统计学CH04 英文版
英文商务统计学ppt_第四章Ch04
X number of face cards Probabilit y of Face Card T total number of cards
X 12 face cards 3 T 52 total cards 13
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
In this chapter, you learn:
Basic probability concepts Conditional probability To use Bayes’ Theorem to revise probabilities
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Joint event
Complement of an event A (denoted A’)
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Chap 4-5
Example of empirical probability
Find the probability of selecting a male taking statistics from the population described in the following table:
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Chap 4-6
ch04
-0.577
-0.04882
-0.557
4-12
Expected Value - Blackjack
A blackjack player with a count of 16 who “stands” against the dealer’s ten will lose 78.9% of the time and win 21.2% of the time, for an expected value of – 0.577. A player who “hits” 16 against the dealer’s ten, will lose 77.8% of the time and will win 22.1% of the time, for an expected value of – 0.557.
4-7
Expected Value State 1 Heads Decision 1 Heads Decision 2 Tails State 2 Tails Expected Value
+ $1 X .5 - $1 X .5
- $1 X .5 + $1 X .5
$0 $0
V(d1, S1) = $0 The value of decision 1, given state 1 = + $.50 The value of decision 1, given state 2 = - $.50
4-14
Expected Value - Insurance Decisions
State 1 No Loss
State 2 Loss Occurs
Expected Value
Insure Retain
统计学CH04
Simple Random Sampling （简单随机抽样） Point Estimation （点估计） Introduction to Sampling Distributions (抽样分布简介） Sampling Distribution of x n = 100 Sampling Distribution of p Properties of Point Estimators Other Sampling Methods （其他抽样方法） n = 30
Slide 10
Example: St. Andrew’s
Use of Random Numbers for Sampling 3-Digit Applicant Random Number Included in Sample 744 No. 744 436 No. 436 865 No. 865 790 No. 790 835 No. 835 902 Number exceeds 900 190 No. 190 436 Number already used etc. etc.
Slide 7
Example: St. Andrew’s
The director of admissions would like to know the following information: • the average SAT score for the applicants, and • the proportion of applicants that want to live on campus. We will now look at three alternatives for obtaining the desired information. • Conducting a census of the entire 900 applicants • Selecting a sample of 30 applicants, using a random number table • Selecting a sample of 30 applicants, using computer-generated random numbers
统计学英文
统计学英文Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In this article, we will discuss the key concepts and principles of statistics.Sample and PopulationStatistics is based on the idea of sampling. A sample is a subset of a population that is selected for analysis. The population is the entire group that is the subject of the study. For example, if we want to study the average age of university students in a country, the population is all the university students in the country. We cannot study the entire population, so we select a sample of students from different universities and use statistics to make inferences about the population based on the sample.Descriptive and Inferential StatisticsDescriptive statistics is concerned with summarizing and describing data. It includes measures of central tendency such as mean, median, and mode, and measures of variability such as range and standard deviation. Descriptive statistics helps us understand the characteristics of the data.Inferential statistics, on the other hand, is concerned with making conclusions about a population based on a sample. It involves testing hypotheses and estimating parameters. For example, we may want to test the hypothesis that the average age of university students in the country is 20 years. We would select a sample of students, calculate the sample mean, anduse statistical tests to determine whether the difference between the sample mean and the hypothesized population mean is significant.Variables and Data TypesA variable is a characteristic of a population or a sample that can take on different values. There are two types of variables: quantitative and qualitative. Quantitative variables are numerical, such as age, weight, and height. Qualitative variables are categorical, such as gender, ethnicity, and occupation.Data can be collected in different ways, such as through