Chapter 2 dispersion Statistics

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Chapter 3 Descriptive statistics(Numerical methods)

Chapter 3 Descriptirth noticing (1) Weight（权数）: The number to measure the importance (weights) of variables→ “f or f/∑f” ∑ [Example] During the “Oct. 1st”, 10 students go to different tourist site: Mt. Huang→5 persons, Mt. Wuyi→2 , Mt. Tai→2 , Mt. Laofu→1.
Total age 15 + 16 + 16 + L + 18 170 x= = = = 17 Number of persons 1+1+1+L+1 10
x1 + x 2 + x 3 + L + x n Σx ∴x = = = E ( x) 1+1+1+L+1 n Σx （1）Simple arithmentic mean：x = n
Difficulties
1. Mean； Mean； 2. Variance and standard deviation。 deviation。
Chapter 3 Descriptive statistics
STAT
Section 1 Central tendency and tendency of dispersion 1. Concepts tendency（集中趋势） 1） Central tendency（集中趋势）: The closer to middle the variable gets, the larger the frequency is. The reverse is also true. 2） Tendency of dispersion（离中趋势）: The tendency of dispersion（离中趋势） deviating and dispersed at the two ends.

数理统计dispersion

Sample 1
97
98
99
100
101
102
103
Sample 2
49
50
51
100
149
150
151
Sample 3
1
2
3
100
197
198
199
Three different sample with the same mean as 100 and median 100.
RANGE
The range is the simplest measure of dispersion. The range can be thought of in two ways. As a quantity: the difference between the highest and lowest scores in a distribution. - "The range of scores on the exam was 32." As an interval; the lowest and highest scores may be reported as the range. - "The range was 62 to 94," which would be written (62, 94).
INTERQUARTILE RANGE
A second measure of variability - not quite as influenced by extreme values – is the interquartile range. This is easily calculated by subtracting the value at the 25% position from the value at the 75%.

statistics

statisticsStatisticsStatistics is a branch of mathematics that focuses on collecting, analyzing, interpreting and presenting data. It plays a vital role in various fields, including business, economics, social sciences, and even sports. By employing statistical methods, researchers and analysts can make sense of complex data and draw meaningful conclusions.The fundamental concept in statistics is data. Data can take different forms, such as numerical or categorical, and can be collected through surveys, experiments, or observations. To analyze data effectively, statisticians organize it into datasets, which are collections of individual data points. These datasets serve as the basis for statistical analysis.One key aspect of statistical analysis is descriptive statistics. Descriptive statistics involves summarizing and describing the main features of a dataset. Measures of central tendency, such as mean, median, and mode, provide information about the average or typical value of the data. Measures of dispersion, such as range and standard deviation, indicate how spread out the data is. Descriptive statistics provide afoundation for understanding the characteristics of the data and can be used to compare different datasets.In addition to descriptive statistics, inferential statistics is another important branch of statistics. Inferential statistics involves drawing conclusions and making predictions about a larger population based on a sample of data. Through the use of sampling techniques and probability theory, statisticians can estimate population parameters and test hypotheses. For example, in political polls, a sample of likely voters is used to make predictions about the voting preferences of the entire population.Statistical methods also play a crucial role in experimental design. When conducting experiments, researchers carefully control variables to determine cause-and-effect relationships. Randomization helps ensure that any observed effects are not due to chance. Statistical analysis helps determine whether the observed differences between groups are statistically significant or simply the result of random fluctuations.One common statistical tool used in data analysis is regression analysis. Regression analysis aims to identify the relationship between a dependent variable and one or more independent variables. It can be used to predict futureoutcomes based on historical data or to determine the impact of various factors on a particular outcome. Regression analysis is widely used in fields such as finance, economics, and social sciences.Data visualization is another key aspect of statistics. Visualizing data through graphs, charts, and other visual representations allows for a better understanding of complex patterns and relationships. Visualizations help communicate insights and findings to a wider audience, making statistics more accessible and easier to interpret.In recent years, the field of statistics has seen rapid advancements due to advancements in technology. The availability of large datasets, often referred to as \。

名词解释(谢哲宇修改

Chapter 1Statistics（统计学）：研究数据资料的收集、整理、分析和解释（interpretation）的科学。

Biostatistics（生物统计学）：统计学应用于生物科学Variable（变量）：指某种特征，它的表现在不同个体间或不同组间存在变异性。

Observation（观测值）：指对变量的表现进行观察或测量所获得的数值，有时也被称为变数（variate）Population（总体）：又叫“统计总体”，是指一个统计问题研究对象的全体，它是具有某种（或某些）共同特征的元素的集合。

