一夜。統計學：敘述統計

Summary

The video script introduces 'One Night of Statistics,' an educational presentation designed to give students a fundamental understanding of computer statistical analysis within a short timeframe. The instructor emphasizes that while a deep grasp of statistics isn't achievable overnight, the course can provide a practical application overview. The session covers ten common statistical techniques used in social science research, with a focus on five key methods: narrative statistics, average tests, reliability analysis, correlation analysis, and linear regression analysis. The script also provides a step-by-step guide on using SPSS for descriptive statistics, including calculating frequencies, percentages, means, and standard deviations, to demystify statistical analysis for students.

Takeaways

• 📚 The lecture aims to provide a basic understanding of computer statistical analysis in a short time frame, focusing on application rather than comprehensive knowledge.
• 📈 The concept of 'One Night of Statistics' is introduced to demystify statistical analysis and make it less intimidating for students.
• 🔢 The course covers ten common statistical techniques, but it's emphasized that not all techniques are necessary for every research paper; the choice depends on the research purpose or question.
• 📝 The first part of narrative statistics involves calculating frequencies and percentages to understand the demographic characteristics of the sample, such as gender, education level, and marital status.
• 📋 Descriptive statistics, the second part, includes calculating the mean and standard deviation to understand the central tendency and dispersion of responses to survey questions.
• 📊 SPSS is the primary software introduced for conducting narrative statistics, with a focus on its interface and environment for data analysis.
• 👉 The process of using SPSS involves selecting variables, placing them into the calculation area, and executing commands to generate professional reports.
• 📉 In SPSS, descriptive statistics can be found under the 'Analyze' menu, with options to calculate frequencies, percentages, means, and standard deviations.
• 🔑 The script guides students through the steps of using SPSS to perform narrative statistics, including selecting the right options and interpreting the output.
• 📚 The importance of practicing with the provided handouts and files is highlighted to ensure students can apply the techniques independently.
• 🎓 The lecture is tailored for master's students, with an emphasis on the most relevant statistical techniques for their theses.

Q & A

What is the main goal of the 'One Night of Statistics' presentation?

The main goal of the 'One Night of Statistics' presentation is to provide a rough idea of computer statistical analysis and to reduce the fear associated with statistical analysis, rather than to fully understand all of statistics in one night.

What are the two main parts of descriptive statistics as mentioned in the script?

The two main parts of descriptive statistics are calculating demographic characteristics of the sample, which includes counts and percentages, and analyzing the scores and distribution of each question, including their mean and standard deviation.

Why is it not necessary to include all ten statistical techniques in a thesis?

It is not necessary to include all ten statistical techniques in a thesis because statistics are just a tool, and the choice of method should depend on the research purpose or research question.

What are the five most common statistical techniques highlighted in the script?

The five most common statistical techniques highlighted in the script are narrative statistics, average test, reliability analysis, related analysis, and linear regression analysis.

How does the script suggest students familiarize themselves with SPSS interface and environment?

The script suggests that students who have taken the class should already be a little familiar with the SPSS interface and environment, and they should be able to find where to download handouts or files for further practice.

What is the purpose of calculating frequency and percentage in descriptive statistics?

The purpose of calculating frequency and percentage in descriptive statistics is to understand the population distribution in the sample, such as the characteristics and conditions of gender, education level, and other demographic variables.

How does the script describe the process of selecting variables for descriptive statistics in SPSS?

The script describes the process as dragging the variables or items to be calculated to the right side of the SPSS window, where the computer recognizes the selected items and performs calculations according to the instructions given.

What does the script suggest about the default settings in SPSS for generating frequency distribution tables?

The script suggests that in SPSS, the default settings for generating frequency distribution tables are already set to display the counts and percentages, which simplifies the process for the user.

How does the script explain the use of descriptive statistics to calculate mean and standard deviation?

The script explains that descriptive statistics can be used to calculate the mean and standard deviation by selecting the 'Descriptive Statistics' option in SPSS, which then allows the user to input the variables and obtain the desired statistical measures.

What is the significance of calculating the mean and standard deviation for each question in a survey?

Calculating the mean and standard deviation for each question in a survey helps to understand the central tendency and dispersion of the responses, providing insights into which questions have the highest scores and which have more variability in responses.