surveys, experiments, and observations. Data can also be classified into different types: nominal, ordinal, interval, and ratio. Nominal data are categorical, such as gender or race. Ordinal data are ranked, such as academic achievement or social status. Interval data are numerical, such as temperature or time, but lack a true zero point. Ratio data are numerical and have a true zero point, such as weight or height.Measures of Central TendencyMeasures of central tendency are used to summarize the data and provide a single value that represents the typical score. The three most commonly used measures of central tendency are the mean, median, and mode.The mean is the arithmetic average of the scores. It is calculated by adding up all the scores and dividing by the number of scores. The mean is sensitive to outliers, or extreme scores, which can skew the results.The median is the middle score when the scores are arranged in order. It is not affected by outliers and is a better measure of central tendency when the distribution is skewed.The mode is the most common score. It is useful for nominal data and can be used with ordinal data.Measures of VariabilityMeasures of variability are used to describe the spread or dispersion of the data. The most commonly used measures of variability are the range, variance, and standard deviation.The range is the difference between the largest and smallest scores. It is affected by outliers and is not a very reliable measure of variability.The variance is a measure of how much the scores deviate from the mean. It is calculated by subtracting each score from the mean, squaring the differences, and averaging the squares. The variance is not as intuitive as the other measures of variability, but it is useful for statistical analysis.The standard deviation is the square root of the variance. It is a more intuitive and commonly used measure of variability. The standard deviation is useful for determining how much the scores deviate from the mean and for estimating confidence intervals.Hypothesis TestingHypothesis testing is a process of determining whether a statement about a population is likely to be true or false based on a sample of data. The statement is called a null hypothesis, and the alternative to the null hypothesis is called the alternative hypothesis. We collect data and use statistics to test the null hypothesis.We use a significance level, or alpha, to determine whether the results are statistically significant. If the p-value is less than the significance level, we reject the null hypothesis and accept the alternative hypothesis.ConclusionStatistics is a powerful tool for analyzing and interpreting data. Understanding the concepts and principles of statistics is essential for making informed decisions and drawing accurate conclusions from data.。
ch04统计分布的数值特征
此称为加权算术平均公式。 可以证明，当f1= f2=…= fn时，
加权算术平均公式，将化为简 单算术平均公式。
表4－1 单变量分组表
组数i 1 2 3 …
标志变量xi x1 x2 x3 …
频数fi f1 f2 f3 …
n-1
xn-1
f n-1
n
xn
fn
-
合计
f
• Ch4 统计分布的数值特征
•
§4.1 数值平均数
6160
• Ch4 统计分布的数值特征
•
§4.1 数值平均数
§4.1.1 算术平均数
解：上表是50个工作日车流量的分布情况，只能作大概估计其日平均 车流量数。方法是计算其各组的组中值，用其组中值变量代替各组 的一般水平，然后进行加权求平均。即
n
x
(xi fi )
i 1 n
fi
6160 50
i 1
123.2(辆 /时).
f(x). 15
10
123.2
5
0
100 110 120 130 140 x
图4－3 某路口车流量分布
同时，我们也整理得到了该路口比较准确的车流量分布规律。
• Ch4 统计分布的数值特征
•
§4.1 数值平均数
§4.1.1 算术平均数
三、算术平均数的数学性质 ■各变量值与算术平均数的离差之和为零。
f1 f2 f3 ... fn
50
• Ch4 统计分布的数值特征
•
§4.1 数值平均数
§4.4.1 算术平均数
如果整理后的分布为组距变量分布，则必须用组中值变量 设数据组中值变量序列及相应的频数序列fi为
x i代替组距变量xi。
ch04new资料
3. 估计值：估计参数时计算出来的统计量的 具体值
如果样本均值 x =80，则80就是的估计值
一、点估计 (point estimate)
1. 用样本的估计量直接作为总体参数的估计 值
▪ 例如：用样本均值直接作为总体均值的估计 ▪ 例如：用两个样本均值之差直接作为总体均
一、点估计
二、点估计的优良性准则 估 计 方 法 三、区间估计
参
数 点估计
估
计 的
矩估计法 顺序统计量法 最大似然法
方
最小二乘法
法
区间估计
估计量与估计值
(estimator & estimated value)
1. 估计量：用于估计总体参数的随机变量
如样本均值，样本比例、样本方差等
例如: 样本均值就是总体均值 的一个估计量
（一）、总体和样本
1.总体：又称全及总体、母体，指所要研究对象 的全体，由许多客观存在的具有某种共同性质
的单位构成。总体单位数用 N 表示。
2.样本：又称子样，来自总体，是从总体中按随 机原则抽选出来的部分，由抽选的单位构成。
样本单位数用 n 表示。
3.总体是唯一的、确定的，而样本是不确定的、 可变的、随机的。
P(ˆ)
无偏
有偏
A
B
ˆ
有效性
(efficiency)
有效性：对同一总体参数的两个无偏点估计量
，有更小标准差的估计量更有效
P(ˆ)
ˆ1 的抽样分布
B
A
ˆ2 的抽样分布
ˆ
一致性
(consistency)
一致性：随着样本容量的增大，估计量的 值越来越接近被估计的总体参数
统计学英文版教材课件
Combining Events
There are some important ways in which events can be combined that we will encounter repeatedly throughout this course. Suppose we have two events, A and B .
