought about by sales prices

那么接下来我们就对刚才的这些数字
Next, let's look at these numbers that we said just now

来进行一个文字上的解释
and make a literal explanation of them

文字可以由你自由来组织
You can organize the words freely

只要把这个事情说清楚了就可以
Just make the thing clear

比如我可能会这样说
For example, I may say it like this

总体上看 天猫（5种商品）双十二和双十一相比
On the whole, compared with that on November 11, the turnover of Tmall (five commodities) on December 12

营业额下降了11.95%
dropped by 11.95%

减少了295718元
295,718 yuan

其中销售量报告期和基期相比
Compared with that in the base period

减少了8.62%
the sales volume in the report period dropped by 8.62%

使销售额减少了213268元
thus leading to a reduction of 213,268 yuan in sales amount

由于价格报告期和基期
Because the prices in the report period and base period

综合下降了3.65%
dropped by 3.65% in total

使得销售额减少了82450元
the sales amount decreased by 82,450 yuan

这样我们就完成了整个体系的分析
In this way, we finish the analysis of the whole system

我们就知道销售额或者营业额的变动
We know about the change in sales amount or turnover

由销售量带来的影响
the impact of sales volume

是213268元
is 213,268 yuan

而由于价格变动所带来的影响是
and the impact of prices is

减少了82450元
- 82,450 yuan

整个过程就非常地思路清晰
The whole process is very clear

那我们在具体地遇到
Then when we meet

指数分析的题目的时候
a specific question about index analysis

都可以参照我刚才前面的做法来分解
We can decompose factors following the way I just did

一步一步的来进行运算
and calculate them step by step

我们可以再回顾一下
Now let's review the above

计算的过程是先左后右
the calculation proceeds from left to right

先相对数后绝对数
from relative quantity to absolute quantity

左边对应的是总变动
The left corresponds to the general change

右边对应的是它的因素的变动
The right corresponds to

所带来的影响
the impact brought about by the change of its factors

当然在计算右边这两个指数的时候
Of course, when we calculate the two indexes on the right

K{\fs8}q{\r}bar K{\fs8}p{\r}bar

哪一个在前 哪一个在后
which one will come before the other

这个无关影响
is irrespective

当然你主要要注意的是
Of course, the main thing you should pay attention to is

206he
00:09:49,185 --> 00:09:50,656
如果是数量指标指数
If it's a quantity index

一定选择拉氏指数的算法
we must select the algorithm of Laspeyres index

而如果是价格指数
and if it's a price index

我们一般选择的是帕氏指数的算法
we usually select the algorithm of Paasche index

这是我们一般的原则
This is our general principle

当然并不是说如果我的数量指标指数
Of course, it doesn't mean that it must be wrong

选择了帕氏的做法
If we select the algorithm of Paasche index

它就一定是错的
for a quantity index

其实从理论上来讲
In fact, in theory

它也不一定就是错的
it's not necessarily wrong

只不过从它的意义上面来分析
Just as a matter of meaning

它的含义可能不如拉氏指数
its meaning may not be as realistic

那么符合现实
as that of Laspeyres index

而帕氏指数计算价格指数
While, for a price index, Paasche index

刚才我们也分析它
as we analyzed just now

更符合实际的经济意义
is of more practical economic significance

而拉氏的价格指数相比较而言
In comparison

它的经济意义可能要更弱一些
Laspeyres index may be of weaker economic significance

好 这是利用指数体系
Well, this is the process of factor analysis

来进行因素分析的过程
Based on the index system

那接下来给大家准备了
then I will assign

一个小小的练习
a small exercise to you

让大家把刚才前面学过的知识
to consolidate

稍稍地巩固一下
what you have just learned to some degree

题目很简单
The question is very simple

大家可以拿出纸和笔
You can take out the paper and pen

来把刚才我们学习的
to consolidate the process of factor analysis

因素分析的过程巩固一下
that we have just learned

好 同学们
OK, students

我们继续回到课堂
Let's go back to class

来看一看你们计算的结果
to check whether the results of your calculation

和我的下面的解析过程
are same as

是不是一样的
my following analysis process

如果有哪里不同
If there's any difference

你一定要注意
you must pay attention

第一步我们要做的工作是
the first step we should do is

先分析题目里边这几个数字
to analyze the numbers in the question

然后用相应的符号去表达它们
and then we should use corresponding symbols to express them

比如第一个数字
For example, the first number

8600万元 它是什么
86 million yuan, what is it

它是基期的社会商品零售额
It is the retail sales amount of social goods in the base period

那我们应该用∑p{\fs8}0{\r}q{\fs8}0{\r}代表它
Then we should use ∑p{\fs8}0{\r}q{\fs8}0{\r} to represent i