Individual（个体）：总体中每一个研究对象称作个体。

Sample（样本）：从总体中按一定方法抽取部分具有代表性的个体，这部分个体称为样本。

Parameter（参数）：描述总体特征的数，如总体平均数、总体方差等。

Statistic（统计量）：描述样本特征的量，如样本平均数、样本方差、样本相关系数等。

Accuracy（准确性）：指观测值或估计值与真值的接近程度。

Precision（精确性）：对同一物体的重复观察值或估计值彼此之间的接近程度。

Chapter 2Raw data（直接数据）:数据调查与实验未经处理的数据；Continuous data（连续性数据）：指在一定范围内可取任何实数值的数据。

Discrete data（离散性数据）：在一定范围内只能取有限种可能值的数据。

Count data（计数数据）：用计数的方式得到的数据资料，必须用整数来表示。

Classification data（分类资料）：可自然的或人为的分为2个或多个不同类别的资料。

例如：男生记做1 女生记做2频数（率）分布（frequency distribution）；；下四分位数（lower quartile）；中位数（median）；上四分位数（upper quartile）；条形图（bar chart）；直方图（histogram）；饼图（pie chart）；散点图（scatter plot），组间距（interval）Percentile（百分位数）：一组n个观测值按数值大小排列，小于某数值的数据个数占全体个数的x%,则为x%分位数。

Statistics S2单词汇总

Conditions for binomial distribution:A fixed number of trials ,n.Each trial should be success or failure.The trials are independent.The probability of success p,at each trial is constant.Conditions for poisson distribution:Singly in space or time.Independently of each other.At a constant rate in the sense that the mean number of occurrences in the interval is proportional to the length of the interval.Approximation:Binomial distribution can be approximated by Poisson: n is large p is small Binomial distribution can be approximated by Normal: n is large p is close to 0.5 Poisson distribution can be approximated by Normal: is largePopulation:a collection of individual people or items.Census: if the information is to be obtained from all members of the population,the investigation is census.Advantages and disadvantages of taking a census:AD:Every single member of the population is used.It is unbiased.It gives an accurate answer.DISAD:It takes a long time to do.It is costlyIt is often difficult to ensure that the whole population is surveyed. Advantages and disadvantages of taking sampling:AD:It is cheaperIt is readily availableSampling is advantageous where the testing of items results in their destruction. DISAD:Not contain all the individual units of a population.An uncertainty about sampling in that there will be a natural variation between any two samples due to the natural variation between the individual units that make up the samples.Another source of uncertainty is called bias.Sample survey: an investigation using a sample.Sampling unit: the individual units of a population.Sampling frame: the list of sampling units.Statistic: a quantity calculated solely from the observations in a sample.Sampling distribution:a probability distribution of a statisticHypothesis:a statement made about the value of a population parameter. Hypothesis test: a mathematical procedure to examine a value of a population parameter proposed by the null hypothesis compared with an alternative hypothesis. Critical region: the range of values of the test statistic that would lead to you rejecting H0Level of significance: the probability of rejecting H0 when H0is true。

医学统计学第1-2章(2015)

36
3. 方差（variance , 2 , S2）和标准差（standard deviation , S）
2 X 2
N
S2
2
XX
n1
总体方差
样本方差
37
4.标准差：
X 2
N
总体标准差
标准差或方差越大，说明个体差异越大，则均数的代表性越差。
•应用: 对称分布，尤其是正态分布
7
101-
10
104-
18
107-
25
110-
21
113-
15
116-
15
119-
7
122-125
1
合计
120
19
115名正常成年女子的血清转氨酶 (mmol/L)含量分布
血清转氨酶含量
人数
12-
2
15-
9
18-
14
21-
23
24-
19
27-
14
30-
11
33-
9
36-
7
39-
4
42-45
3
20
第二节集中趋势的描述——平均数
66.67
7
25
32
21.88
62
40
102
60.78
6
分组血栓组正常组合计
表 3. 9 正常妇女和血栓形成者的血型分布
A型
B型
AB 型 O 型
合计
32
8
10
9
59
51
19
12
70
152
83
27
22