Outlines

00:00

📚 Introduction to One-Night Statistics Course

The instructor introduces a course aimed at giving students a basic understanding of computer statistical analysis in a short amount of time, specifically within one night. The course is not meant to make students experts in statistics but to familiarize them with its application. The instructor emphasizes that while the application can be quickly learned, understanding the underlying operations and principles takes more time. The course will cover ten common statistical techniques, but students are not expected to use all of them in their papers. Instead, the choice of technique depends on the research purpose or question. The instructor plans to explain each of these techniques in detail during the course.

05:03

📈 Demonstrating Descriptive Statistics in SPSS

The instructor provides a step-by-step guide on how to perform descriptive statistics in SPSS, starting with accessing the 'Analysis' command and selecting 'Descriptive Statistics' from the drop-down menu. The focus is on calculating frequencies and percentages to understand the demographic distribution within a sample, such as gender, education level, and marital status. The SPSS interface is described, with instructions on how to drag variables into the calculation area. The default settings for displaying frequency tables are discussed, and the instructor guides students on how to execute the command to generate a professional report. The output includes counts and percentages for each demographic variable, offering a clear presentation of the sample's characteristics.

10:05

📊 Calculating Descriptive Statistics for Scaled Questions

Building on the previous paragraph, the instructor explains how to calculate descriptive statistics for questions scored on a five-point scale, such as those measuring corporate reputation. The process involves selecting the relevant questions and using the 'Descriptive Statistics' feature in SPSS to find out the mean and standard deviation for each question. This helps in understanding the central tendency and dispersion of the responses. The instructor guides students through the process of selecting options in SPSS to display the desired statistics, such as minimum value, maximum value, mean, standard deviation, and other descriptive measures. The summary of the SPSS report allows students to quickly assess which questions have the highest and lowest scores and which ones show the most variation in responses.

Keywords

💡Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In the context of the video, statistics is the core subject being discussed, with the aim of giving students a basic understanding of statistical analysis through computer software within a short period.

💡Descriptive Statistics

Descriptive statistics refers to the methods that summarize and organize the characteristics of a set of data. The video explains that descriptive statistics is divided into two main parts: calculating demographic characteristics of a sample, which includes counts and percentages, and analyzing the scores and distribution of responses to survey questions, focusing on mean and standard deviation.

💡SPSS

SPSS, which stands for Statistical Package for the Social Sciences, is a widely used software for statistical analysis in social science research. The script describes using SPSS to perform narrative statistics, including generating frequency distribution tables and descriptive statistics like mean and standard deviation.

💡Frequency Distribution Table

A frequency distribution table is a table that displays the frequency of various outcomes of a data set. In the script, the instructor demonstrates how to use SPSS to create a frequency distribution table to show the demographic characteristics of the sample, such as gender and educational level.

💡Mean

The mean, often referred to as the average, is a measure of central tendency that calculates the average value of a data set. The video script uses the mean to determine the average scores for different survey questions, such as corporate reputation, and to compare the central tendency of responses.

💡Standard Deviation

Standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of values. The script explains that standard deviation helps to understand the spread of the responses to survey questions, indicating how much individual data points deviate from the mean.

💡Narrative Statistics

Narrative statistics involves presenting statistical data in a narrative form to make it more understandable. The video script introduces narrative statistics as a way to provide a rough idea of computer statistical analysis, focusing on demographic characteristics and scores of survey questions.

💡Research Methodology

Research methodology refers to the systematic analysis of the body of methods used in a field of study to guide academic and research inquiries. The video script mentions that the ten statistical techniques discussed are from the perspective of traditional social science research methodology.

💡Linear Regression Analysis

Linear regression analysis is a statistical method for modeling the relationship between dependent variable and one or more independent variables by fitting a linear equation. The script identifies linear regression as one of the most common statistical techniques used in research, particularly in master's theses.

💡Reliability Analysis

Reliability analysis is a statistical method used to evaluate the consistency and stability of a measurement instrument. In the script, reliability analysis is listed as one of the key techniques that students might use in their research, though it is not elaborated upon in detail.

Highlights

Introduction to 'One Night of Statistics' concept aiming to provide a basic understanding of computer statistical analysis within a short time frame.

Explanation that the course is application-oriented and not about mastering all statistics in one night.

The course covers ten common statistical techniques based on traditional social science research methodology.

Emphasis on the selection of statistical methods depending on the research purpose or question, rather than including all techniques in a thesis.

