5.6.1 Average index index: first average and then compare 平均指标指数：先平均后对比在线视频

同学们 大家好
Hello, everyone

接下来我们学习第五讲的内容
Next, let's begin the fifth lesson

平均指标指数 先平均，后对比
about average index numbers: average before comparison

你是不是立马反应
You may react immediately

老师我们前面不是刚学过
teacher, we have learned earlier

平均数指数
average number indexes

怎么又来一个平均指标指数呢
why do you come up with average index numbers now

对 第四讲确实是平均数指数
Yes, indeed we learned average number indexes in the fourth lesson

但是大家还记得吗
But do you remember

平均数指数是属于总指数的范畴
average number indexes belong to the category of general indexes

它反映的是总量指标的变动
Because they reflect the changes of aggregate indexes

只不过从形式上
Only

采用了平均数的形式
general indexes are calculated

来计算总指数
in form of average numbers

而今天我们要讲的
But today we're going to learn

叫平均指标指数
Average index numbers

那就是说从反映的对象上
That is to say, in terms of objects reflected

它就有差异
They are different

前面是反映总量指标的变动
What we learned earlier reflects the changes in aggregate indexes

而我们现在反映的是
while what we're going to learn reflects

平均指标的变动
the changes of average index numbers

因为在我们的日常生活里面
Because in our daily life

经常也会面临着要反映
we often face circumstances where

平均指标变动的情形
the changes in average index numbers need to be reflected

那同样的可以通过计算
Similarly, this reflection can also be achieved

指数的形式来反映
in form of index calculation

那我们这一讲主要会包括
Today what we're going to learn mainly include

平均指标指数的定义
the definition

平均指标指数的种类
and types of average index numbers

以及它的指数体系这三个内容
and their index system

我们接下来看
Next, let's take a look at

平均指标指数的定义
the definition of average index numbers

平均指标指数是指
An average index number means

两个不同时期的
the result obtained

平均指标进行对比
by comparison of average indexes

所得到的结果
in two different periods

通常情况下这个平均指标的
Usually,

计算方法是加权算数平均数的形式
average indexes are calculated in form of weighted arithmetic averages

我们也同样地通过一个例子
Likewise, we also take an example

来展开对平均指标指数的学习
to learn average index numbers

首先我们看到
First of all, we see

表格里面的数字
the numbers in the table

表格里面的数字是
These numbers show

某制造业企业员工的薪酬表
the wages of employees from a manufacturing enterprise

那么我现在将工人
Now I divide these employees

分成了研发人员
into technicians

和一般的职工两大类
and general workers

我收集了报告期的人数
I collected the number of people in the report period

基期的人数
and the number of people in the base period

我用了f来表示
I use f to represent

收集了研发人员所对应的
the corresponding monthly average wage of

月平均工资（字符如上）
technicians collected (character as above)

有基期的 有报告期的
for both the base period and the report period

那从表格里边来看
Then from the table

我们可以看一下
we can see

研发人员的工资
that the average wage of technicians

基期是14000（元）
for the base period is 14,000 yuan

报告期是16500（元）
and that for the report period is 16,500 yuan

上涨了吗
Does it rise

涨了
Yes

我们计算它的指数是117%
The index calculated is 117%

说明工资是上涨了17%的
That means the wage is up 17%

那一般职员
For a general worker

他的工资从5000（元）上涨到6000（元）
his wage rises from 5,000 yuan to 6,000 yuan

那上涨的幅度比研发人员
an increase

还来得更高20%
20% higher than that of a technician

那一般来讲
Generally speaking

我们可能会认为
we may believe

研发人员的工资涨了
If the wages of technicians rise

一般职工的工资也涨了
so do those of general workers

那平均工资是不是也应该涨了
and also so does the average wage

那接下来我们就先来算一算
Next let's calculate

两个不同时期的平均工资
the average wages in two different periods separately

看看它是不是如我们所想的
to see if they

真的涨了
really rise as we think

基期的平均工资怎么算
How to calculate the average wage in the base period

当然用基期的总工资
Of course, it equals to the total wages in the base period

除以基期的人数就可以了
divided by the number of people in the base period

它当然等于（字符如上）
Of course, it equals to (character as above)

计算的结果是10400（元）
The result calculated is 10,400 yuan

报告期的工资
The average wage in the report period

可以用同样的方法
can be calculated

来进行计算
in the same way

还是用（字符如上）的形式来计算
That is, in the form of (character as above)