统计学专业英语翻译

汉译英Population 总体，样本总体sample 样本，标本parameter 限制因素median 中位数odd 奇数，单数even 偶数range 极差variance 方差standard deviation 标准差Covariance 协方差empty event 空事件product event 积事件conditional probability 条件概率Random variable 随机变量binominal distribution 二项式分布uniform distribution 均匀分布Poisson distribution 泊松分布residual 残差central limit theorem 中心极限定律英译汉descriptive statistics 描述统计学mathematical statistics 数理统计学inductive statistics 归纳统计学Inferential statistics 推断统计学dimension 维，维数continuous variable 连续变量ordinal variable 有序变量nominal variable 名义变量dichotomous 两分的；二歧的discrete variable 离散变量categorical variable 分类变量location 定位，位置，场所dispersion 分散mean 均值unimodal单峰的multimodal 多峰的chaotic 无秩序的grouped data 分组数据frequency distribution频数分布cumulative frequency 累加频数tallying 计算Uniformly distribution 均匀分布histogram 直方图frequency polygon 频率多边图rectangle 矩形Percentile 百分位数quartile 四分位数interquartile range 四分位数间距simple event 简单事件Compound event 复合事件mutually exclusive 互斥的，互补相交的complementary event 对立事件Independent 独立的joint probability function 联合概率函数jacobian雅克比行列式Law of large numbers大数定律point estimate 点估计estimate 估计值statistic 统计量optimality 最优性Unbiased estimate 无偏估计量efficient estimate 有偏估计量unbiasedness无偏性efficience有效性Consistent estimate 一致估计量asymptotic properties 渐近性质Confidence interval 置信区间interval estimation 区间估计null hypothesis 原假设alternative hypothesis 备择假设significance level 显著性水平power function 幂函数testing procedures 检验方法test statistic 检验统计量rejection region 拒绝区域acceptance region 接受区域critical region 临界区域first-derivatives 一阶导数second-derivatives 二阶导数Likelihood ratio 似然比dependent variable因变量unexplanatory variable未解释变量independent variable自变量Error term 误差项regression coefficients 回归系数Sum of squared residuals 残差平方和Marginal probability function 边际概率函数joint probability density function 联合概率密度函数Marginal probability density function边际概率密度函数stochastically independent 随机独立的Mutually independently distribution 相互独立的分布independently and identically distribution 独立同分布的likelihood function 似然函数maximum likelihood estimator 最大似然估计量maximum likelihood estimate 最大似然估计值log-likelihood function 对数似然函数ordinary least squares estimation/estimate/estimator 普通最小二乘估计/估计值/估计量linear unbiased estimator 线性无偏估计第三章、概念与符号[An index]把指数定义成是对一组相关变量之中变化进行测算的一个实数。

统计学CH01 英文教材

Cengage Learning
1.6
Example 2.6 Stats Anxiety
Are most of the marks clustered around the mean or are they more spread out? Range = Maximum – minimum = 92-53 = 39 Variance Standard deviation
Copyright © 2009 Cengage Learning
1.7
Example 2.6 Stats Anxiety
Are there many marks below 60 or above 80?
What proportion are A, B, C, D grades?
A graphical technique –histogram can provide us with this and other information
Chapter 2 introduces several graphical methods.
Copyright © 2009 Cengage Learning
1.10
Descriptive Statistics
Another form of descriptive statistics uses numerical techniques to summarize data. The mean and median are popular numerical techniques to describe the location of the data. The range, variance, and standard deviation measure the variability of the data Chapter 4 introduces several numerical statistical measures that describe different features of the data.

2-数值变量与分类变量的统计描述分析

实习二统计描述第164～180页实习二统计描述医学统计资料类型¾数值变量资料：又称为计量资料。

变量值是定量的，有单位的，表示为数值的大小。

¾无序分类资料：又称为计数资料。

变量值是定性的，没有单位，表示为相互独立的类别。

¾有序分类资料：又称为等级资料。

变量值是定性的，没有单位，各类别具有程度上的差异。

注：不同类型的资料，统计方法不同；各种类型的资料之间是可以相互转化的。

一、数值变量资料的统计描述统计描述包括两个方面：集中趋势的描述和离散趋势的描述一、数值变量资料的统计描述（一）数值变量资料的频数表频数表（frequency table）：当变量值或者观测值较多时，将变量值分为适当的组段，统计各组段中相应的频数（或者人数），以描述数值变量资料的分布特征和分布类型。

一、数值变量资料的统计描述（一）数值变量资料的频数表频数表的用途1.描述数值变量资料的分布特征集中趋势（central tendency）：频数最多的组段代表了中心位置（平均水平），从两侧到中心，频数分布是逐渐增加的。

离散趋势（tendency of dispersion）：从中心到两侧，频数分布是逐渐减少的。

反映了数据的离散程度或者变异程度。

一、数值变量资料的统计描述（一）数值变量资料的频数表频数表的用途2.描述数值变量资料的分布类型正态分布：集中位置居中，左右两侧频数基本对称。

常见近似正态分布。

偏态分布：集中位置偏向一侧，频数分布不对称。

正偏态分布：集中位置偏向数值小的一侧或者左侧，有较长的右尾部。

负偏态分布：集中位置偏向数值大的一侧或者右侧，有较长的左尾部。

一、数值变量资料的统计描述（二）数值变量资料的频数分布图及正态曲线直方图及近似正态分布直方图及正偏态分布（二）数值变量资料的频数分布图及正态曲线一、数值变量资料的统计描述（三）集中趋势指标描述1.算数均数（均数mean ）适用于正态分布或者近似正态分布总体均数：µ；样本均数：一、数值变量资料的统计描述一、数值变量资料的统计描述（三）集中趋势指标描述2.几何均数（geometric mean，G）适用于一种特殊的偏态分布资料：等比资料（常见于抗体滴度）。