Highlighting five key techniques often used in master's theses: narrative statistics, average test, reliability analysis, related analysis, and linear regression analysis.

Introduction to SPSS software and its interface for statistical analysis.

Description of the first part of narrative statistics focusing on demographic characteristics through frequency and percentage calculations.

Demonstration of how to use SPSS to calculate frequencies and percentages for categorical variables like gender and education level.

Explanation of the second part of narrative statistics involving the calculation of mean and standard deviation for Likert-scale questions.

Guidance on using SPSS to generate professional reports for demographic variables and question scores.

Illustration of how to select and analyze data in SPSS to produce descriptive statistics.

Discussion on identifying the highest and lowest scoring questions based on mean values.

Analysis of standard deviation to understand the dispersion of responses for different questions.

Advice for students to download handouts and practice using SPSS to become proficient in narrative statistics.

Summary of the key components of narrative statistics: demographic characteristics and question scores with mean and standard deviation.

Encouragement for students to engage with the material and practice to overcome any fear of statistical analysis.

Transcripts

各位同學好 那我們接著來講 有關於統計學的一些相關技術

Hello, students, let’s continue talking about some related techniques about statistics.

那這一份投影片呢 有上過我的課的同學都有看過 他叫做一夜統計學

What about this slide? Everyone who has taken my class has seen it. It’s called One Night of Statistics.

那之所以叫做一夜統計學 其實很簡單 我就是希望能夠在一個晚上左右的時間

The reason why it is called one-night statistics is actually very simple. I just hope to be able to do it in about one night.

讓你對於電腦統計分析有一點點粗淺的概念

Give you a rough idea of ​​computer statistical analysis

主要的用意是在應用 並不是說一個晚上真的能夠搞懂所有的統計

The main purpose is to apply it. It does not mean that you can really understand all the statistics in one night.

好 那如果只是在應用層次上面 的確可以在短時間之內速成 不過

Okay, if it's just at the application level, it can indeed be done in a short time. But

有一些相關的操作還有原理還是會在

There are some related operations and principles that will still be there

這個教學裡面穿插的跟同學做一些簡介 那希望可以讓各位同學對於

This teaching is interspersed with some introductions to classmates. I hope it can make all students understand

統計的分析 不會這樣的恐懼

Statistical analysis does not have such fear

那有關於一夜統計學 我的安排是如下所示

What about statistics overnight? My schedule is as follows:

所以 老實說 嗯 我們在論文裡面所用到的統計技術 我整理如下

So, to be honest, um, the statistical techniques we used in the paper are summarized as follows:

大概是這十種技術

Probably these ten technologies

我指的是從一般比較傳統的社會科學研究方法論來說 大概就是這十種技術

What I mean is that from the perspective of the more traditional social science research methodology, it is probably these ten techniques.

這十種技術並不是要你

These ten techniques do not require you to

把所有的技術都放在你的論文裡面

Put all the technology in your paper

畢竟我們在用這個統計 它只是一種工具的手段

After all, we are using this statistic. It is just a tool.

你該用哪一種方法 要看你的研究目的或研究目問題而定

Which method you should use depends on your research purpose or research question.

所以今天的十種技術只是在我經驗中

So today’s ten techniques are just in my experience

比較常見的十種技術 但並不是說

Ten common technologies, but that doesn’t mean

每一本論文一定得涵蓋這十種技術 好 那等一下的教學

Every paper must cover these ten technologies. Okay, let’s talk about the teaching later.

我都會把這十種技術分別去跟各位同學做一個說明

I will explain these ten technologies to each of my classmates.

好 那有上過我課的同學 大概都能夠找到能夠下載講義或者檔案的地方 好 那原則上來說

Okay, then students who have taken my class can probably find a place where they can download handouts or files. Okay, in principle.

我覺得在一般的碩士論文 尤其是各位來講 一定會用到的幾種技術 我先把它圈起來

I think there are several techniques that will be used in general master's thesis, especially for you. I will circle them first.

第一個是敘述統計 第二個是平均數檢定

The first is narrative statistics and the second is the average test.

再來是信度分析

Next is reliability analysis

還有相關分析 那右手邊最常見的是線性迴歸分析

There is also related analysis. The most common one on the right hand side is linear regression analysis.

我圈起來這五種 又是從這十種裡面看到的最常見的這五種技術

I have circled these five, which are the five most common technologies seen among these ten.

