5.2.1 Comprehensive index: first comprehensive and then compare 综合指数：先综合后对比在线视频

好 同学们
Hello everyone

我们接着来学习
now let's start

指数第二讲的知识
Lecture 2

综合指数
composite index

这一讲我们会学习综合指数的概念
In this lecture, we will learn the definition of composite index

以及综合指数的编制
and its compilation

首先来看一下
First let's take a look at

综合指数的概念
the definition of composite index

综合指数是指用两个总量指标
Composite index refers to an index

对比形成的指数
formed by comparing two total amount indicators

在总量指标中包含两个
There are two or more factors

或两个以上的因素
in the total amount indicators

指数计算中仅观察被研究因素的变动
but only the changes of the factor under study are observed

它的特点是先综合后对比
The calculation follows the steps of synthesis first and then comparison

接下来我们来介绍
Next, let's take a look at

综合指数的编制
the compilation of composite indexes

来看它的编制是如何体现
and see how the compilation follows

先综合后对比的
the steps of synthesis first and then comparison

我们来以下面的例子
Here is an example

展开综合指数的编制
in which we are to compile the composite index

假如我们现在要了解的是
Suppose we are to investigate

天猫2015年双十一和双十二
changes in the quantitative characteristics

促销活动中
of some of Tmall's products

要了解天猫的商品的数量特征的
during the Double Twelve promotion of Tmall in 2015

变动情况
compared with the data during the Double Eleven promotion of the same year

为了了解天猫的销售量和
In order to find out the fluctuations

销售价格的波动情况
in the sales volume and sales price

我收集了部分商品
I have collected data of some of the products

在我们黑板上的数据里面
on the blackboard

我收集了太平鸟某款女羊毛大衣
I collected data on a PeaceBird women's wool coat

创维电视 还有骆驼的男鞋
a Skyworth TV, Camel men's shoes

飞利浦吸尘器
a Philips vacuum cleaner

以及海尔的某一款电冰箱
and a Haier refrigerator

那么它们在双十一和双十二期间的
I have collected data on their sales volumes and sales prices

销量以及价格我都一一收集到了
during the Double Eleven and Double Twelve promotions

在表格中有了这些数据
With these data in the table

我们可以尝试着来分析
we can compare the turnover

天猫商城双十二和双十一相比
(of the 5 commodities) of Tmall

它的（5种商品）营业额
during the Double Twelve promotion

发生了什么样的变化
and the Double Eleven promotion

第二
Secondly

我可以了解天猫（5种）商品的销售量
we can find out changes in the sales volume

发生了什么样的变化
(of the 5 commodities) of Tmall

由于销售量的变化
and how much is the impact

那么它对于营业额又造成了
caused by changes

多少的影响
in the sales volume

第三 我还可以利用这些数据
Thirdly, with these data

分析天猫（5种）商品的销售价格
we can also find out the changes

发生了怎样的变化
in the sales prices (of the 5 commodities) of Tmall

那么由于价格的变化
and the impact

又对天猫的营业额产生了
of price changes

多大的影响
on the turnover of Tmall

那么一般情况下
In general

我们在计算的时候
we keep two decimal places

都保留两位小数
in calculation

接下来我们就来看一下
Next, let's see

这三个任务
how to perform

应该怎么样来完成呢
these three steps

首先我们来看第一个
First let's figure out

总变动指数
the total index of change

如果要了解总变动指数
If we want to figure out the total index of change

通常情况下
or here

我们可以把它称之为营业额总指数
we can call it the total index of turnover

那么我们可以先来分析一下
Let's see

营业额总指数应该如何来计算呢
how to work out the total index of turnover

我们从前面的学习知道
As we've learned in the previous lecture

指数是反映报告期和基期相比的
index reflects the fluctuations of quantity

数量的波动情况
between the given period and the base period

那就意味着我们需要找到
It means that

报告期的营业额和基期的营业额
we need to compare

来进行比较
the turnover of the given period

基期的销售额
and the base period

那就是p{\fs8}0{\r}×q{\fs8}0{\r}
Turnover in the base period is p{\fs8}0{\r}×q{\fs8}0{\r}

报告期的销售额是p{\fs8}1{\r}× q{\fs8}1{\r}
and turnover in the given period is p{\fs8}1{\r}× q{\fs8}1{\r}