大二统计学知识点总结双语

大二统计学知识点总结双语Statistics is a fundamental subject for students majoring in mathematics, economics, and many other fields. In the second year of college, students delve deeper into statistical concepts and methods. In this article, we will summarize the key knowledge points of second-year statistics in both Chinese and English.1. 数据与变量 (Data and Variables)在统计学中，数据是指收集到的事实或观察的结果。

变量是研究中所关注的特征或属性。

数据可以分为定量数据和定性数据两种。

定量数据通常以数字形式表示，而定性数据描述的是非数量性质的特征。

In statistics, data refers to the facts or observations that have been collected. Variables are the characteristics or attributes of interest in a study. Data can be categorized into quantitative data and qualitative data. Quantitative data is usually expressed in numerical form, while qualitative data describes non-quantitative features.2. 描述统计学 (Descriptive Statistics)描述统计学是对已有数据进行总结、展示和分析的方法。

1010 USP39-NF34 ANALYTICAL DATA INTERPRETATION AND TREATMENT (中英文)

<1010> ANALYTICAL DATA—INTERPRETATION AND TREATMENT分析数据的解释和处理INTRODUCTION前言This chapter provides information regarding acceptable practices for the analysis and consistent interpretation of data obtained from chemical and other analyses. Basic statistical approaches for evaluating data are described, and the treatment of outliers and comparison of analytical procedures are discussed in some detail.对于分析化学分析和其他分析工作中获得的数据资料并给出相应解释的工作，本章提供了一些可接受的操作信息。

针对评价数据资料的一些基础统计学方法、异常值的处理和分析方法的比较，本章都进行了较为详细的讨论。

[NOTE—It should not be inferred that the analysis tools mentioned in this chapter form an exhaustive list. Other, equally valid, statistical methods may be used at the discretion of the manufacturer and other users of this chapter.] [注：本章所列的并非是所有的分析工具。

根据生产商和其他使用者的慎重判断，也可使用其他的一些等效统计方法。

]Assurance of the quality of pharmaceuticals is accomplished by combining a number of practices, including robust formulation design, validation, testing of starting materials, in-process testing, and final-product testing. Each of these practices is dependent on reliable test procedures. In the development process, test procedures are developed and validated to ensure that the manufactured products are thoroughly characterized. Final-product testing provides further assurance that the products are consistently safe, efficacious, and in compliance with their specifications.药品的质量保证是由一系列实践活动联合完成的，这些活动包括了耐用性的处方设计、确认、起始物料的检测、过程监测和终产品检测等。

独家Alevel数学StatisticS考试知识点

Summary of key points in S1Chapter 1: Binomial distribution1. （重点***）计算二项分布的概率：（1）公式法（**），由),(~p n B X ，则有x n x n x p p x X P --==)1()()( （2）查表法（***）：利用书中135-139页中的)()(x X P x F ≤=，其中p 是0.05的倍数、一直到0.50，n 最小是5、最大是50。

2. （重点**）计算二项分布的期望和方差：),(~p n B X ，则有np X E =)( )1()(p np X Var -=3. （考点*）二项分布的条件：● A fixed number of trials,n .● Each trial should be success or failure.● The trials are independent.● The probability of success,p , at each trial is constant.其中，n 为指数（index ），p 为参数（parameter ）。

难点是要求根据题意写出二项分布的条件，如果有题意背景的，要根据题意写。

4. （考点*）如果),(~p n B X ，其中5.0>p ，则)1,(~p n B Y -，那么5.01≤-p ；如果p 是0.05的倍数，则可以用查表法求概率。