這裡呢先簡單的介紹 那我們在以下的每一段影片裡面會把每一個

Here is a brief introduction. In each of the following videos, we will introduce each

技術 詳細的 做一個講解的動作

Technical Detailed Make an action to explain

好 那我們就到spss的畫面來跟各位同學先介紹所謂的敘述統計

Okay, then let’s go to the spss screen to introduce to you the so-called narrative statistics.

好 這有關於spss的介面跟環境 大家應該要有一點熟悉了

Okay, this is about the interface and environment of spss. Everyone should be a little familiar with it.

好 這個問卷是我們的教學檔案 它是一個已經 key in 完成的 spss檔案

Okay, this questionnaire is our teaching file. It is a spss file that has been keyed in.

那我們今天呢 第一步要做的是敘述統計 簡單來講 敘述統計有兩大塊

So what are we doing today? The first step is narrative statistics. To put it simply, narrative statistics has two major parts.

第一塊是處理次數跟百分比

The first block is the number of processing times and percentages

就是你所回收的樣本裡面 它的人口分佈大概是怎麼樣的一個特徵與狀況

It means what are the characteristics and conditions of the population distribution in the sample you collected.

例如性別

For example gender

男性佔了多少人 女性佔了多少人 各有多少百分比

How many people are men, how many people are women, and what percentage of each is

或者是他的學歷 大學畢業的有多少人 研究所學歷的有多少人 各佔多少百分比

Or his academic qualifications. How many people have graduated from university? How many people have graduated from graduate school? What percentage of each is

也就是說 這種人口分佈的狀況 它是敘述統計的一環

In other words, this population distribution is part of narrative statistics.

那在人口分佈的特徵 我們要算的就是次數跟百分比

As for the characteristics of population distribution, what we need to calculate is the frequency and percentage.

好 那這個時候我就來先示範給各位同學看

Okay, then I will demonstrate it to all the students at this time.

在spss的介面裡面 我們最常使用的指令其實就是上面的分析

In the spss interface, the most commonly used command is actually the above analysis.

Analysis 在spss的分析裡面

Analysis in the analysis of spss

大概90%的起手式都是從這個分析指令 著手

About 90% of the starting moves start from this analysis command.

我們按下去之後 你會看到很多下拉式的選單 它裡面有各式各樣統計的技術

After we click on it, you will see a lot of drop-down menus, which contain various statistical techniques.

那我們會在不同的影片裡面跟各位同學做介紹

Then we will introduce it to students in different videos.

我們現在要執行的是敘述統計 所以你不難發現這個下拉式選單裡面的第二個

What we are going to perform now is narrative statistics. So you can easily find the second item in this drop-down menu.

寫的就是敘述統計

What I write is narrative statistics.

好 那當然敘述統計 他又出現了第二個下拉式選單

Okay, then of course the statistics will be described, and a second drop-down menu will appear.

不過你不用擔心 我們剛才說的是要計算次數跟百分比 所以顧名思義 你應該

But you don't have to worry. What we just said is to calculate the number and percentage. So as the name suggests, you should

很容易就看到他右手邊的第一個叫做次數分配表

It is easy to see that the first one on the right is called the rep allocation table.

Frequency就是 頻率 次數 的 意思 好 那我們就把它點選下去

Frequency means frequency. Okay, let’s click on it.

好 你就會發現 spss 的這個視窗就浮出來了

OK, you will find that the window of spss will pop up.

一般來講 這個spss的這個工作視窗 它長相差不多都是左邊的欄位

Generally speaking, the spss working window looks almost like the column on the left.

右邊的欄位 一般來講 左邊的欄位丟到右邊去 右邊就是你的運算區

Generally speaking, the field on the right is thrown to the right. The right is your calculation area.

將你想要計算的變數或者是題項

Put the variables or items you want to calculate

拉到右邊去啊 拉到右邊去 這邊有一個箭頭 所以你可以把你的題目拉到右邊去

Drag it to the right. Drag it to the right. There is an arrow here, so you can drag your question to the right.

那基本上電腦就知道你選取的專案是哪些 接著就可以去按照你的指令去做一些調配

Basically, the computer will know which projects you have selected, and then it can make some adjustments according to your instructions.

好 那我們現在要算的是次數跟百分比 譬如說像性別 我已經放進來了

Okay, so what we want to calculate now is the frequency and percentage. For example, gender, I have already included it.