把数字代入进去
We put the numbers into the formula

计算的结果是10200（元）
Then the result calculated is 10,200 yuan

怎么样
All right

比基期增加了吗
Is it higher than that in the base period

10200（元）比10400（元）少了
10,200 yuan is less than 10,400 yuan

有点奇怪
It's a bit weird

明明每个人都涨了工资
It's obvious that everyone's wage rise

平均工资怎么还会减少呢
But why does the average wage drops

问题出在哪里了
What's the problem

是不是和我们一般的想象
It's a little different from

有点不同呢
our imagination, isn't it

这是不是出现了一个悖论呢
There is a paradox, right

这种悖论有一个特别的名字
This paradox has a special name

叫辛普森悖论
-- Simpson's paradox

如果大家感兴趣
If you're interested

可以搜集更多的资料来了解
you can collect more information to understand

辛普森悖论有关方面的知识
the knowledge about Simpson's paradox

那我们就要来分析分析
Then we need to analyze

这里面的原因了
the reasons for this phenomenon

平均工资它的变动
The change in average wage

是已经从数字上可以看出来的
can be seen from the number

那么平均工资的变动
So can the change in average wage also

是不是也可以通过指数的形式
be calculated

来计算呢
in form of index

那么我们可以用（字符如上）
Then we can use (character as above)

来反映平均工资的变动
to reflect the change of average wage

那（字符如上）
Then (character as above)