5. 典型例题：例7/8/9*/10/11/12/13(a)/14*6. 复习题：Review Exercise 1: 1/4/87. 练习册部分题目：12-01-2, 10-01-1, 08-01-2Chapter 2: Representation and summary of data – location1、Frequency tables and grouped datacumulative frequency ：to add a column to the frequency table showing the running total of the frequencies.A grouped frequency distribution consists of classes and their related class frequencies.Classes 30-31 32-33 34-35For the class 32-33Lower class boundary is 31.5Upper class boundary is 33.5Class width is 33.5-31.5=2Class mid-point is (31.5+33.5)/2=32.52、The measurements of location of the centre of a set of data – mode, median and mean● The mode is the value that occurs most often.● The median is the middle value or the half of the two middle values, when the data is put in order.● The mean is the sum of all the observations divided by the total number of the observations. The mean of a sample of data in a frequency distribution, is x where∑∑=ffx x 3、Coding for large data valuesCoding is normally of the formba x y -= where a andb are to be chosen.To find the mean of the original data; find the mean of the coded data , equate this to the coding used and solve.Chapter 3:Representation and summary of data – measures if dispersion1、The range of a set of data is the difference between the highest and lowest value in the set.The quartiles, ,1Q ,2Q ,3Q split the data into four parts. To calculate the lower quartile , divide n by 4.For discrete data for the lower quartile, ,1Q divide n by 4. To calculate the upper quartile, ,3Q divide n by 4 and multiply by 3. When the result is a whole numberfind the mid-point of the corresponding term and the term above. When the result is not a whole number round the number up and pick the corresponding term. For continuous grouped data for ,1Q divide n by 4, for 3Q divide n by 4 and multiply by 3. Use interpolation to find the value of the corresponding term. The inter-quartile range is .13Q Q -2、The standard deviation and variance of discrete data variance=222)(⎪⎪⎭⎫ ⎝⎛-=-∑∑∑n x n x n x x standard deviation= VarianceIf you let f stand for the frequency, then ∑=f n andVariance=222)(⎪⎪⎭⎫ ⎝⎛-=-∑∑∑∑∑∑f fx f fx f x x f 3、Adding or subtracting numbers does not change the standard deviation of the data. Multiplying or dividing the data by a number does affect the standard deviation.To find the standard deviation of the original data, find the standard deviation of the coded data and either multiply this by what you divide the data by, or divide this by what you multiplied the data by.Chapter 4: Representation of data1. A stem and leaf diagram is used to order and present data given to two or three significant figures. Each number is first split into its stem and leaf .Two set of data can be compared by using back-to-back stem and leaf diagrams.2、An outlier is an extreme value that lies outside the overall pattern of the data, which is⏹ greater that the upper quartile +1.5⨯inter-quartile rangeor⏹ less that the lower quartile -1.5⨯inter-quartile range.3、Box plotUsing box plots to compare two sets of data4、HistogramA histogram gives a good picture of how data are distributed. It enables you to see a rough location, the general shape of the data and how spread out the data are.A histogram is similar to a bar chart but are two major differences● There are no gaps between the bars.● The area of the bar is proportional to the frequency.To calculate the height of each bar (the frequency density ) use the formulaArea of bar=⨯k frequency.1=k is the easiest value to use when drawing a histogram thenFrequency density=ClassWidthFrequency 5、The shape (skewness) of a data setThe ways of describing whether a distribution is skewed:⏹ You can use the quartiles.If 2312Q Q Q Q -=- then the distribution is symmetrical .If 2312Q Q Q Q -<- then the distribution is positively skewed .If 2312Q Q Q Q ->- then the distribution is negatively skewed .⏹ You can use the measures of locationmode=median=mean describes a distribution which is symmetrical .mode<median<mean describes a distribution with positive skew .mode>median>mean describes a distribution with negative skew .6、Comparing the distributions of data sets● The IQR is often used together with the median when the data are skewed .● The mean and standard deviation are generally used when the data are fairlysymmetrical .Chapter 5: Probability1、Vocabulary used in probabilityA sample space is the set of all possible outcomes of an experiment.The probability of an event is the chance that the event will occur as a result of an experiment. Where outcomes are equally likely the probability of an event is the number of outcomes in the event divided by the total number of possible outcomes in the sample space.2、Venn diagramsYou can use Venn diagrams to solve probability problems for two or three events. A rectangle represents the sample space and it contains closed curves that represent events.3、Using formulae to solve problemsAddition Rule)()()()(B A P B P A P B A P -+=Conditional probabilityThe probability of B given A , written )|(A B P , is called the conditional probability of B given A and so:)()()|(A P A B P A B P =Multiplication Rule)()|()(A P A B P A B P ⨯=4、Tree diagrams5、Mutually exclusive and independent eventsWhen A and B are mutually exclusive, then Φ=B A , so .0)(=B A PThe Addition Rule applied to mutually exclusive events:)()()(B P A P B A P +=If A and B are independent, then:)()()(B P A P B A P ⨯=Chapter 6: Correlation6.1 Scatter diagramsIf both variables increase together they are said to be positively correlated . For a positive correlation the points on the scatter diagram increase as you go from left to right. Most points lie in the first and third quadrants.If one variable increases as the other decreases they are said to be negatively correlated . For a negative correlation the points on the scatter diagram decrease as you go from left to right. Most points lie in the second and fourth quadrants.If no straight line (linear) pattern can be seen there is said to be no correlation . For no correlation the points on the scatter diagram lie fairly evenly in all four quadrants. Examples: 1/2/3 6.2 You can calculate measures for the variability of bivariate data()()()()∑∑∑∑∑∑∑∑∑∑-=--=-=-=-=-=ny x y y y x x S n y y y S n x x x S ii i i i xy ii yy i i xx i 22i 222i 2x ))((y )(x )(注：上面的公式在公式本中有。