一种商品营业额的变动
Changes in the turnover of a commodity

可以用p{\fs8}0{\r} q{\fs8}0{\r}
can be expressed as p{\fs8}0{\r} q{\fs8}0{\r}

变动的p{\fs8}1{\r} q{\fs8}1{\r}来展示
and p{\fs8}1{\r} q{\fs8}1{\r}

但是我们现在需要有五种商品
But we now need to find out the general changes

营业额的综合变动
in the turnover of the five commodities

那么现在问题来了
So here is a question

营业额这个指标
can the indicator of turnover

能直接求和吗
be summed up directly

能不能
Yes, or not

大家分析一下
Let's think about the answer

对
Yes

根据我们在第一讲里边的提示
According to what we learned in lecture 1

类似于销售额
although indicators such as sales

类似于营业额 总成本
turnover, total costs

总费用这一类指标
and total expenses

虽然它们也属于数量指标
are quantitative indicators

但是由于它们是用价值量计量的
they are measured by value

因此它们在不同的商品之间
so they can be directly summed up

是可以直接求和的
between different commodities

因此五种商品基期的营业额
So the turnover of the five commodities in the base period

可以用五种商品各自的营业额
can be obtained

直接求和来得到
by directly summing up the turnovers of the five commodities

那当然报告期也可以用
Surely, turnover of the given period

同样的方法来计算
can also be figured out in the same way

因此我们就可以用（字符如上）
So, we can use (character as the above)

来代表基期的营业额
to represent the turnover of the base period

用（字符如上）来代表报告期的营业额
and use (character as the above) to represent the turnover of the given period

也就意味着其实在计算营业额
So we can easily collect

总指数的时候
the data needed

我们是非常顺利地就可以采集到
for the calculation

我们想要的资料
of the total turnover index

因此
So

我们可以来计算指数
By having sales of given period

用报告期的销售额
divided by sales in the base period

除以基期的销售额
we can figure out the index

也就像我们黑板上所显示的
It can be calculated via the formula as shown on the blackboard

（公式如上）来反映
(formula as the above)

同时我们还可以计算
Meanwhile, we can also figure out

报告期和基期相比
the change in turnover

它的营业额发生了多少的变动
between the given period and the base period

当然这就是从绝对数的角度
This is a method

来分析销售的变动情况
to analyze changes in sales

计算的方法
from the perspective of absolute numbers

也在黑板上用（公式如上）
which can be achieved via the formula

就可以实现
(the formula is as above) as shown on the blackboard

那具体的数字
For specific numbers

我们可以回到表格里面
we can go back to the table

把p{\fs8}0{\r} q{\fs8}0{\r}
and figure out the numbers corresponding to p{\fs8}0{\r} q{\fs8}0{\r}

把p{\fs8}1{\r} q{\fs8}1{\r}所对应的数字
and p{\fs8}1{\r} q{\fs8}1{\r}

一一计算出来
one by one

比如太平鸟女羊毛大衣
For example, for the PeaceBird women wool coat

它的基期的销售额是359898元
sales in the base period is CNY 359,898

它的报告期的销售额是121506元
sales in the given period is CNY 121,506

对应的基期的综合是2474927元
the corresponding sales total in base period is CNY 2,474,927

对应的报告期的营业总额是
the corresponding total turnover in base period is

2179209元
CNY 2,179,209

那有了这个汇总的数据
With these data

我们很快可以计算营业额总指数
we are able to figure out the total index of turnover

通常营业额总指数
Generally, the total index of turnover

用大写的（字符如上）来表示
is expressed in uppercase (character as the above)

它的计算的方法用报告期的营业额
It is equal to the turnover of the given period

除以基期的营业额
divided by the turnover of the base period

也就是我们说的（公式如上）
which is what we’ve mentioned (formula as the above)

把表格中的数字代入进来
Plug the numbers in the table into the formula

计算的结果88.05%
the result obtained is 88.05%

通常指数是用百分数来表示的
Usually, indexes are expressed in percentage

那么88.05%说明了什么呢
But what does 88.05% mean

说明天猫（5种商品）双十二和双十一相比
It means that the turnover (of the 5 commodities) of Tmall has dropped

它的营业额是下降了
during Double Twelve promotion, compared with the that in Double Eleven promotion

对不对
right

下降了多少呢
How much is the drop

下降了11.95%
It has dropped by 11.95%

对吧
right

那这样通过这个指数
Through this index

我们就可以了解天猫商城（5种商品）在
we get to know the changes in sales (of the 5 commodities) of Tmall

双十二和双十一期间
during the Double Twelve promotion

它的销售额的变动的情况
Compared with that in the Double Eleven promotion

那么下降11.95%意味着
So with a drop of 11.95%

它的总额上面减少了多少呢
how much is the reduction in turnover

那我们可以进一步计算
We can make further calculation

（公式如上）
(formula as the above)