把数字代入进去以后
after putting the numbers in the formula

我们发现它的结果是98.08%
we find that the result is 98.08%

下降了1.92%
down 1.92%

减少的绝对数很快可以看得出来
The reduced absolute number will be visible soon

200块
200 yuan

那刚才我们也说了
We said just now that

我们接下来就要分析
We are going to analyze

这200块钱的下降
the cause of

是由什么原因所造成的
the reduction of 200 yuan

那么在这个下降的过程里边
So in the process of reduction

我们仔细观察平均工资的
let's take a closer look at

计算的式子可以发现
the calculation formula for average wage

它受到两个因素的影响
It is influenced by two factors

第一个就是我们符号x代表
The first one is our symbol x that stands for

月平均工资
the monthly average wage

还有一个符号就是f
and the other one is the symbol f

只有这两个符号
Only these two symbols

当然从算术平均数的计算来看
Of course, from the calculation of arithmetic average

起权数作用的
The weigher

本质上应该是相对数
in essence, should be the relative number

也就是我们说的结构
That is, the structure we said

而不是这个f本身
instead of f itself

所以这两个影响因素
So about these two factors

我们近一步的可以分解为
we can further decompose them like this

一个受x也就是月平均工资的影响
One is affected by X, the average monthly wage

一个分解为受结构的影响
The other is affected by the structure

也就是研发人员
That is, the proportion of

一般职工在总职工里边
the number of technicians in general workers

所占的比重来影响
to that of all employees

这样从思路上面看起来
Therefore, in terms of idea

非常类似于我们前面在
it is very similar to

综合指数计算里边
the calculation of composite indexes that we learned earlier

销售额变了
If the sales amount

那它的构成有两个要素
consisting of two factors

一个是p一个是q
p and q changes

那销售额的变动只能
Then the change in sales amount can only

要不由p来影响
be affected by p

要不由q来影响
or q

从结构上来看
In terms of structure

它非常类似于这个结构
it's very similar to this structure

只不过现在从形式上
but now in form

来得更加地复杂
is more complicated

它是平均数除平均数了
It equals to an average divided by another average

所以参照前面的思路
So regarding the previous idea

我们可以将平均指标指数
we can introduce

来介绍它的种类
the types of average index numbers

第一个作为总变动指数的变形
The first type are transformed from general change indexes

我们称之为可变构成指数
We call them variable construction indexes

可变构成指数分子分母
The numerator and denominator of an variable construction index

一个是报告期一个是基期
correspond the report period and the base period respectively

两个因素的时期
The periods corresponding to two factors

同时都在发生变动
are changing simultaneously

也就是刚才
That is, just now

咱们所计算的平均工资的变动了
the average wage we calculated has changed

从形式上面来看
In terms of form

和我们前面的总变动指数
it is very similar

也就是营业额指数
to the general change index mentioned above

很类似
That is, the sales amount index

两个因素
Two factors

同时都在变
are changing simultaneously

那么这个我们就可以把它
Then we can regard it

看成是总变动指数的变形
as a transformed form of general change index

从数据上面来看
In terms of data

刚才我们已经念过一遍
we have read it just now

相对数上面是下降了1.92%
In terms of relative number, it drops by 1.92%

绝对数上面
while in terms of absolute number

是减少了200块钱一个人
it is reduced by 200 yuan/person

好 接下来我们就来进行分解
OK, let's decompose it

分解的时候既然可变构成指数
Since the variable construction index

它是总变动指数的变形
is a transformed form of general change index

那么我们在将可变构成指数
when we are decomposing

去进行分解
the variable construction index

一个是x变化所带来的影响
into the impact brought about by the change of x

一个是（字符如上）变动
and the impact brought about by

所带来的影响的时候
the change of (character as above)

也可以参照
we can also refer to

前面的指数的编制原理来进行
the compilation principle of indexes we learned earlier

比如 如果我们要反映的是
For example, if we want to reflect

结构的变动
the impact

所带来的影响
brought about by the change of structure

那我们就要先分析分析看
then we need to analyze first

结构在我们这个指数的构成里边
whether the structure is in the composition of the index

它是属于数量指标
a quantity index

还是属于质量指标
or a quality index

那结构如果确定了
If structure is determined

另外一个跟它对应的就是x
it will correspond to X

也就是月平均工资
That is, the average monthly wage

在这两个指标本质上来看
In essence, of these two indexes

一个是平均数
one is the average number

一个是比重
the other is the proportion

也就是我们的一个相对数
which is a relative number

从指数的归属上面来看
In terms of index attribution

都属于质量指标
they are all quality indexes

但是我记得在前面
But I remember when we

讲数量指标指数
were classifying

和质量指标指数的
quantity index numbers

分类的时候
and quality index numbers earlier

我们也讲了
we have learnt that

这个指标的定性不是绝对的
the property of indexes is not absolute

它是相对的
but relative

要看它在整个构造里边
It depends on

另一个指标
the property of another index in the whole structure

和它相比的性质
in comparison with it

在这两个指标的比较里边
In the comparison of these two indexes

x也就是月平均工资
X, the monthly average wage

它属于质量指标
belongs to a quality index

而（字符如上）
but (character as above)

这一次它属于数量指标
This time it's a quantity index

因此这一次如果我们要反映
So this time, if we want to reflect

结构变动所带来的影响
the impact brought about by the change of structure

当然首先它自己的下标
of course, first of all, the subscript

在分母里面一定是0
must be 0 in the denominator

在分子里面一定是1
and 1 in the numerator

报告期除以基期
That is the report period divided by that in the base period

而x这一次
And this time X

就应该充当同度量因素的作用
should act as an isometric factor

它的时间就应该固定下来
The time should be fixed

固定在什么时候呢
When is it fixed

既然刚才咱们分析
Since we just analyzed

（字符如上）
(character as above)

它是类似于数量指标
it's similar to a quantity index

那么同度量因素 质量指标
the isometric factor, quality index

就应该被固定在基期
should be fixed in the base period

那它就可以看成是
Then it can be seen as

拉氏指数的变形了
a transformed form of Laspeyres index

按照这样的思路去变形
If you transform according to this idea

我想你不容易出错
I don't think you are easy to make mistakes

也说明前面综合指数的基本原理
It also shows that you have had a good command of

掌握得好
the basic principles of composite indexes we learned earlier

因此我们可变构成指数
So our variable construction index

分解第一个得到的结构影响指数
is decomposed into the structural impact index first

反映结构的变动
which reflects

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

那么结构影响指数
Then the structural impact index

它相当于是
corresponds to

数量指标指数的变形
the transformed form of quantity index number

注意基本原理还是拉氏指数
Please note that the basic principle is still Laspeyres index

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

来看一下
Let's take a look at

数据计算的结果
the results of data calculation

我们仍然可以利用
We can still use

表格里面的数字
the numbers in the table

首先我们可以将分子（字符如上）
First, we can set the numerator (character as above)

令它等于（字符如上）
to be (character above)

一个假想时期的平均工资
the average wage in an assumption period

把数字代入进来计算的结果是
Putting the numbers in the formula

8600（元）除以10400（元）
8,600 (yuan) ÷ 10,400 (yuan)

