1.4.3 Basic concepts: the cornerstone of statistics 基本概念：统计的基石在线视频

统计的基本概念
Basic Concepts of Statistics

统计学的基本概念
Basic concepts of statistics

是一对一对地提出来的
always appear in pairs

第一对概念呢
The first pair we are going to discuss

就是总体与总体单位
is population and unit

什么叫总体呢
What is population

第一次接触的人可能不清楚
We can compare this abstract concept[The person learning for the first time may not be clear]

如果学过数学集合的话呢
to mathematical aggregation[If you have learned Math Set]

总体就相当于集合
Population is [Is like]the aggregation

它是由许多性质相同的元素
a whole part made of

所组成的一个整体
elements of the same nature

那就是集合
that is, an aggregation.

那总体是什么呢
What about population

它是由许多性质相同的
The population is a collection made of

总体单位构成的一个整体
units of the same nature

那就是统计总体
referred to as statistical population

它呢 有三个特点
It has three characteristics

第一 大量性
first, volume

数量特别大
in large quantity

里面的总体单位数量特别大
the total number of units is huge

第二 同质性
Second, homogeneity

你要成为一个总体
To form a population

你必须 总体单位某些性质是要相同的
there must be units of the same nature[Some properties of the overall unit are the same]

第三 它必须具有差异性
Third, differences

总体单位是在某些性质上
The units are homoplasmic

或某些标志上它是同质的
in some properties or in some characters

但是在大部分标志表现上
But most of the characters must display

是不相同的
differences

这也是统计存在的前提条件
This is also a precondition for statistics

总体呢
The population

这里讲的总体是经济统计的总体
we discuss here is statistical population of economy

还有个总体
There is also a concept of collection

在我们的教科书
in our textbook

就是中学的教科书里面
high school textbook

它里面写的总体
in which the concept of collection

它特别指明 说
is clearly specified, saying

我们这个总体是不对的
The statistical population we discuss here is different from

它那个总体是对的
the concept of collection in the book

它的那个总体是怎么解释的呢
How does the textbook explain the collection

它是由一组性质相同的数
It is a collection consisting of a set of

构成的总体
numbers of the same nature

它这个总体和数理统计的总体是相同的
This collection is similar to the population of mathematical statistics

那我们现在来分析
Now let us analyze

这两个总体的差别
the differences between the two concepts of collection

比如说
For example

按照经济统计学来研究高血压
if we study high-blood pressure by economic statistics

比如说 我有一种药 A
say, I have a medicine, A

这种药 A药能治高血压病
this medicine A can treat high-blood pressure

那我们的研究对象
Then what is our object of study

研究总体是什么
or population

经济统计的总体就是说
In economic statistics, population refers to

患高血压的所有患者构成的整体
the total collection of all the high-blood pressure patients

就是我们研究的总体
This is the population of our research

而数理统计
But in mathematical statistics

也就是中学的那个统计它说不是
of the collection in high school textbook

它说是什么呢
What does it tell us

它说是（把那些）
It means (to collect)

患高血压患者的血压数
the blood pressure of all these patients

构成一个整体
to form a collection

它是把血压数
It collects the set of data

就是一组数据构成一个整体
of the blood pressure to form a collection

这样的话呢
In this case

就跟我们经济统计总体不同
the collection is different from the economic statistical population

其实我们经济总体跟
In fact, economic statistical population

那个数理的总体
mathematical statistical population

或者叫中学里面的那个总体呢
and the collection in high school textbook

只是一个层次不同
are of different levels

我们高血压患者构成一个总体
Our population is a made of high blood pressure patients.

高血压患者他有好多标志
These patients have many characters

第一 血压是一个标志
such as blood pressure

年龄是一个标志
age

性别是一个标志
and gender

按照他们的（观点）来构成总体的话
If economic statistical population is formed

那经济统计的总体可以
in the same way of those two collections

构成比多他N倍的总体出来
our population would be N times bigger

所以 我们的总体比他的总体范围大
Therefore, our population has a larger range

当然
Of course

总体还可以分为有限总体和无限总体
the population can be further divided into finite population and infinite population