得到的结果是报告期和基期相比
The result is that

它的营业额减少了
its turnover has decreased by CNY 295,718

295718元
compared with the base period

可以得到一个基本的结论
We can draw a conclusion that

天猫商城双十二和双十一相比
the turnover of Tmall during the Double Twelve promotion

它的营业额
has decreased by CNY 295,718

下降了295718元
compared with that in Double Eleven promotion

那通过这个指数
Through this index

我们就可以反映营业额的变动
the change in turnover can be reflected

那么营业额发生变动
But what are the causes

它可能由什么原因来造成呢
of change in turnover

一般来讲要不 是销售量发生了变化
Generally speaking, it is caused by either changes in sales volume

要不 是销售价格发生了变化对不对
or changes in sales price, right

所以我们接下来就可以来分析
So, next, we can analyze

这个销售额的变动里边
how much of the change in sales

有多少是销售量变动引起的
is caused by changes in sales volume

有多少是销售价格变动来引起的
and how much is caused by changes in sales prices

接下来我们来看
Now, let's proceed to

数量指标指数的计算
the calculation of quantitative indicator index

在这里具体的我们可以把它称之为
Here we can call it

销售量总指数
the total index of sales volumes

还是刚才前面的数据
Still, we will use the previous data

还是那五种商品双十一和双十二的
the data of sales and prices of the five commodities

销量以及价格的资料
during the Double Eleven and Double Twelve promotion

那么如果我现在要计算五种商品
So if I want to figure out the comprehensive change in sales volumes

销售量的综合变动程度
of the five commodities

也就意味着我要算一个销售量总指数
I will need to work out a total index of sales volumes

我们还是可以像刚才那样
Like what we did previously

先来分析一下
Let's see

如果我要反映某一种商品的
if I want to find out the changes in sales volume

销售量的变动
of a certain commodity

那么计算
then I need only to

个体销量指数就可以了
figure out the individual index of sales

那五种商品综合在一起的
As we've mentioned in the first lecture

销售量变动
changes in the synthesized sales volume

刚才第一讲里边我们也提过
of the five commodities

它是不能够直接通过
cannot be directly figured out

（公式如上）来实现的
via (formula as the above)

因为q的计量单位各不相同
because the measurement unit of q is different

对不对
right

那这种情况下面
In this case, how can we follow the

我们怎么样来完成先综合后对比
steps of synthesis first and then comparison

其实所谓先综合后对比
In fact, the so-called synthesis first and then comparison steps

刚才在营业额总指数里边
as we've found out

已经体会到
when calculating the total index of turnover

就是我们先要求报告期的总量
refer to figuring out the total amount of the given period first

再求基期的总量
and then to work out the total amount of the base period

然后用报告期的总量
Finally, the total amount of the given period

来除以基期的总量
is divided by the total amount of the base period

那么Σq{\fs8}1{\r} Σq{\fs8}0{\r}此路不通
So if Σq{\fs8}1{\r} and Σq{\fs8}0{\r} are not working,