对不对
right

你写对了没有
Did you answer like this

第二个数字
The second number

12890万元 它是报告期的
128.9 million yuan，in the report period

社会商品零售额
it's the retail sales amount of social goods

那我们对应的符号就应该是∑p{\fs8}1{\r}q{\fs8}1{\r}
Then its corresponding symbol should be ∑p{\fs8}1{\r}q{\fs8}1{\r}

同学们一定要注意
Students, you must pay attention to

前面的∑这个符号
the front symbol ∑

求和的这个符号千万不能忘掉了
This symbol of summation must not be forgotten

一定要加进去
It must be added

第三个数字
The third number

也就是零售物价上涨15%
that is, a 15% retail price increase

那么就告诉我们物价的变动情况
This tells us about the price change

它对应的是物价的综合变动对不对
It corresponds to the general price change, right

所以它的符号应该是大写的（字符如上）
So its symbol should be uppercase (as above)

而不是写小写的k{\fs8}p{\r}
instead of lowercase k{\fs8}p{\r}

这个地方一定要注意
You must pay attention to this

把这三个数字先表达完了
After expressing these three numbers

接下来我们可以利用前面介绍的
then we can use the previous

因素分析的步骤
steps of factor analysis

先左后右 先相对数后绝对数的过程
-- the process from left to right, from relative quantity to absolute quantity

来把这个题目进行分析
to analyze the question

首先第一个来计算
First of all, we should calculate

零售额总指数（公式如上）
The general retail sales amount index (formula as above)

p{\fs8}1{\r}q{\fs8}1{\r}的和我们刚才已经说过
p{\fs8}1{\r}q{\fs8}1{\r} and what we have just said

是12890万元
128.9 million yuan

而∑p{\fs8}0{\r}q{\fs8}0{\r}＝8600万元
and ∑p{\fs8}0{\r}q{\fs8}0{\r}＝86 million yuan

分子除以分母
Numerator ÷ denominator

等于149.88%
is equal to 149.88%

那报告期和基期相比
Compared with the base period

零售额变动了多少呢
what is the change in retail sales amount

那用（公式如上）
Then we use (formula as above)

等于4290万元
= 42.9 million yuan

增加了4290万元
an increase of 42.9 million yuan

那社会商品零售额增加了
Of the increase in retail sales amount of social goods

由物价上涨带来多少
how much is brought about by rising prices

由销售量的变动又带来多少呢
and How much is brought about by the change in sales volume

所以我们接下来就进行因素的分解
Next, let's decompose factors

首先零售物价指数
At first, the retail price index

K{\fs8}p{\r}bar已经告诉我们
K{\fs8}p{\r}bar is known

等于15%对不对
15%, right

那是上涨了15%也就意味着
That's a 15% increase, which means

它的指数是等于115%对不对
its index is 115%, right

所以这个地方我们一定要注意
So we must pay attention to this

那K{\fs8}p{\r}bar它是用什么算法呢
What algorithm should we use for K{\fs8}p{\r}bar

回顾一下我们前面
Just review what we have learned earlier

帕氏指数对不对
Paasche index, right

那就写成（公式如上）
Then write it as (formula as above)

等于115%
= 115%

那有了这个式子
That's the formula

我们已知∑p{\fs8}1{\r}q{\fs8}1{\r}＝12890万元
We know that ∑p{\fs8}1{\r}q{\fs8}1{\r}＝128.9 million yuan

就可以推算出分母∑p{\fs8}0{\r}q{\fs8}1{\r}
so we can calculate denominator ∑p{\fs8}0{\r}q{\fs8}1{\r}

是等于11209万元
= 112.09 million yuan

这一步非常重要
This step is very important

不知道有多少同学在草稿纸上
I don't know how many students

是按照和我一样的步骤
follow the same steps as I took on the draft paper

推算了∑p{\fs8}0{\r}q{\fs8}1{\r}＝11209万元
to calculate ∑p{\fs8}0{\r}q{\fs8}1{\r}=112.09 million yuan