AP统计学教材

AP统计学教材AP统计学教材内容提要AP，全称Advanced Placement，中文名称为大学预修课程。

AP课程及考试始于1955年，由美国大学理事会(College Board)主办，在高中阶段开设的具有大学水平的课程，共有22个门类、37个学科。

该项考试的目的在于使高中学生提前接触大学课程，完成一些美国大学的学分课程及考试。

本书作为国内第一本中英文结合的AP统计学教材，适合有一定数学基础的学生使用。

在研究了统计学的知识体系及教学体系的基础上，本书搭建了较易于中国学生理解与接受的AP统计学知识体系，真正全面覆盖了AP统计学的考点。

本书提供了大量的例题和习题，为夺取AP统计学的高分奠定了扎实的基础。

AP统计学教材目录Chapter 1 Introduction of AP Statistics Exam AP统计学考试简介Chapter 2 Descriptive Analysis of Categorical Data分类数据的描述分析2.1 Types of variables变量类型2.2 Analysis of univariate categorical data单变量分类数据的分析2.3 Analysis of bivariate categorical data双变量分类数据的分析Chapter 3 Descriptive Analysis of Continuous Data连续型数据的描述分析3.1 Analysis of univariate continuous data单变量连续型数据的分析3.2 Analysis of bivariate continuous data双变量连续型数据的分析Chapter 4 Sampling，Surveys and Experiments抽样，调查和实验设计4.1 Some basic concepts几个基本概念4.2 Methods of data collection收集数据的方式4.3 Some simple sampling methods几种简单的抽样方法4.4 Terms and concept of experiments实验设计中的基本概念4.5 Single—blind experiment and double—blind experiment单盲试验和双盲实验4.6 Experiments实验设计Chapter 1 Introduction of AP Statistics Exam AP统计学考试简介Chapter 2 Descriptive Analysis of Categorical Data分类数据的描述分析2.1 Types of variables变量类型2.2 Analysis of univariate categorical data单变量分类数据的分析2.3 Analysis of bivariate categorical data双变量分类数据的分析Chapter 3 Descriptive Analysis of Continuous Data连续型数据的描述分析3.1 Analysis of univariate continuous data单变量连续型数据的分析3.2 Analysis of bivariate continuous data双变量连续型数据的分析Chapter 4 Sampling，Surveys and Experiments抽样，调查和实验设计上海托福培训多少钱?这个问题是学生和家长在考虑培训学校时主要考虑的问题。

第二语言研究中的统计案例分析

第二语言研究中的统计案例分析第一章统计基本概念万万不能唯“统计结果”马首是瞻。

需要铭记在心的是，研究问题中的变量类型以及研究者所探索的关系才是第一位的，统计是第二位的。

统计推断有犯错误的可能性。

1.1总体、样本、抽样与抽样误差总体population：是我们研究的具有某种共同特征的个体总和。

样本sample:是从总体中按照一定的原则和程序抽取的作为观察对象的一部分个体。

样本容量用n表示，n＞30为大样本；n≤30为小样本（样本容量一般不会低于5）。

抽样sampling：是按照一定的原则从总体中选择个体构成样本的过程。

随机random sampling抽样：总体中每一个体被抽中的机会是相等的，如抽签、随机数字表；系统抽样quasi-random sampling：样本中的第一个个体按照抽签法选取，其余个体则在总体中按照一定的间距抽取，直到达到样本容量为止。

整群抽样cluster sampling：以总体中的群体为单位随机抽取个体。

分层抽样stratified sampling：先把总体按照某一特征的比例分成若干层（子体），再在每个层中随机抽样。

注意:样本的统计量不一定和总体参数完全一致，这种差异不是错误。

而是必然会出现的抽样误差，sampling error。

这种抽样误差是不可避免的。

1.2描述统计与推断统计描述统计descriptive statistics：是指利用统计量（如集中趋势和离散趋势）和/或统计图表展示样本数据的状态（描述数据的现状）。

推断统计inferential statistics：是指按照一定的原理，利用样本统计量对总体参数进行推论的过程。

1.3研究问题与假设统计学是为研究问题服务的，不同的研究问题需要用不同的统计方法（一类是问题现象，一类是研究问题research question--明确指出核心概念和研究焦点的疑问句）。