那我们怎么办呢
what should we do

一定要找到一种方法
We shall find a way

来结果先综合的问题
to solve this problem first

对不对
right

所以接下来我们来介绍一下
So next we will discuss

解决问题的办法
the solution to the problem

既然q直接不能综合
Since q cannot be synthesized directly

那对于我们来讲
we are only able to

就只能采取迂回的线路
take an indirect method

也就是说我能不能通过引入
That is to say, can we

某一个桥梁或者
use a bridge

某一个媒介的方式
or a medium

把它转换成能够求和的指标呢
so that it is converted into a summable index

来看一下我们整个系统里边
Let's see, in the entire system

q不能被直接求和
q cannot be summed up directly,

p也不能被直接求和
neither can p

对不对
right

但是有一个指标
But there is an indicator

能被直接求和
can be summed up directly

它就是
it is

对
yes

营业额
it is the turnover

那我们是不是可能通过将q
Can we convert

转换成营业额的形式
q into turnover

就可以完成求和的过程呢
and finish the step of summation

对
Yes

在理论上面
theoretically

我们确实有是这样来处理的
we do deal with it this way

所以我们解决思路的第一步是
So, the first step in our solution

引入一个媒介
is to introduce a medium

通常情况下
Normally

我们把引入的这个媒介
the medium introduced

称之为同度量因素
is called the isometric factor

而把我们准备分析的这个指标的
and the change of the indicator which we are to analyze

变动称之为指数化因素
is called the indexation factor

比如在我们这一次的分析里边
For example, here

指数化因素
the indexation factor

就是销售量
is the sales volume

那么销售量不能直接求和
Since sales volume cannot be summed up directly

我要把它转换成
We need to convert it

营业额
into turnover

我必须引入一个媒介
We shall introduce a medium

这个媒介就是销售价格
which is the sales price

那么我们就把销售价格
And here the sales price

称之为同度量因素
is called the isometric factor

引入这个媒介以后
After introducing this medium

我们的销售量就转换成营业额
sales volume is converted into turnover

那营业额这个数据
Since turnover

它是可以被直接求和的
can be summed up directly

对不对
right

因此第一步综合的问题
so the first step of synthesis

是通过这样的方法
is performed

来解决的
in this way

同度量因素
The isometric factor

是指这样的一个媒介
is a medium that

使同度量指标转换成同度量
converts the different measurements of an index into the same measurement

同度量就是同样的计量单位
The same measurement means the same unit of measurement

那就可以直接被求和了
so the data can be summed up directly

所以它起来的是
So it plays the role

这样一个媒介的作用
of a medium

那完成了第一步综合
Here is first step of synthesis

接下来就是对比
the next step is comparison

对不对
right

那是不是意味着我们接下来
Does it mean that

只要（公式如上）
as long as we follow (formula as the above)

计算的就是销售量总指数
we can figure out the total index of sales volumes

（公式如上）
(formula as the above)

这个指数形式
Are you familiar

我们是不是有点熟悉它呢
with the form of this index

对
Yes

它就是我们刚刚介绍的
It is the total index of turnover

营业额总指数
we’ve just discussed

对不对
right

那问题出在哪里呢
So what is the problem

销售量总指数
The total index of sales volume

应该单独只反映销售量的变动
should reflect changes in sales volume only

对不对
right

那价格就不能跟着一起来动
Then the price shall not change with it

所以第二步
So after finishing

完成了综合以后
the second step

我们要单独反映指数化因素的变动
to reflect the changes in the indexation factor separately

那就要把同度量因素
we shall fix the time

时间给固定下来
of the isometric factor

当然我们既可以把它的时间
Surely, we can either fix its time

固定在基期
at the base period

也可以把它的时间都固定在报告期
or fix it at the given period

这两种是最常见的
These two methods are the most common

甚至也可以选择将同度量因素
We can even fix the time of the isometric factor

固定在中间的某一个时间段
at a certain period in the middle

这都是可行的
All are feasible

但是最常用的是两种
But two of them are the most common method

一种是固定在基期的
One is to fix it at the base period

我们通常把它称之为拉氏指数
and the index worked out in this way is usually called the Laspeyres index

它是由德国的统计学家Laspeyres
because this method is created by

在1864年的时候所提出来的
a German statistician whose name is Laspeyres in 1864

而把同度量因素
The other method is to fix the time of the isometric factor

固定在报告期的指数
at the given period

通常称之为帕氏指数
and the index worked out in this way is usually called the Paasche index

它是由德国的另一个统计学家
This method was proposed by Paasche

Pacsche在1874年的时候
another German statistician

所提出来的
in 1874

好
Well

我们刚才提到了拉氏的
we now have the Laspeyres

销售数量指数和
Laspeyres index of sales volumes

帕氏的销售数量指数
and the Paasche index of sales volume

这个地方提醒大家一下
Here please be noted that

通常我们在写综合指数的时候
in the written form of a composite index

采用的方法是指数化因素在前
the indexation factor is in the front

同度量因素在后
and the isometric factor is behind it

什么意思呢
What does that mean

比如我们在写
For example, when we write

拉氏的销售量指数的时候
a Laspeyres index of sales volumes

那我们写（公式如上）
it is (the formula is as above)

先把架子搭好
We set up the frame first

再把它们的时间放上去
and then put in the time

那q的时间分子是1
The numerator of the time of q is 1

分母是0
and its denominator is 0

p的时间是固定在0 0
while p is fixed at 0 and 0

接下来我们就来看一下
Next, let's see

这两种指数利用我们刚才的数据
what will be the results of the two indexes

所计算的结果
figured out

会是如何
using the previous data

那为了完成拉氏指数
To work out the Laspeyres index

或者是帕氏指数的计算
or the Paasche index

从刚才的计算式子里面来看
according to the formula just now

我们需要在表格里边
we need to add some information

补充一些信息
into the table

比如拉氏指数的计算
For example, the calculation of the Laspeyres index

是Σq{\fs8}1{\r}p{\fs8}0{\r}除以Σp{\fs8}0{\r}q{\fs8}0{\r}
is Σq{\fs8}1{\r}p{\fs8}0{\r} divided by Σp{\fs8}0{\r}q{\fs8}0{\r}