For example, A ∪ B = {1, 3, 4, 5}.
S A 1 5 2
STAT7055 - Lecture 2
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6
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Introduction
Intersection, Union and Complement
Complement
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February 17, 2016
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Introduction
Definitions
Probabilities of Outcomes
The probability of an outcome occurring on a single trial is written as P (Oi ). Probabilities associated with the outcomes in a sample space must satisfy two important requirements:
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Introduction
Events
Events
A simple event is an individual outcome from the sample space. An event is a collection of one or more simple events (or outcomes).
关于统计学的英文介绍
关于统计学的英文介绍【中英文版】Introduction to StatisticsStatistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It plays a crucial role in various fields, including economics, biology, psychology, and many more. By utilizing statistical methods, we can draw meaningful conclusions and make informed decisions based on the information extracted from the data.统计学是一门研究数据的收集、分析、解释、呈现和组织方法的数学分支。
它在经济学、生物学、心理学等多个领域发挥着至关重要的作用。
通过运用统计方法，我们可以从数据中提取有意义的信息，并据此做出明智的决策。
The beauty of statistics lies in its ability to simplify complex phenomena into quantifiable measures, enabling us to understand patterns, trends, and relationships within the data. Fundamental concepts such as mean, median, and mode help us summarize and describe data, while techniques like hypothesis testing and regression analysis allow us to make predictions and draw inferences.统计学的魅力在于它能将复杂的现象简化为可量化的指标，使我们能够理解数据中的模式、趋势和关系。
统计学英文版
统计学英文版Part1GatheringandExploring Data (descriptive statistics)Different Types of Data (2.1) VariableA variable is any characteristic observed on the subjects in a study. Examples: Marital status, Height, Weight, IQ, Sqft, Price, NE.A variable can be classified as eitherCategorical (in Categories), orQuantitative (Numerical)A variable can be classified as categorical if each observation belongs to one of a set of categories:Examples:Gender (Male or Female)Religious Affiliation (Catholic, Jewish, …)Type of Residence (Apartment, Condo, …)Belief in Life After Death (Yes or No)NE (Located in northeast sector of city (1) or not (0) )A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable. Examples:Age, Number of Siblings, Annual Income, Selling price, Sqft Discrete versus continuous quantitative variablesA quantitative variable is discrete if its possible values form a set ofseparate numbers, such as 0,1,2,3,…The set of possible values is not denseExamples:o Number of pets in a householdo Number of children in a familyo Number of foreign languages spoken by an individualA quantitative variable is continuous if its possible values form anintervalThe set of possible values is denseExamples:o Height/Weighto Ageo Blood pressureExerciseIdentify the variable type1.Number of siblings in a family2.County of residence3.Distance (in miles) of commute to school4.Marital status5.Length of time to take a test6.Number of people waiting in line7.Number of speeding tickets received last year8.Your dog’s weightProportion & Percentage (Relative Frequencies)The proportion of the observations that fall in a certain category is the frequency (count) of observations in that category divided by the total number of observations Frequency of that categorySum of all frequenciesThe percentage is the proportion multiplied by 100Proportions and percentages are also called relative frequenciesExampleTable classifies the 630 parliamentary seats of the Italian chamber of deputies by coalition (2013 elections).Coalition SeatsFreq. Prop. Perc.Pierluigi Bersani 345 0.548 54.8Silvio Berlusconi 125 0.198 19.8Beppe Grillo 109 0.173 17.3Mario Monti 47 0.075 7.46Vallee d'Aoste 1 0.002 0.16MAIAE 