有限总体就是总体单位可穷尽
Finite population has finite number of units

无限总体呢 总体单位不可穷尽
Infinite population has infinite units

为什么要区别呢
Why do we distinguish them

因为等下统计调查里面
Because in statistical survey

普查 全面调查针对的是有限总体
census and overall surveys are aimed at finite population

无限总体不能进行全面调查
We cannot conduct overall surveys in infinite population

在这里
Here

大家理解总体的时候
when we understand the concept of population

一定要注意
we should pay attention to the fact

总体一定是有单位
that there must be units in population

一定跟研究目的联系在一起
and it relates to our research purposes

大家理解了这些才好理解
A clear understanding of the concept helps us to

比如说
distinguish

中国是不是总体
whether China is a population

中国不是总体
China is not a population

你要讲清楚
to be clear

你是研究中国的人口
our research is about the population in China

那么中国的所有的常住的
So the population here is composed of

具有中国国籍的人构成的整体才是总体
all permanent residents with Chinese nationality

这个总体里面
In this population

一定有每一个中华人民共和国国民
there must be individual unit

这个作为总体单位
of every citizen of PRC

如果你笼统讲中国
If we take China as a population here

那总体单位是什么
then what are the units

可能是固定资产
They could be fixed assets

可能是树
trees

可能是铁路
or railways

他必须指研究目的和里面的总体单位
It must specify the research purpose and the units contained

标志和指标
Character and indicator

标志指的是反映总体单位
Character is a term used to reflect

属性或特征的名称
the attributes or features of the unit

这就叫标志
This is character

标志就是个名称
Character is a term

是什么名称呢
What term

是总体单位的名称
The term of the unit

总体单位什么的名称呢
How do we name the unit

属性或者特征的名称
By its attributes or features

为了大家好理解
To make it clear

我举一下例子
please look at this example

比如 我要了解江西财经大学学生的
Suppose I want to know the test results of CET-4 and 6

四六级考试情况
of the students in JUFE

总体就是江西财经大学
Then JUFE is the population

这个学期参加四六级考试
all the students taking CET-4 and 6

的所有学生
this semester

每一个学生就是一个总体单位
are units in this population

你说明每个学生 他的属性或特征
What are the characters that can be used

的名称有哪些呢
to define individual students’ attributes or features

姓名 性别 民族
Name, gender, nationality

身高 体重 年龄
height, weight and age

这些都属于我们讲的属性或者特征的名称
these are all terms that we can use to define the attribute or features.