刚才咱们算营业额总指数的时候
When calculating the total index of turnover just now

已经算好了p{\fs8}0{\r}q{\fs8}0{\r}
we have figured out p{\fs8}0{\r}q{\fs8}0{\r}

已经算好了p{\fs8}1{\r}q{\fs8}1{\r}
and p{\fs8}1{\r}q{\fs8}1{\r}

但是并没有q{\fs8}0{\r}p{\fs8}1{\r}的组合
but we have not the combination of q{\fs8}0{\r}p{\fs8}1{\r}

也没有p{\fs8}0{\r}q{\fs8}1{\r}的组合
nor of p{\fs8}0{\r}q{\fs8}1{\r}

所以我们需要在表格里面
So we need to supplement these two combinations

再把这两个组合补充上来
in the table

并计算它们的总量
and figure out their total

有了这个表格里面的这些信息以后
With the data in this table

接下来我们就可以来算拉氏指数
we can then calculate the Laspeyres index

和帕氏指数
and the Paasche index

当然这里都是计算的销售量总指数
Surely here it is the total index of sales volume that is calculated

把表格中的数字代入到
We plug the numbers in the table

拉氏指数的计算式子里边
into the formula of the Laspeyres index

我们来看它的结果
and see its result

那Σq{\fs8}1{\r}p{\fs8}0{\r}
We see Σq{\fs8}1{\r}p{\fs8}0{\r}

是2261659元
is equal to CNY 2,261,659

Σq{\fs8}0{\r}p{\fs8}0{\r}是2474927元
and Σq{\fs8}0{\r}p{\fs8}0{\r} is equal to CNY 2,474,927

那把分子除以分母
After the numerator is divided by the denominator

可以得到91.38%
we get 91.38%

这个数字计算出来告诉我们
This result tells us that

如果用拉氏指数来计算
if we use the Laspeyres index for calculation

天猫商城（5种商品）双十二和双十一相比较
the sales volume (of the 5 commodities) of Tmall
during the Double Twelve promotion

销售量是减少了
has dropped, compared with that in the Double Eleven promotion

对不对
right

减少了多少呢
How much is the drop

减少了8.62个百分点
It is 8.62%

那么它的销售量减少
Since the sales volume has dropped

如果价格没有变
if the prices are the same

是不是会导致营业额减少呢
then the turnover will be reduced, right

肯定对的
Absolutely

那么我们可以进一步计算
Then we can further calculate

由于销售量的减少
the change in turnover

所导致的营业额的变动
due to the decrease in sales volume

用报告期减去基期的数字
which is figured out by subtracting the turnover of the base period from that of the given period

那就是用（公式如上）
using (formula as the above)

那么结果是-213268元
and the result is CNY -213,268

也就意味着由于销售量下降
This means that due to decline in sales volume

价格保持不变
when the price remains the same

那么营业额就发生了一个波动
a fluctuation in turnover will occur

这个波动是减少了213268元
In this fluctuation, the turnover is reduced by CNY 213,268

那同样地
Similarly

我们可以把表格中的数字
we can plug the numbers in the table

代入到帕氏指数的计算式子里面
into the formula of the Paasche index

结果是87.11%
and its result is 87.11%

说明用这个指数来算
It shows that if we use this index to calculate the changes in sales volume of Tmall

天猫双十二的销量比双十一的销量
the sales volume during the Double Twelve promotion had a reduction of 12.89%

是下降了12.89个百分点
compared with that in the Double Eleven promotion

同样的由于它的减少
Similarly, due to this reduction

使得营业额减少了322338元
the turnover decreased by CNY 322,338

我们是不是就发现一个问题呢
Do you the problem

用拉氏指数和帕氏指数计算的结果
The results worked out using the Laspeyres index and the Paasche index