研究问题在统计实务中以假设的形式出现。

假设hypothesis：根据一定的原理或事实对结果做出的预测。

Chapter 9 Using Numbers

from Statistics in Foreign Language Teaching and Research by Han Baocheng
2.1 Extreme values may distort or "skew" a mean.
with extreme values in the interval data, the median acts as the typical vaule
2.2 Normal distribution(正态分布)
Descriptive Statistics
Three approaches of descriptive statistics 1. Central tendency: represent the typical value 2.Dispersion: represnt how typical the raw score is 3. Correlation: association
data
positive
(ampirical) approach and normative
approach
qualitative
research and quantitative research
statistics
1.2 Why to count and what to count
A teacher might wish:
2. Descriptive Statistics
the
definition
measures of descriptive statistics
Three
1. Central tendency 2. Dispersion 3. Correlation

英语数学词汇

Algebraic Equation代数方程Elementary Operations-Addition基础混算-加法Elementary Operations-Subtaction基础混算-减法Elementary Operations-Multiplication 基础混算-乘法Elementary Operations-Division基础混算-除法Elementary Operation基础四则混算Decimal Operations小数混算Fractional Operations分数混算Convert fractional no. into decimal no. 分数转小数Convert fractional no. into percentage. 分数转百分数Convert decimal no. into percentage. 小数转百分数Convert percentage into decimal no. 百分数转小数Percentage百分数Numerals数字符号Common factors and multiples公因子及公倍数Sorting数字排序Area图形面积Perimeter图形周界Change Units : Time单位转换-时间Change Units : Weight单位转换-重量Change Units :Length单位转换-长度Directed Numbers有向数Fractional Operations分数混算Decimal Operations小数混算Convert fractional no. into decimal no. 分数转小数Convert fractional no. into percentage.分数转百分数Convert decimal no. into percentage.小数转百分数Convert percentage into decimal no.百分数转小数Percentage百分数Indices指数Algebraic Substitution代数代入Polynomials多项式Co-Geometry坐标几何学Solving Linear Equation解一元线性方程Solving Simultaneous Equation解联立方程Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Geometry几何学Inequalities不等式Rate and Ratio比和比例Bearing方位角Trigonometry三角学Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of central tendency统计学-量度集中趋势Salary Tax薪俸税Bridging Game汉英对对碰Indices指数Function函数Rate and Ratio比和比例Trigonometry三角学Inequalities不等式Linear Programming线性规划Co-Geometry坐标几何学Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Method of Bisection分半方法Polynomials多项式Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of central tendency统计学-量度集中趋势Statistics-Measure of dispersion统计学-量度分布Statistics-Normal Distribution统计学-正态分布Surds根式Probability概率Statistics-Measure of dispersion 统计学-量度离差Statistics-Normal Distribution统计学-正态分布Statistics-Binomial Distribution 统计学Statistics-Poisson Distribution 统计学Statistics-Geometric Distribution 统计学Co-Geometry坐标几何学Sequence序列十万Hundred thousand三位数3-digit number千Thousand千万Ten million小数Decimal分子Numerator分母Denominator分数Fraction五位数5-digit number公因子Common factor公倍数Common multiple中国数字Chinese numeral平方Square平方根Square root古代计时工具Ancient timing device古代记时工具Ancient time-recording device 古代记数方法Ancient counting method古代数字Ancient numeral包含Grouping四位数4-digit number四则计算Mixed operations (The four operations)加Plus加法Addition加法交换性质Commutative property of addition未知数Unknown百分数Percentage百万Million合成数Composite number多位数Large number因子Factor折扣Discount近似值Approximation阿拉伯数字Hindu-Arabic numeral定价Marked price括号Bracket计算器Calculator差Difference真分数Proper fraction退位Decomposition除Divide除法Division除数Divisor乘Multiply乘法Multiplication乘法交换性质Commutative property of multiplication乘法表Multiplication table乘法结合性质Associative property of multiplication被除数Dividend珠算Computation using Chinese abacus倍数Multiple假分数Improper fraction带分数mixed number现代计算工具Modern calculating devices售价Selling price万Ten thousand最大公因子Highest Common Factor (H.C.F.)最小公倍数Lowest Common Multiple (L.C.M.)减Minus / Subtract减少Decrease减法Subtraction等分Sharing等于Equal进位Carrying短除法Short division单数Odd number循环小数Recurring decimal零Zero算盘Chinese abacus亿Hundred million增加Increase质数Prime number积Product整除性Divisibility双数Even number罗马数字Roman numeral数学 mathematics, maths(BrE), math(AmE) 公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和 sum减 minus(prep.), subtract(v.), subtraction(n.) 被减数 minuend减数 subtrahend差 remainder乘 times(prep.), multiply(v.), multiplication(n .)被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided by(prep.), divide(v.), division(n.) 