有了这个数字
With that number

接下来我们就可以顺利地计算
then we can calculate smoothly

由于物价上涨15%
A 15% price increase

使得零售额增加的幅度
leads to an increase in retail sales amount

用（公式如上）
Use (formula as above)

等于1681万元
= 16.81 million yuan

这个很容易就可以算出来
This is easy to calculate

当然也由于我们计算出来了∑p{\fs8}0{\r}q{\fs8}1{\r}
Of course, because we have calculated ∑p{\fs8}0{\r}q{\fs8}1{\r}

接下来一步K{\fs8}q{\r}bar的计算
the next step to calculate K{\fs8}q{\r}bar

就非常顺利了
will go very well

那一定要注意的是K{\fs8}q{\r}bar
It must be noted that K{\fs8}q{\r}bar

要用拉氏指数来计算
should be calculated by the algorithm of Laspeyres index

（公式如上）
(formula as above)

等于11209除以8600
That is,11209 ÷ 8600

结果是130.34%
The result is 130.34%

反映了零售量它是增加的 上涨的
This reflects an increase in retail sales volume

那增加它所带来的
That increases its impact

零售额的变动是多少呢
in retail sales amount

用分子减去分母
Numerator - Denominator

（公式如上）
(formula as above)

等于2609万元
= 26.09 million yuan

这样的话我们就完成了先左后右
In this way, we finish the basic analysis process from left to right

先相对数后绝对数的基本的分析过程
the basic analysis process of relative number before absolute number

当然我们一定要验证一下
Of course, we have to test it

那两个数量关系成不成立
whether the two quantitative equivalences are satisfied

从相对数上面来看
In terms of relative quantity

149.88%确实会等于
Indeed, 149.88% is equal to

130.34%×115%

而从绝对数上面来看
While in terms of absolute quantity

4290万元确实也会等于
indeed, 42.9 million yuan

2609万+1681万
= 26.09 million + 16.81 million

很有可能你经过运算以后
It's very likely that after you finish the calculation

去验证你这两个等式它不成立
your two equations are tested to be unsatisfied

这有可能说明什么呢
What may it mean

对 有可能说明我们在计算
Yes, it may mean that

数量指标指数
we used a wrong method

和计算质量指标指数的时候
When calculating the quantity index

方法用错了
and quality index

两个同时都用了拉氏指数
That is, we use the algorithm of Laspeyres index

或者两个同时都用了帕氏指数
or Paasche index for both of them

那么我们的数量关系
So our quantitative equivalences

就肯定不会成立的
must be unsatisfied

所以从这个角度来讲
Therefore, from this point of view

指数体系还有一个纠错的功能是不是
index system has another function of error correction, doesn't it

它可以帮助我们检验一下
It can help us test

我们前面的算法是不是对的
whether our previous calculation is correct

最后我们也可以对刚才的
In the end, we can also

这个计算过程进行一个简单的
make a simple literal description

文字说明
on our calculation process

比如我们可以说报告期和基期相比
For example, we can say that compare the report period with the base period

社会商品零售额上升了49.88%
The retail sales amount of social goods in the report period increased by 49.88%

增加了4290万元
42.9 million yuan

其中零售物价报告期和基期相比
Among it, compared with that in the base period, the retail prices in the report period

综合上涨了15%
rose by 15% in total

使社会商品零售额增加了1681万元
thus leading to an increase of 16.81 million yuan in the retail sales amount of social goods

而零售量报告期和基期相比
Compared with that in the base period, the retail volume in the report period