那我還可以放 例如像 最高學歷 婚姻的屬性

Then I can also put, for example, the highest educational level and the attributes of marriage.

工作的狀況等等 我們都把它放進來

Work status, etc. We put it all in.

只要是名義尺度的部分 人口的基本資料 人口統計變數等等 我都可以一次把它放進來

As long as it's part of the nominal scale, basic information on the population, demographic variables, etc., I can put it all in at once.

那次數跟百分比選取了之後 其實你會發現

After selecting the number and percentage, you will actually find

他底下的

underneath him

有一個叫做顯示次數分配表 電腦的預設 已經把它勾起來了

There is something called the display times allocation table. The computer's default setting has already hooked it up.

那這樣子我們只要把我們要的題項丟到右手邊 丟到右手邊

In this case, we just need to throw the item we want to the right hand side.

那其實按下確定之後 那電腦就會幫你跑出還蠻專業的報表

In fact, after pressing OK, the computer will help you run a fairly professional report.

好 那接著我們來試試看

Okay, then let's try it out

就按下確定 那他就會跑出該有的報表

Just press OK and he will run out the report that should be there.

我們來看這個輸出

Let's look at this output

這是spss的輸出畫面

This is the output screen of spss

原則上 只要你執行任何一個動作 在他的輸出表裡面 他都會記載

In principle, as long as you perform any action, it will be recorded in its output table.

好 這個次數分配表各位在畫面上有看到 這叫做次數分配表 他寫在這裡

Okay, you have seen this rep allocation table on the screen. This is called the rep allocation table. It is written here.

好 例如說性別

Okay, for example, gender

我們就發現男生的人數有154人

We found that the number of boys was 154

女生有251人

There are 251 girls

他各佔多少百分比呢 男生是38%

What percentage does each account for? Boys are 38%

女生是62% 好 那底下的學歷也是以此類推

For girls, 62% is good. Then the academic qualifications are also deduced in the same way.

你可以看到每一個學歷

You can see every qualification

它的分層還有各佔多少人數 以及它的每一層的百分比

Its layers also include the number of people in each layer and the percentage of each layer.

所以很清楚的可以對於人口統計變數做一個簡單的呈現

So it is clear that we can make a simple presentation of the demographic variables

好 所以我們瀏覽一下 底下有婚姻狀況 還有工作屬性 工作位階等等 然後 公司規模

Okay, so let's take a look. There's marital status, job attributes, job rank, etc. and then company size.

這些都是不會很困難的資訊 所以我們只要用

This is not very difficult information, so we'll just use

一個動作就可以把我們的敘述統計給做出來了 好 這是敘述統計的第一大塊

One action can create our narrative statistics. Okay, this is the first big piece of narrative statistics.

除了敘述統計之外 除了敘述統計的這個人口統計變數之外

In addition to narrative statistics In addition to this demographic variable of narrative statistics

我們還有另外一個

we have another one

地方是要計算的

Place needs to be calculated

例如說像你看到的企業聲望 我現在所圈起來的企業聲望這幾題

For example, let’s take the questions about the corporate reputation you see and the corporate reputation I’ve circled now.

你會發現 他的題目是用五點尺度去計分的 也就是說他就好像考卷一樣

You will find that his questions are scored on a five-point scale, which means it is like a test paper.

這每一個題目都有每一個題目的得分

Each of these questions has a score for each question

那他是五點尺度就代表每一題最低分是一分 最高分是五分

Then it is a five-point scale, which means that the minimum score for each question is one point and the maximum score is five points.

好 那我如何知道

Okay, then how do I know?

在每一個題目

in every topic

在受試者的回答中 他們得到了多少 平均數 跟 標準差

In the subjects' responses, what did they get as mean and standard deviation?

我們希望能夠算出來才知道這個資料

We hope we can calculate it before we know this information

的集中程度或是分散的程度 所以平均數跟標準差的一個概念

The degree of concentration or dispersion is a concept of average and standard deviation.

我們也是在敘述統計裡面 可以看到這個指令

We can also see this command in narrative statistics.

在敘述統計裡面 下拉式選單的

In the narrative statistics drop-down menu

第二個描述性統計量 它能夠幫你計算出我們想要的

The second descriptive statistic can help you calculate what we want

平均數與標準差 所以我們把它點選下來之後呢 你就可以看到一樣的工作視窗

Mean and standard deviation. So once we click on it, you can see the same work window.