2 0.003 0.32USEI 1 0.002 0.16Antonio Ingroia 0 0 0Total 630 1 100so, for Grillo,345 is the frequency.0.548 = 345/630 is the proportion and relative frequency.54.8 is the percentage 0.548×100 = 54.8%.Frequency TableA frequency table is a listing of possible values for a variable, together with the number of observations and/or relative frequencies for each value.Raw data Frequency tableCode Gender Gender n i f i p i000001 F F 1000 0.01 1000002 M M 99000 0.99 99 ... ...100000 FExampleA stock broker has been following different stocks over the last month and has recorded whether a stock is up, the same, or down in value. The results were:1.Performance of stock Up Same DownCount 21 7 12What are the subjects?What is the variable of interest?What type of variable is it?Add proportions to this frequency table.Describe data using graphical summaries (2.2) DistributionA graph or frequency table describes a distribution.A distribution tells us the possible values/categories a variable takesas well as the occurrence of those values (frequency or relativefrequency or percentage)In the 2008 General Social Survey, 2020 respondents answered the question, "How many children have you ever had?" The results wereGraphs for categorical data: bar graphs and pie charts Use pie charts and bar graphs to summarize categorical variables: Pie Chart.o A circle where each category is represented as a “slice of the pie”o The size of each pie slice is proportional to the percentage ofobservations falling in that categoryBar Graph.o Bar Graphs display a vertical bar for each categoryo The height of each bar represents either counts (“frequencies”) or percentages (“relative frequencies”) for that categoryPie Chart52%18%17%13%Cars soldFIAT FORD OPEL RENAULTBar GraphBar graph: easier to compare categoriesBar graphs are called Pareto Charts when the categories are ordered by their frequency, from the tallest bar to the shortest barGraphs for quantitative data: dot plotShows a dot for each subject (observation) placed above its value on a number line. To construct a dot plotDraw a horizontal line and label it with the name of the variable. ?Mark regular values of the variable on it.For each observation, place a dot above its value on the number line.Graphs for quantitative data: histogramsA Histogram is a graph that uses bars to portray the frequencies or the relative frequencies of the possible outcomes for a quantitative variable Steps for constructing a histogram1.Divide the range of the data into intervals of equal width2.Count the number of observations in each interval, creating afrequency table3.On the horizontal axis, label the values or the endpoints of theintervals.4.Draw a bar over each value or interval with height equal to itsfrequency (or proportion or percentage), values of which are marked on the vertical axis.bel and title appropriatelyDisplaying Data over Time: time plotsUsed for displaying a time series, a data set collected over time.Plots each observation on the vertical scale against the time it was measured on the horizontal scale. Points are usually connected.Common patterns in the data over time, known as trends, should be noted.Measuring the Center of Quantitative Data (2.3)。
统计学CH04_英文版
Measures of Variability
Range, Standard Deviation, Variance, Coefficient of Variation
Measures of Relative Standing
Percentiles, Quartiles
Measures of Linear Relationship
Copyright © 2009 Cengage Learning
4.3
Notation…
When referring to the number of observations in a population, we use uppercase letter N
When referring to the number of observations in a sample, we use lower case letter n
The mean is generally our first selection. However, there are several circumstances when the median is better.
The mode is seldom the best measure of central location.
To illustrate, consider the data in Example 4.1.
The mean was 11.0 and the median was 8.5.