那说明属性的名称
Terms used to describe attributes

我们一般叫它品质标志
are called qualitative character

说明特征的名称
Terms used to describe features

一般把它叫作数量标志
are called numerical indication

因为特征的名称
because there are often numerical values

想年龄 身高 体重
involved to represent features

它是 都有数值表示的
such as age, height and weight

那标志的表现 就是我们
This character is expressed, in what we call,

刚才讲的具体的数值
specific numerical values

和具体的属性
and specific attributes

比如说
such as

性别是男 民族（是）汉
gender-male and nationality-Han

这就是标志的表现
are expressed in character

那指标它指的是什么
So what is indicator

指标是说明
Indicator is a term and value

总体数量特征的名称和数值
to represent the overall quantity

比如说
For example

要说明中华人民共和国
if we need to represent

他的经济总量 经济状况
the GDP or the overall economy in China

那他的总体是我国所有的常住单位
then the population of the research is all the residential units

把所有的常住单位的标志值
Put the character value of all the residential units

它的标志值是什么呢
together

比如说 它的增加值
its growth, for instance

加起来就属于它的指标 GDP
can form an indicator, GDP

所以GDP呢 既有GDP的名称
Therefore, GDP is a term

也有GDP的数值
and also a numerical value

比如说
For example

GDP 74万亿人民币
suppose the GDP is RMB74 trillion

那就是一个统计指标
then it is also a statistical indicator

统计指标分类比较多
There are many statistical indicators

按它的表现形式分
Based on form of expression

它有绝对数 绝对指标
there are absolute number, absolute indicator

相对数 相对指标
relative number, relative indicator

有平均数 平均指标
and average number, average indicator

按它的性质分呢
Based on its nature

有数量指标
there are numerical indication

有质量指标
and qualitative indicator

这里把它们分开来的目的呢
Why do we separate the two

是等一下后面我们在讲
We will come back to this question later

指数的时候会用到
Indicator is used in

像价格指数
like, price indicator

上海证券交易所的价格指数
Price index at Shanghai Stock Exchange

深圳成份指数
Shenzhen stock market’s constituent index

它（们）就属于质量指标指数
they belong to qualitative indicators

而成交量指数 它属于数量指标指数
Volume indicator belongs to numerical indications

那什么叫质量指标
What is qualitative indicator

什么叫数量指标呢
And what is numerical indication

反映总体深度的指标
Qualitative indicator represents

那就属于质量指标
the overall depth

它跟总体的范围大小没多大关系
It has no connection with the range of the population

反映总体的广度的指标
An indicator that marks the range of the population

那就属于数量指标
should belong to numerical indication

它跟总体的范围大小有直接关系
which is directly linked to the range of the population

这是第二对概念
This the second pair of concepts

第三对概念是变量和变异
The third pair of concepts is variable and variance

变异指的是 所有的变动
Variance refers to all kinds of changes

指标会变 标志也会变
of indicators and characters

那变量呢
As for variable

我们原来一般认为
we used to think

变量指的是可变的数量标志
variable is numerical indication or statistical indicator

及统计指标
that can change

但是你也可以讲
But we can also say

变量是所有的标志和指标
variable means all the indicators and characters

它都是变量
They are all variable

因为数量标志会变
Numerical indications change

品质标志也会变
so do qualitative characters

比如性别 可以变为男 女
such as sex, from male to female

我们的单位的属性也会变
The unit characters can also be changed

这些都属于变量
They are all variables

变量（按其取值是否连续）可以分为几类
Variables (based on whether its value is continuous) can be divided to

有连续变量和离散变量
continuous variable and discrete variable

这个在统计分组的时候
This is very important

特别是（整理）组距数列的时候
in statistical grouping, especially in (sorting)

特别重要
class width series

连续变量它是不可分割的
Continuous variables are inseparable

而离散变量可以一一列举
but discrete variables can be listed

所以大家在这里一定要分清楚
We should distinguish the differences

就是不要受我们的习惯所约束
and avoid being affected by general knowledge

大家一般认为
We generally think

年龄是离散变量
age is a discrete variable

体重是离散变量
body weight is a discreet variable

分数是离散变量
and fraction is a discrete variable.

这个都是不正确的
But it is not true

比如年龄 它应该是连续变量
For example, age is a continuous variable

只是我们在现实生活中
In real life

我们习惯用周岁来讲
we count the age by year

某某人的年龄
The age of a person

就是说没满一岁为零岁
grows only by whole number

没满两岁为一岁
A child is considered one year old until he reaches two

其实年龄是一个连续的
In fact, age grows as a continuous

不（间）断的一个变量
and progressive variable

变量还可以进行分类
The variable can also be divided

按它的类型（计量尺度）分为
based on its type (measurement)

定类（变量） 定序（变量）
into nominal (variable), ordinal (variable)

定距（变量） 定比（变量）
interval (variable) and ratio (variable)

这个分（类）呢
The division (type)

对以后我们的数据处理非常有用
is helpful in data processing

定类（变量）呢
Nominal (variable)

就像我们（前面）讲的
as what we said (earlier)

人按性别分 最简单的分为男女两类
if divided by sex, there are male and female

据说还有一种分成五类
I heard there was also a division of five categories

这是定类分析（变量）
This is nominal analysis (variable)

像我们的生物 动物还有植物
like in the division of living creatures

也进行分类
animals and plants

还有定序（变量）
There is also ordinal (variable)

像我们的产品按等级分
if the division is based on level

一级 二级 三级
there are first, second and third level products

这些属于定序变量
Th is ordinal variable[These are ordinal variables]

还有定距（变量）
There is interval (variable)[And fixed distance (variable)]

定距变量
Interval variable

像我们讲的
as what we said

温度 华氏 摄氏
there are Fahrenheit temperature and Celsius temperature

这些属于定距变量
This is interval variable

还有一个叫定比变量
And there is ratio (variable)

像我们刚才讲的
as what we said

GDP等等
GDP etc.

大部分（变量）属于定比变量
Most of the variables are ratio variables

定比变量跟前面的那些变量比
You (will) find that

你们（可以）发现
compared to other variables

定比变量可以进行四则运算
ratio variable can be used in arithmetic operations

而前面那些变量有些不行
But other variables cannot

大部分不行
or most of them cannot

就像男女 你不可能进行四则运算
For instance, you can’t put the variables of male and female in arithmetic operations

它是定类变量 好 这个是第三对概念
They are nominal variable. And this is the third pair of concepts learned today

这三对概念之间
Among the three pairs of concepts

有个关系 大家搞清楚
there is a relationship that we should make clear

就是我们的目的是说明总体情况
Our purpose of using these concepts

所以一切是围绕着总体来的
is to describe the overall situation of the population

那总体是由什么构成的呢
What is population made of

是由总体单位构成的
It is made of units

那说明总体单位是什么呢
How can we describe units

是标志
By characters

那说明总体的是指标
And indicators are used to describe the population

那大部分标志汇总就变成了指标
If we put characters together, we will get an indicator

指标和标志都属于变量
Both indicators and characters are variables

它既可以分为连续变量
They can be continuous variables

也可以分为离散变量
and discrete variables

所以这三对概念是联系在一起的
So, there is a connection among the three pairs of concepts

好 今天就讲到这里
Ok, that is all for today
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