好 我們這邊舉個例子

Okay, let's give an example here

我們今天執行例如 聲望1到聲望8 這八個題目 我們想要知道平均數跟標準差

Today we will perform eight questions from Reputation 1 to Reputation 8. We want to know the average and standard deviation.

你們把他拉到右邊去

You pull him to the right

好 那到右邊去之後呢 你會發現這個視窗呢 有一個選項可以讓你勾選

Okay, then when you go to the right, you will find this window. There is an option for you to check.

按下去之後 他會浮出第二個工作視窗

After pressing it, a second working window will pop up.

好 在這第二個工作視窗裡面 你會發現有一些設定 他已經幫你預設好了

Okay, in this second working window, you will find some settings that have been preset for you.

然後你幫你預設好了 所以你可以看到這些資訊 如果你想要的你就留下來 或者是你有額外想要

Then you preset it for you, so you can see this information. If you want, you can stay, or if you have additional wants.

更加了解的地方 你就打勾 所以目前的預設資訊有最小值 最大值 還有平均數與標準差

If you want to know more about it, you can check it. So the current default information includes minimum value, maximum value, average value and standard deviation.

好 那我們就按照電腦的設定 先不改變 那我們就繼續將它執行

Okay, then let's follow the computer's settings. If we don't change it for now, then we'll continue to execute it.

按下繼續之後 他會回到第一個工作視窗 然後我們按確定

After pressing Continue, he will return to the first working window and then we press OK

他就會跑出報表來 好 我們來看一下這個spss的報表

He will run out the report. Okay, let's take a look at this spss report.

各位同學 你可以看得到

Dear students, you can see

這個就是描述性的統計量 它基本上要計算的是平均數與標準差 當然

This is a descriptive statistic. It basically calculates the mean and standard deviation. Of course

最小值 最大值 全距

Minimum value Maximum value Full range

還有眾數 或者是變異數等等 它其實都是描述性統計的

There are also modes or variations, etc. These are actually descriptive statistics.

一環 不過 我們最主要想要知道的是平均數與標準差好 你可以看到我們有八個題目被我們選進來

One link, but the main thing we want to know is the mean and standard deviation. You can see that we have eight questions that we selected.

好 那這八個題目裡面 每一個題目各有各的平均數

Okay, then each of these eight questions has its own average.

然後 各有各的 標準差

Then each has its own standard deviation

所以我們就可以一目瞭然的知道

So we can know clearly at a glance

像以平均數來講 哪一個題目的得分是最高的呢 你可以看到最高的好像是

In terms of average, which question has the highest score? You can see that the highest score seems to be

聲望8 聲望8它的平均數是4.1161 它是在這八題裡面得分是最高的

Reputation 8 Reputation 8, its average is 4.1161, it has the highest score among these eight questions.

那得分第二高的是聲望4

The second highest score is Reputation 4

那他是4.0469 所以你就可以大略的去排序

Then it is 4.0469, so you can roughly sort it.

那大概知道哪一個題目的平均數是比較

Then you probably know which question the average is compared to

高的 然後標準差 你也可以看到 誰的題目在回答上面是比較分散的

High and then the standard deviation, you can also see whose answers are more scattered.

從這個表格你就可以很快的看出來

You can quickly see from this table

好 以上是有關於spss去執行敘述統計的部分 那這邊再跟大家強調一次

Okay, the above is about spss to implement narrative statistics. Let me emphasize it to you again.

敘述統計分成兩大塊 第一塊是去計算你的樣本人口特徵 我們有次數跟百分比

Narrative statistics is divided into two parts. The first part is to calculate the demographic characteristics of your sample. We have counts and percentages.

第二大塊是有關於你的受試者回答每一個題目 它的得分還有分散的狀況 我們是要去算這個題項

The second big part is about your subjects’ answers to each question, their scores and distribution. We have to calculate this question.

它本身的平均數與標準差

its own mean and standard deviation

好 那這部分其實並不是很困難 請各位同學下載講義跟檔案之後 自行多練習 好 那應該就不會有問題了

Okay, then this part is actually not very difficult. Please download the handouts and files and practice more on your own. Okay, then there should be no problem.

好 謝謝

Okay, thank you