Now suppose that the respondent who reported 33 hours actually reported 133 hours (obviously an Internet addict). The mean becomes
赵瑞红统计学ch04综合指标修改
备注：
除了数量指标，质量指标按时间属性也有时期与时点两种形式。其判 别标准为：由两个时期指标对比形成的质量指标为时期质量指标；由两个 时点指标对比形成的质量指标为时点质量指标；而由一个时期指标和一个 时点指标对比形成的质量指标，其时间属性以该质量指标的分子为准，分 子是时期指标则为时期质量指标，分子是时点指标则为时点质量指标。
* 2019年全国货物周转量38232亿吨公里，其中铁路 13098亿吨公里，公路5168亿吨公里，水运19352亿 吨公里，航空29亿吨公里。
三、总量指标的种类
（一）按反映总体的内容分 分为：总体标志总量、总体单位总量
1.总体标志总量 （ population mark total amount） ~ 是反映总体中各单位某一数量标志的变量值
1.时期总量指标 简称时期指标 time period indicator
~ 是反映社会经济现象在一段时间内发展过程的 总量。（反映流量。具有可加性。）
例如：国内生产总值、 固定资产新增投资额、 社会商品零售额、 财政收入 、 人口出生数、 产品产量、 进口贸易总额 、 出口贸易总额
2.时点总量指标 简称时点指标
例如：各月工业增加值 全年的工业增加值。 每天的产成品库存量相加就缺乏实际意义。
2.时点指标数值的大小与计算期的间隔长短没有直接 关系。时期指标数值的大小与计算期的长短有直接 关系，即计算期愈长，指标数值就愈大。
例如：月度生产总值＜季度生产总值＜年度生产总值 年末人口数不一定比年中的人口数多 月末的商品库存额不一定比月初的库存额大
例： 2019年年中中国的人口总数为128,453万人，美 国的人口总数为29,104万人。则中国人口数是美国人 口数的4.41倍。也可以将分子、分母互换，美国人口 数只相当于中国人口数的22.7%。
统计思想英文版课件Cha课件
常用统计软件介绍
● R语言：一种开源的统计计算和绘图软件，具有丰富的统计函数和灵活的编程语言。
● Stata：一种功能强大的统计软件，广泛应用于社会科学、医学、生物等领域，支持多种数据格式。
● SPSS：一种广泛使用的统计软件，具有简单易用的界面和强大的统计分析功能，适用于各种领域 的数据分析。
统计思想在数据分析中的应用：统计思想能够指导数据分析师进行有效的数据分析和挖掘，发现数 据背后的规律和趋势。
统计思想在预测和决策中的应用：统计思想能够通过建立数学模型对未来进行预测，为决策者提供 更加准确和可靠的数据支持。
统计思想在社会科学领域的应用：统计思想在社会科学领域中具有广泛的应用，如社会调查、市场 研究、政策评估等。
软件操作技巧和注意事项
熟悉软件界面和功能：掌握软件的 基本操作和功能，方便后续的数据 处理和分析。
数据输入和处理：掌握数据输入和 处理的技巧，包括数据清洗、数据 筛选、数据转换等，提高数据处理 效率。
图表制作和可视化：掌握图表制 作和可视化的技巧，根据数据分 析结果选择合适的图表类型，使 数据呈现更加直观和易于理解。
统计思想英文版课 件Cha课件
PPT,a click to unlimited possibilities
汇报人：PPT
目录
CONTENTS
01 添加目录标题 02 统计思想概述 03 统计方法的应用 04 统计软件的应用 05 案例分析
06 总结与展望
单击添加章节标题
第一章
统计思想概述
第二章
数据分析：对数据 进行整理、分析和 解读
结果呈现：将分析 结果以图表、文字 等形式呈现
结果呈现和讨论
案例分析结果展示
《计量经济学》ch_04_wooldridge_5e_ppt
Chapter 4 Multiple Regression Analysis: Inference
4.1 Sampling Distributions of the OLS Estimators (2/5)
Assumption MLR.6 (Normality of error terms)
independently of
Chapter End © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 4 Multiple Regression Analysis: Inference
4.1 Sampling Distributions of the OLS Estimators 4.2 Testing Hypotheses about a Single Population Parameter: The t Test 4.3 Confidence Intervals 4.4 Testing Hypotheses about a Single Linear Combination of the Parameters 4.5 Testing Multiple Linear Restrictions: The F Test 4.6 An application— estimation of the weights of CPI components in China
【统计课件】ch04综合指标共42页文档
1、战鼓一响，法律无声。——英国 2、任何法律的根本；不，不成文法本 身就是 讲道理 ……法 律，也 ----即 明示道 理。— —爱·科 克
3、法律是最保险的头盔。——爱·科 克 4、一个国家如果纲纪不正，其国风一 定颓败 。—— 塞内加 5、法律不能使人人平等，但是在法律 面前人 人是平 等的。 —财富 ❖ 丰富你的人生
71、既然我已经踏上这条道路，那么，任何东西都不应妨碍我沿着这条路走下去。——康德 72、家庭成为快乐的种子在外也不致成为障碍物但在旅行之际却是夜间的伴侣。——西塞罗 73、坚持意志伟大的事业需要始终不渝的精神。——伏尔泰 74、路漫漫其修道远，吾将上下而求索。——屈原 75、内外相应，言行相称。——韩非
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Copyright © 2009 Cengage Learning
4.15
Mean, Median, & Modes for Ordinal & Nominal Data
For ordinal and nominal data the calculation of the mean is not valid. Median is appropriate for ordinal data. For nominal data, a mode calculation is useful for determining highest frequency but not “central location”.