它不等
are not equal to each other

不等对我们来讲
which is not a good sign

可能不是一件好事情
for us

因为不等
Since the results are different

就意味着我们要面临着选择
it means that we have to choose from one of them

如果等
If they are equal to each other

那就无所谓了
then there will be no problem

随便用拉氏（指数）还是用帕氏（指数）来计算
We can calculate the total index of sales volumes

销售量总指数都是可行的
using either the Laspeyres index or the Paasche index

对不对
right

那它们不等
But they are not equal to each other

就意味着我们要面临着选择
meaning that we have to make a choice

到底是用拉氏指数更好
Is it better to use the Laspeyres index

还是用帕氏指数更好呢
or the Paasche index

那么同学们
So, everyone

我们来思考一下
let's think about it

如果我现在的目标是单独反映
If only the total change in sales volume

销售量的总变动
is to be reflected

这两个指数
which of these two indexes

你们觉得哪一个真的
do you think

只有销售量的变动
reflects only changes in sales volume

而没有价格的变动呢
but no changes in price

是拉氏指数的算法
Is it the Laspeyres index

还是帕氏指数的算法呢
or the Paasche index

我们观察的结果是
According to our observation

虽然拉氏指数也好
although the time of both the Laspeyres index

帕氏指数也好
and the Paasche index

它们的同度量因素时间都被固定了
is fixed

但是帕氏指数里边已经隐含了
the change in the isometric factor

同度量因素
from the base period to the given period

从基期到报告期的变动
is already contained in the Paasche index

对不对
right

所以如果从这个角度来看
So from this point of view

拉氏指数是真正意义上没有
the Laspeyres index reflects

价格的变动
no changes in price

而单独只有销售量的变动
but only changes in sales volume

因此它是更准确地能够
So, it can reflect the changes

反映销售量这个指标的变动情况
in the indicator of sales volume more accurately

在我们指数编制的操作里边
During our compilation of index

一般我们编制数量指标的原则
generally, we use the Laspeyres index method

就是采用拉氏指数的方法
to compile indexes for

来编制的
quantitative indicators

和我们刚才的分析
which is consistent

也是对应的
with our analysis just now

因此在拉氏指数和帕氏指数里边
So, between the Laspeyres index and the Paasche index

我们通常会选择拉氏指数来计算
we usually choose the Laspeyres index

销售量总指数
to calculate the total index of sales volume

也就是说（公式如上）
That is (formula as the above)

它是等于91.38
which is equal to 91.38

而由于它的减少
Due to this reduction

它的下降
in total sales volume

使得营业额是减少了213268元
the turnover was reduced by CNY 213,268

这就是销售量总指数
This is the calculation of

它的计算的方法
the total index of sales volume

好

有了这个基本原理
Well, based on this basic principle

我们接下来介绍
let's proceed to the calculation

质量指标指数
of quality index

也就是销售价格总指数的计算
which is the total index of sales price here

我想有了刚才分析的思路
With the idea

对于销售价格总指数的计算
for the calculation of the total index of sales price

我们可以自己来给它做一个推导
we can make

做一个分析
a deduction

既然还是综合指数的范畴
Since it is still composite index we are to calculate

那么它的特点还是先综合后对比
we shall still follow the steps of synthesis first and then comparison