等于82.69%
= 82.69%

分子减去分母则可以反映
numerator minus denominator can reflect

结构变动给平均工资所带来的影响
the impact brought about by the change of structure on the average wage

从数字上来看
In terms of numbers

使得每个人的平均工资
everyone's average wage

是下降了1800（元）的
drops by 1,800 yuan

也就是说
In other words

排除工人月平均工资的变动
excluding the change in the average monthly wage of employees

纯粹由于工人结构的影响
only due to the impact of employee structure

使得总平均工资是下降了17.31%
the total average wage is reduced by 17.31%

人均减少了1800（元）
an average decrease of 1,800 yuan/person

这样第一个指数也就是
So the first index

影响因素里面的第一个指数
that is, the first index among influencing factors

我们就给它分解出来了
has been decomposed

第二个指数
As for the second index

我想大家都已经猜到了
I think you've already guessed it

肯定是质量指标指数的变形
It must be a transformed form of quality index number

因为刚才我们已经有一个
Because we already get

数量指标指数的变形
a transformed form of quality index number

那质量指标这一次
So this time the quality index

它就应该是对应x
should corresponds to X

那分子毫无疑问x{\fs8}1{\r}
Undoubtedly, the numerator is x{\fs8}1{\r}

分母毫无疑问x{\fs9}0{\r}
and the denominator is x{\fs9}0{\r}

那f的时间也应该被固定下来
The time corresponding to f should be fixed

所有的f的时间
All time corresponding to f

这一次都应该被固定在报告期
should be fixed in the report period this time

因为它是帕氏指数的变形
because it's a transformed form of Paasche index

所以我们就可以得到
So we can get

固定构成指数
an invariable construction index

你可以看出来
You can see that

为什么叫固定构成指数
why is it called invariable construction index

因为结构是固定下来的
Because the structure is fixed

那它可以简化成（字符如上）
Then it can be reduced to (character as above)

它相当于质量指标指数的变形
It is equivalent to a transformed form of quality index number

采用帕氏指数同度量因素
Which, by use of isometric factor for Paasche index

被固定在报告期
is fixed in the report period

同样的我们可以把数据代入进去
In the same way, we can put the data in the formula

计算固定构成指数
to calculate relative number and absolute number

所对应的相对数和绝对数
corresponding to invariable construction index

分别是118.6%
The results are 118.6% respectively

从绝对数上面来看
In terms of absolute number

它使得平均工资
it makes the average wage

每个人增加了1600（元）
rise by 1,600 yuan/person

那这个指数也可以做简短的
Then we can also make a brief

文字说明
literal description on this index

排除工人结构的变动
Excluding the change in employee structure

纯粹由于月平均工资的影响
only due to the impact of the monthly average wage

使得总平均工资上升了18.6%
the total average wage rise by 18.6%

平均每个人增加了1600（元）
an average increase of 1600 yuan/person

这样的话
In that case

我们就利用指数编制的基本原理
We can take the basic principle of index compilation

基本原理还是来自于综合指数
which is still based on composite indexes

数量指标指数
The quantity index number

用拉氏指数计算
is calculated through Laspeyres index

同度量因素被固定了基期
If the isometric factor is fixed in the base period

而质量指标指数用帕氏指数来计算
the quality index number should be calculated through the Paasche index

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

如果我们现在来捋一捋
If we can sum up

指数的计算原理
the principles of index calculation

我们发现从前到后
we find that from beginning to end

我们的指数计算原理
our principles of index calculation

主要都来自于综合指数
are mainly based on composite indexes

我们一起全部捋一下
Let's sort out all

综合指数
composite indexes

数量指标指数用拉氏指数计算
Quantity index numbers should be calculated through Laspeyres index