Measures of Variability
Range, Standard Deviation, Variance, Coefficient of Variation
Measures of Relative Standing
Percentiles, Quartiles
Measures of Linear Relationship
4.13
Copyright © 2009 Cengage Learning
Mean, Median, Mode: Which Is Best?
To illustrate, consider the data in Example 4.1.
The mean was 11.0 and the median was 8.5.
Sample and population modes are computed the same way.
Copyright © 2009 Cengage Learning
4.8
Mode…
E.g. Data: {0, 7, 12, 5, 14, 8, 0, 9, 22, 33} N=10
Which observation appears most often? The mode for this data set is 0. How is this a measure of “central” location?
Sample and population medians are computed the same way.
Copyright © 2009 Cengage Learning
4.7
Measures of Central Location…
The mode of a set of observations is the value that occurs most frequently. A set of data may have one mode (or modal class), or two, or more modes. Mode is a useful for all data types, though mainly used for nominal data. For large data sets the modal class is much more relevant than a single-value mode.
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4.6
Measures of Central Location…
The median is calculated by placing all the observations in order; the observation that falls in the middle is the median.
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Population Mean
Sample Mean
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4.5
The Arithmetic Mean…
…is appropriate for describing measurement data, e.g. heights of people, marks of student papers, etc. …is seriously affected by extreme values called “outliers”. E.g. as soon as a billionaire moves into a neighborhood, the average household income increases beyond what it was previously!
Sum of the observations Mean = Number of observations
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4.3
Notation…
When referring to the number of observations in a population, we use uppercase letter N When referring to the number of observations in a sample, we use lower case letter n The arithmetic mean for a population is denoted with Greek letter “mu”: The arithmetic mean for a sample is denoted with an “x-bar”:
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4.10
Mean, Median, Mode…
If a distribution is symmetrical, the mean, median and mode may coincide…
mode median
mean
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Covariance, Correlation, Determination, Least Squares Line
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4.2
Measures of Central Location…
The arithmetic mean, a.k.a. average, shortened to mean, is the most popular & useful measure of central location. It is computed by simply adding up all the observations and dividing by the total number of observations:
Chapter Four
Numerical Descriptive Techniques
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4.1
Numerical Descriptive Techniques…
Measures of Central Location
Mean, Median, Mode
Data: {0, 7, 12, 5, 14, 8, 0, 9, 22} N=9 (odd) Sort them bottom to top, find the middle: 0 0 5 7 8 9 12 14 22 Data: {0, 7, 12, 5, 14, 8, 0, 9, 22, 33} N=10 (even) Sort them bottom to top, the middle is the simple average between 8 & 9: 0 0 5 7 8 9 12 14 22 33 median = (8+9)÷2 = 8.5
4.12
Mean, Median, Mode: Which Is Best?
With three measures from which to choose, which one should we use? The mean is generally our first selection. However, there are several circumstances when the median is better. The mode is seldom the best measure of central location. One advantage the median holds is that it not as sensitive to extreme values as is the mean.
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4.16
Measures of Central Location • Summary…
Compute the Mean to • Describe the central location of a single set of interval data Compute the Median to • Describe the central location of a single set of interval or ordinal data Compute the Mode to • Describe a single set of nominal data
Now suppose that the respondent who reported 33 hours actually reported 133 hours (obviously an Internet addict). The mean becomes