增加了30.34%
increased by 30.34%

使得社会商品零售额
Thus leading to an increase of 26.09 million yuan

增加了2609万元
In the retail sales amount of social goods

你可以用自己的语言来组织
you can organize the words on your own

这个无所谓
It doesn't matter

反正你只要把这几个关系
Anyway, all you have to do is

说清楚了就可以
just make these relations clear

这就是利用指数体系
That is the basic process of analysis

对刚才前面这么简单的数据
of the above simple data

进行分析的基本过程
through the index system

我想问一下
I would like to ask

有没有同学计算销售量总指数的时候
whether any of you obtained the general sales amount index

直接使用了149.88%
by directly dividing 149.88%

去除以115%得到的
by 115%

如果你用了这个方法来得到
If you use this method to obtain the result

从数据上来讲也没有错
there's nothing wrong with the data

但是从因素分析的思路上来讲
but from the perspective of factor analysis

你的过程是反了的
your process is reversed

因为你先假设指数体系成立了
because you assumed that the index system was satisfied in advance

你去推算了另外一个指数
and then you calculated another index

这其实是指数体系的另外一个功能
This is another function of the index system

所以大家检查一下
So please check

你们刚才所计算的过程
whether your calculation process

是不是和我的过程是一样的
is same as mine

一定要先左后右
Be sure to proceed from left to right

先相对数后绝对数
from relative quantity to absolute quantity

这三个指数一定是先单独计算出来的
These three indexes must be calculated separately first

用拉氏指数
by the algorithm of Laspeyres index

用帕氏指数的方法先单独编制
They are compiled separately by the algorithm of Paasche index

后面才形成两个数量上的对等关系
and then form two quantitative equivalences

因为我们一定是先有三个独立的指数
because we must have three independent indexes first

然后来验证它们关系是不是成立的
And then we'll see if their relationship can be established

好 这是利用指数体系
Well, this is the process of factor analysis

来进行因素分析的过程
through the index system

第二 我们来看一下
Second, let's take a look at

指数体系的应用
the application of index system

可以帮助我们进行同度量因素
It can help us determine

时期的确定
the periods of isometric factors

同学们看到这个描述的时候
When you listen to this description

是不是立马就会说
you may ask me right away

老师 你不是说数量指标指数
Teacher, you said that a quantitative index

用拉氏指数来计算
should be calculated by the algorithm of Laspeyres index

而质量指标指数用帕氏指数来计算吗
And a quality index should be calculated by the algorithm of Paasche index

为什么这里又冒出来一个同度量因素
Why do you come up with

时期的确定
the determination of periods of isometric factors here

对的 其实我们前面说的是
Yes, as we said before

数量指标指数和质量指标指数
with regard to the calculation of a quantity index or quality index

计算的一般的原则
the general principle lies in

是数量指标指数用拉氏指数来计算
that a quantity index is calculated by the algorithm of Laspeyres index

同度量因素被固定在基期
If an isometric factor is fixed in the base period

质量指标指数用帕氏指数来计算
the quality index is calculated by the algorithm of the Paasche index

同度量因素被固定在报告期
If an isometric factor is fixed in the report period

但是我们不排除有这样的情况出现
we can't rule this case out

在某些情况下
In some cases

它要假定数量指标指数
it is assumed that a quantity index

用帕氏指数的方法来算
will be calculated by the algorithm of Paasche index

那当然如果数量指标指数
Of course, if the quantity index is calculated

用了帕氏指数来算的话
by the algorithm of Paasche index

我们可以推算质量指标指数
we can calculate the quality index

这个时候就不能再使用帕氏指数来算
At this time, we can't use the algorithm of Paasche index any more

它就要采用拉氏指数来算了
but need to use the algorithm of Laplace index

因为这个我们在前面的
because it can be seen from the previous

分析过程里边已经看到
analysis process

两个指数如果同时都采用
If both indexes are calculated

拉氏指数来算
by the algorithm of Laspeyres index

或者同时都采用帕氏指数来算
or Paasche index

我们指数体系里面的数量关系
the quantitative relations in our index system

就不能成立了
can't be established

那么对我们的因素分析就会产生影响
Then it will have an impact on our factor analysis

也就意味着对我们来讲
It means that for us

其实是存在着两套指数体系的
there are two index systems

第一套指数体系
The first index system

也就是说数量指标指数是拉氏指数
That is to say, a quantity index is a Laspeyres index

质量指标指数是帕氏指数的
and a quality index is a Paasche index

这是我们常用的一套指数体系
This is an index system we often use

还有第二套指数体系
The second index system

是备用的指数体系
is a backup index system

它和我们常用的指数体系
It's quite opposite

正好是相反的
to the index system we often use

也就是说数量指标指数
That is to say, a quantity index

用了帕氏指数的方法
is calculated by the algorithm of Paasche index

而质量指标指数
while a quality index

用了拉氏指数的方法来进行计算的
is calculated by the algorithm of Laspeyres index

所以这一个应用是基于这个前提
So this application

来使用的
is based on this assumption

这是它的第二个应用
This is its second application

第三个应用则是帮助我们
The third application is to help us

进行未知指数的推算
calculate unknown indexes

如果刚才前面的习题里边
If in the previous exercise

有同学130.34%
any of you obtained 130.34%

是用了149.88%除以115%
by dividing 149.88%

来计算的话
by 115%

其实你就已经用到了
you already used

指数体系的这个功能了
this function of index system

未知指数的推算其实很简单
The calculation of unknown indexes is very simple

就是利用（公式如上）
Just use (formula as above)