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

它经过变形以后
After transformation

总指数变形是得到
a general index turns to be

加权的算术平均数指数
a weighted arithmetic average index

平均指标指数
An average index number

它也可以变形
can also be transformed

它变形以后得到的是
and it turns to be

结构影响指数
a structural impact index

所以从数量指数的出发
So from the quantity index number

它可以得到一条线
it can get a line

从质量指标指数
From the quality index number

也可以得到一条线
it can also get a line

质量指标指数
The quality index number

用帕氏指数来计算
should be calculated through Paasche index

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

变形以后可以得到一个
After transformation, it turns to be

加权调和平均数指数
a weighted harmonic average index number

和固定构成指数
and an variable construction index

所以指数计算从前到后
So in the whole calculation process of index calculation

其实就只有这条基本原理
This is the only basic principle

这是我们指数这一章的主线
It is also the mainline of this chapter on indexes

如果大家善于总结
If you are good at summarizing

我想在你们前几次课的学习里面
I believe in previous lessons

说不定已经给它总结出来了
You might have summed up it

所以虽然看起来指数这一张
So even though it seems hard to

从前到后有这么多公式
remember so many formulas

看似很难记
in this chapter on indexes

但其实基本原理都只有这一个
This is the only basic principle

你就记住那六个字就好了
Just remember these six words

我们通常念
We usually call them

“数拉基”，“质帕报”
"number, Laspeyres and base", "quality, Paasche and report"

有这六个字
Only these six words

就可以帮你把指数全部串起来了
can help you string up the knowledge about indexes

这就是平均指标指数的
That is, three independent forms of

三个独立的形式
average index number

有可变构成指数
variable construction index

有结构影响指数
structural impact index

有固定构成指数这三个
and invariable construction index

细心的同学已经发现
Careful students have found that

总平均工资减少了200块
the total average wage is reduced by 200 yuan

而结构影响指数带来的是
What the structural impact index brings is

负的1800块
- 1,800 (yuan)

固定构成指数带来的是
What the invariable construction index brings is

增加了1600块
1,600 (yuan)

加起来不正好是减少了200块吗
The result of adding the two is 200 yuan

没错
Yes

平均指标指数数量上
Average index numbers

也具有这个等量关系
are also quantitatively equivalent

那也就意味着指数体系
That means the index system

依然是有效的
is still valid

既然刚才在讲课的时候
Since, as I said just now

它们都是从综合指数的
they are all transformed from certain indexes consisting of

某一个指数出发变形来到的
a composite index

大家也可以想象
You can imagine

从构造上来讲
In terms of structure

它应该也会有相对数和绝对数上的
they should also be

对等关系
equivalent in relative number and absolute number

那相对数上面
In terms of relative number

它们依然有连乘的关系
they still have a multiplication relationship

绝对数上面也有这个求和的关系
In terms of absolute number, they also bear a summation relationship

所以从数量上面来看
So in terms of quantity

它依然会有这两个等式
these two equations are still satisfied

98.08%＝82.69%×118.6%

从绝对数上面来看
In terms of absolute number

-200（元/人）=-1800（元/人））+1600（元/人）
-200 (yuan/person) = -1,800 (yuan/person)) + 1,600 (yuan/person)

这就是平均指标指数体系
This is the average index number system

它依然帮助我们进行
It still helps us

因素分析
with factor analysis

那总体来说
Well, on the whole

我们可以用文字把它描述一下
we can describe it in words

整个指数体系
the whole index system

排除工人月平均工资的变动
Excluding the change in the monthly average wage of employees

纯粹由于工人结构的变动
only due to change of employee structure

使得总平均工资下降了
the total average wage is reduced by

17.31%

人均减少了1800（元）
an average decrease of 1,800 yuan/person

排除工人结构的变动
Excluding the change in employee structure

纯粹由于月平均工资的影响
only due to the impact of the average monthly wage

使得总平均工资上升18.6%
the total average wage rise by 18.6%

人均增加1600（元）
an average increase of 1,600 yuan/person

两个因素共同作用的结果
The interaction of two factors

使总平均工资下降了1.92%
leads to a 1.92% drop in the total average wage

人均减少了200（元）
an average decrease of 200 yuan/person

这也可以帮助我们利用指数体系
This can also help us use the index system

进行因素分析
to conduct factor analysis

因此从头到尾我们总结一下
So let's summarize the whole process

我们学习的指数体系有三套
We have learned three sets of index system

一 综合指数指数体系
The first is the composite index system

第二平均数指数体系
The second is the average number index system

这两套都是针对总量指标
These two sets are designed for

来进行分析的
analysis of aggregate indexes

第三套则是我们刚刚学过的
The third is the average index number system

平均指标指数体系
that we just learned

它反映的是平均指标的变动
It reflects the changes in average indexes

以及造成它变动的因素
and the analysis of

来进行分析
their influencing factors

所以这就是指数在编制的过程里边
So this is

最核心的内容
the core content of index compilation

这一讲的内容就是这样
That's what this lesson is about