第一步要解决综合的问题
The first step is to solve the problem of synthesis

价格这个指标同样地也是
The indicator of price can have

不同的计量单位
different units

不同度量的
and different measurements

那么如果要完成它的综合
So if we want to synthesize prices

是不是也要像刚才
shall we introduce a medium

销售量总指数的计算一样
like we did in the calculation of the total index of sales volumes

要先引入一个媒介呢
just now

对的
Yes

只不过
But here

这一次价格是作为指数化因素
price is used as an indexation factor

而销售量
while sales volume

是作为同度量因素
is used as the isometric factor

它们的位置
Their positions

互换了一下
are reversed

被综合以后的指标
The indicator after the synthesis

其实都是营业额这个指标
is actually the indicator of turnover

对不对
right

所以这里的第一步
So the first step here

跟刚才前面的第一步基本一致
is basically the same as the previous one

引入同度量因素
which is the introduction of the isometric factor

指数化因素是p
The indexation factor is p

同度量因素是q
the isometric factor is q

转换以后的能综合的指标
the composite indicator after the conversion

是p q的组合
is a combination of p and q

也就是营业额了
which is actually the turnover

好
Okay

完成了综合
after synthesis

接下来我们就要进行对比
let's proceed to comparison

对比我们依然要用报告期的
For comparison, we will still have the data of given period

除以基期的
divided by that of the base period

同样地
Similarly

如果我们不将同度量因素的时间
if we do not fix the time

固定下来
of the isometric factor

那两个因素的时间
the time of those two factors

同时都会发生变化
will change simultaneously

这样我们得到的就会是
In this way, the index we obtain will be

营业额总指数
the total index of turnover

我们接下来就要把同度量的因素
So in the next step, we need to fix the time

固定下来
of the isometric factor

单独反映指数化因素的变动
in order to reflect the changes of indexation factor separately

同样地我们会得到两个指数
Similarly, we will get two indexes

第一是拉氏的价格指数
The first is the Laspeyres index of price

第二是帕氏的价格指数
The second is the Paasche price index

可以想象用刚才表格里边的数据
We can imagine that the Laspeyres index of price

去计算拉氏的价格指数和
and the Paasche index of price

帕氏的价格指数
figured out

得到的结果
using the data in the previous table

应该也不一样
shall not be equal to each other

对不对
right

不信我们来看一下
If you don't think so, let's take a look at

具体的计算结果
the results of the calculation

那我们看到用拉氏的价格指数
We see the Laspeyres index of price

所计算的结果是101.08%
figured out is 101.08%

由于价格上升
Since there price has risen

那么肯定要使得营业额增加
there is sure to be increase in turnover

增加了多少呢
but how much

增加了26620块钱
The turnover has increased by CNY 26,620

那用帕氏的方法
What about

所计算的指数结果呢
the Paasche price index

是96.35%
It is 96.35%

下降了是不是
which is lower than the Laspeyres price index

下降了多少呢
How much is the decrease

下降了3.65%
It has decreased by 3.65%

由于价格下降销售量保持不变
Since the price has dropped, but the sales volume remains the same

那肯定销售额 营业额
then surely the sales volume and the turnover

是要减少的
will be reduced

减少了多少
How much is the reduction

82450元
It is CNY 82,450

好 在刚才的营业额总指数的计算中
Well, from the calculation of the total index of turnover just now

我们已经发现
we have found that

天猫（5种商品）双十二和双十一相比
the turnover of (of the 5 commodities) of Tmall during the Double Twelve promotion

它的营业额是减少了295718元
was reduced by CNY 295,718, compared with that in the Double Eleven promotion

那如果前面的销售量总指数
If in the previous calculation

已经选择了拉氏价格指数计算的话
The Laspeyres index of price was selected as the index of sales volume

那么由于销售量的减少
Then the decrease of total turnover

使得它减少的金额
due to the reduction in sales volume

是213268元
is CNY 213,268

那用这两个数字一减
By subtracting CNY 295,718 from CNY 213,268

得到的结果正好是-82450元
the result obtained is CNY -82,450

我们来看一下
We see

它对应的正好是
this number is exactly

帕氏指数的计算的结果对不对
the number of the Paasche index, right

这也就告诉我们
This tells us that

如果销售量总指数已经选择了
if the Laspeyres index was selected as

拉氏指数来计算的话
the total index of sales volume in the calculation

那么价格指数
then we can no longer use the Laspeyres index of price

不能再选择拉氏价格指数来计算
as the index of price

要不然营业额的变动
otherwise there will be a third factor

就还会有第三个因素的影响了
affecting the change in turnover

对不对
right

那我们也可以从另外一个角度
We can also analyze the meaning of index from another perspective of view

就是指数本身的构造
which is the construction of the index

这个角度来分析
From this point of view

指数所代表的含义
we can know the meaning of index

我们可以首先来看一下
First let's take a look at

拉氏价格指数
the Laspeyres index of price

（公式如上）
(formula as the above)

那如果站在消费者的角度来想象
If from the perspective of a consumer

这个指数的含义是
the meaning of index is in that

是我上个月买水果
I bought fruits last month

我记住我买了多少
which cost me a certain amount of money

然后由于这个水果
and in this month

这个月比上个月价格上涨
due to changes in the fruit prices, I paid another amount of money for fruits

或者下跌
and the money I paid for fruits in this month has increased or decrease by a certain amount

我多支付或者少支付的钱对不对
compared with that in last month, right

那如果是帕氏价格指数呢
If it is the Paasche index of price that we choose

它用的（公式如上）
The formula is (formula as the above)

它的同度量因素是被固定在
The time of the isometric factor

报告期的
is fixed at the given period

也就意味着是我当期买水果
which means that, due to price change

由于水果的价格的变化
the difference in payment for fruits between this and last month

使得我多支付或者是少支付的钱
is based on the time of the given period

同学们想一想
Which of these two situations

这两种情形
do you think

哪一种更符合我们消费者（的行为习惯）
is more in line with consumers' behavior

你是总是牢牢地记住
When buying fruits, do you always remember

你上个月的买水果的情况
the money paid last month and use it as a base to calculate the changes