如果告诉了你其中两个
If I tell you two of them

那另外一个指数不就可以
then another index can be calculated

通过这个体系来进行推算吗
through this system

我们来看一个简单的例子
Let's take a simple example

假如已知2015年12月份
If it is known that prices in December 2015

物价同比上涨1.6%
rose by 1.6% year on year

请问2016年元月1号的100块钱
then may I ask how much of January 1, 2015

相当于2015年元月1号的多少钱呢
is equivalent to 100 yuan of January 1, 2016

这种问题是不是在我们日常生活里边
In our daily life

好像也经常会遇到
it seems that we often meet this question

你马上会不会问
You may ask me immediately

老师 怎么只有一个数字
teacher, there's only one number

是只有一个数字吗
is there only one number

大家看一看
Let's take a look

按照我刚才前面的提示
Following my previous tips

我们首先应该将这个题目里边的数字
we should first express the numbers in the question

用它相应的符号来表达
with their corresponding symbols

第一个数字 物价同比上涨1.6%
The first number is a 1.6% year-on-year increase

那就告诉我们K{\fs8}p{\r}bar是等于多少
This tell us what is K{\fs8}p{\r}bar equal to

101.6%对不对
101.6%, right

那他再问2016年
Then you may ask again

元月1号的100块钱
how much of January 1, 2015

相当于2015年元月1号的多少钱
is equivalent to100 yuan of January 1, 2016

那其实是问如果我现在拿100块钱
You are asking about the change in purchasing power

和2015年元月1号拿100块钱
between 100 yuan of now

它的购买力的变动对不对
and 100 yuan of January 1, 2015

那购买力的变动当然就是
When you ask about the change in purchasing power, of course

问销售量的变动了
you are asking about the change in sales volume

所以这个100块钱就相当于
So the 100 yuan is equivalent to

我的销售额或者是我的购买额
my sales amount or my purchase amount

是没有发生变化
Yes, it does not change

因此K{\fs8}pq{\r}bar
So K{\fs8}pq{\r}bar

在这个题目里边就是等于100%了
In this question, is equal to 100%

所以这个数字是隐含的
So this number is implicit

大家一定要注意了
All of you must pay attention to it

那就意味着通过这个分析
That means that through the analysis

我们已经知道K{\fs8}pq{\r}bar
we already know that K{\fs8}p{\r}bar

等于100%
is equal to 100%

而K{\fs8}p{\r}bar等于101.6%
and K{\fs8}p{\r}bar is equal to 101.6%

那么我们的K{\fs8}q{\r}bar
So our K{\fs8}q{\r}bar

不就可以通过这个来计算吗
can be calculated in this way

K{\fs8}q{\r}bar计算的结果是
According to the calculation, K{\fs8}q{\r}bar

等于98.4%
= 98.4%

那就告诉我们2016年
That tells us that

元月1号的100块钱
100 yuan of January 1, 2016

其实相当于2015年元月1号的
in fact, is equivalent to

98块4毛钱
98.40 yuan of January 1, 2015

因为它们的购买力是同样的
because they have the same purchasing power

这就是利用来进行
This is a small example

来推算未知指数的小例题
to calculate unknown indexes

其它的情况我们遇到了一个体系里边
Take another example. In a system

告诉了两个指数
two indexes are told

那第三个指数都可以用这种办法
then the third index

去进行推算
can be calculated in this way

好 这就是指数体系的第三个应用
Well, this is the third application of the index system

进行未知指数的推算
--calculation of unknown indexes

到这里为止
Up to this point

关于综合指数体系的内容
about the contents of composite index system

我们就全部介绍给大家
I have introduced them all to you

这一讲的内容就是这样了
So much for this lecture