还是你当期买水果
or do you make comparison based on the current period

然后再去比较价格下跌（或上涨）
and see how much the change in price

给你带来的影响
will affect the cost

更符合我们的实际呢
Which one is more in line with your actual behavior

对
Yes

肯定我们更符合实际的是
surely actually when we buy fruits

我当期买水果
we make comparison based on the current period

然后我可能会比较价格的变动
to see how much the change in price

对我当期的消费行为
will affect the cost

所带来的影响
and the result of this comparison will further affect our behavior

所以从指数构造的实际
So from the perspective of the actual economic significance

经济意义的角度来分析的话
of the structure of index

帕氏价格指数
the Paasche index of price

也更具经济意义
is economically more significant

因此我们在计算价格指数的时候
Therefore, when calculating the index of price

也就是质量指标指数的时候
which is a quality indicator index

通常的编制原则是
the general principle of compilation

帕氏指数的方法来计算
is to use the Paasche index method

那也就意味着我们现在用
By using the using the Paasche index method

帕氏指数的方法来计算得到的
the K{\fs8}p{\r}bar figured out

K{\fs8}p{\r}bar它是等于96.35%
is equivalent to 96.35%

由于价格的变化
The change in turnover

使得营业额的变化额度
caused by change in price

也可以计算出来
can also be figured out

Σp{\fs8}1{\r}q{\fs8}1{\r}-Σp{\fs8}0{\r}q{\fs8}1{\r}等于-82450元
which is Σp{\fs8}1{\r}q{\fs8}1{\r}-Σp{\fs8}0{\r}q{\fs8}1{\r}, and the result is CNY -82,450

这样的话我们就通过
In this way, we have completed the compilation

先综合 后对比的过程
of the total index of sales volumes

完成了销售量总指数的编制
and the total index of sales price

和销售价格总指数的编制
through the steps of first synthesis and then comparison

当然是以它们为代表的
They are examples of the compilation

数量指标指数和
of quantitative indicator index

质量指标指数的编制
and quality indicator index

接下来我们稍稍地来总结一下
Now let's briefly summarize

质量指标指数的编制过程
the process of compiling quality indicator indexes

综合指数的编制
The compilation of a composite index

它的特点是先综合 后对比
is characterized by the calculation steps of synthesis first and then comparison

所以我们的基本步骤
So the first step is to

就是第一步引入同度量因素
introduce the isometric factor

帮助我们完成先综合的过程
to help us with the synthesis

在引入同度量因素的时候
When introducing the isometric factor

我们注意到有这样一个基本特点
we noticed that

就是当我们的指数化因素
when the indexation factor

是q的时候
is q

引入的同度量因素
which is a quantitative indicator

是p
the isometric factor introduced is p

q是数量指标
which is

p是质量指标
a quality indicator

它们在指标性质上是互补的
They are complementary to each other in nature

对不对
right

而当我们的指数化因素是P的时候
When the indexation factor is p

我们引入的同度量因素
the isometric factor introduced

就是q
is q

那么指数化因素是质量指标
Then the indexation factor is a quality indicator

同度量因素
while the isometric factor

又是数量指标
is a quantitative indicator

它们在性质上也是互补的
They are also complementary to each other in nature

所以我们在引入同度量因素的时候
So when introducing the isometric factor

就有这个考虑的方向
we may put this into consideration

它和我们的指数化因素
The isometric factor

是互补的
is complementary to the indexation factor

第二一个
The second step is

对比
comparison

对比要体现指数化因素的单独变动
The purpose of comparison

那么我们必须要做的一个工作是
is to reflect the changes in indexation factor separately

把同度量因素的时间固定下来
so we need to fix the time of the isometric factor

根据咱们前面的计算分析
According to the previous analysis and calculation

我们得到了计算数量指标指数和
We find out the general principle

质量指标指数的一般原则是
of the calculation of quantitative index and quality index

如果是数量指标指数我们采用的是
For a quantitative index

拉氏指数的计算方法
we use the Laspeyres index method

它的同度量因素一般是被固定在
and the time of the isometric factor is generally fixed at

基期的
the base period

而如果是质量指标指数
For a quality index

那么我们通常采用的是帕氏指数的
we usually use the Paasche index

计算方法
method

它的同度量因素是被固定在
and the time of the isometric factor is fixed at

报告期的
the given period

这就是综合指数编制的基本原理
This is the basic principle of the compilation of composite indexes

同学们
Have you got

大家掌握了没有
it now

今天的课就到这里
Here is end

结束了
of this lecture

下一节课
In the next lecture

我们接着再来介绍
we will introduce

综合指数体系的有关内容
the system of composite indexes