被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n 次方根倒数（reciprocal） x的倒数为1/x有理数 rational number无理数 irrational number实数 real number虚数 imaginary number数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil十进制 decimal system二进制 binary system十六进制 hexadecimal system权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit无效数字 insignificant digit代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown, x-factor, y-factor, z-factor等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方 the power of four, the fourth powern次方 the power of n, the nth power开方 evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth rootsqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236常量 constant变量 variable坐标系 coordinates坐标轴 x-axis, y-axis, z-axis横坐标 x-coordinate纵坐标 y-coordinate原点 origin象限quadrant截距(有正负之分)intercede（方程的）解solution几何geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle等腰三角形 isosceles triangle等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width周长 perimeter面积 area相似 similar全等 congruent三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant补充：集合aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition 值域 range单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.)无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral复数 complex number矩阵 matrix行列式 determinant圆 circle 圆心 centre(BrE), center(AmE)半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference轨迹 locus, loca(pl.)平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron旋转 rotation轴 axis球 sphere半球 hemisphere底面 undersurface表面积 surface area体积 volume空间 space双曲线 hyperbola抛物线 parabola四面体 tetrahedron五面体 pentahedron六面体 hexahedron菱形 rhomb, rhombus, rhombi(pl.), diamond正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE), orthocenter(AmE)重心 barycentre(BrE), barycenter(AmE)内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph曲线统计图 curve diagram扇形统计图 pie diagramEnglish Chineseabbreviation 简写符号；简写abscissa 横坐标absolute complement 绝对补集absolute error 绝对误差absolute inequality 绝不等式absolute maximum 绝对极大值absolute minimum 绝对极小值absolute monotonic 绝对单调absolute value 绝对值accelerate 加速acceleration 加速度acceleration due to gravity 重力加速度; 地心加速度accumulation 累积accumulative 累积的accuracy 准确度act on 施于action 作用; 作用力acute angle 锐角acute-angled triangle 锐角三角形add 加addition 加法addition formula 加法公式addition law 加法定律addition law(of probability) （概率）加法定律additive inverse 加法逆元; 加法反元additive property 可加性adjacent angle 邻角adjacent side 邻边adjoint matrix 伴随矩阵algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式algebraic number 代数数algebraic operation 代数运算algebraically closed 代数封闭algorithm 算法系统; 规则系统alternate angle （交）错角alternate segment 内错弓形alternating series 交错级数alternative hypothesis 择一假设; 备择假设; 另一假设altitude 高；高度；顶垂线；高线ambiguous case 两义情况；二义情况amount 本利和；总数analysis 分析；解析analytic geometry 解析几何angle 角angle at the centre 圆心角angle at the circumference 圆周角angle between a line and a plane 直与平面的交角angle between two planes 两平面的交角angle bisection 角平分angle bisector 角平分线；分角线 angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角angle of elevation 仰角angle of friction 静摩擦角; 极限角angle of greatest slope 最大斜率的角angle of inclination 倾斜角angle of intersection 相交角；交角angle of projection 投射角angle of rotation 旋转角angle of the sector 扇形角angle sum of a triangle 三角形内角和angles at a point 同顶角angular displacement 角移位angular momentum 角动量angular motion 角运动angular velocity 角速度annum(X% per annum) 年（年利率X%）anti-clockwise direction 逆时针方向；返时针方向anti-clockwise moment 逆时针力矩anti-derivative 反导数; 反微商anti-logarithm 逆对数；反对数anti-symmetric 反对称apex 顶点approach 接近；趋近approximate value 近似值approximation 近似；略计；逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc length 弧长arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积Argand diagram 阿根图, 阿氏图argument (1)论证; (2)辐角argument of a complex number 复数的辐角argument of a function 函数的自变量arithmetic 算术arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列arithmetic series 等差级数arm 边array 数组; 数组arrow 前号ascending order 递升序ascending powers of X X 的升幂assertion 断语; 断定associative law 结合律assumed mean 假定平均数assumption 假定；假设asymmetrical 非对称asymptote 渐近asymptotic error constant 渐近误差常数at rest 静止augmented matrix 增广矩阵auxiliary angle 辅助角auxiliary circle 辅助圆auxiliary equation 辅助方程average 平均；平均数；平均值average speed 平均速率axiom 公理axiom of existence 存在公理axiom of extension 延伸公理axiom of inclusion 包含公理axiom of pairing 配对公理axiom of power 幂集公理axiom of specification 分类公理axiomatic theory of probability 概率公理论axis 轴axis of parabola 拋物线的轴axis of revolution 旋转轴axis of rotation 旋转轴axis of symmetry 对称轴back substitution 回代bar chart 棒形图；条线图；条形图；线条图base （1）底；（2）基；基数base angle 底角base area 底面base line 底线base number 底数；基数base of logarithm 对数的底basis 基Bayes' theorem 贝叶斯定理bearing 方位（角）；角方向（角）bell-shaped curve 钟形图belong to 属于Bernoulli distribution 伯努利分布Bernoulli trials 伯努利试验bias 偏差；偏倚biconditional 双修件式; 双修件句bijection 对射; 双射; 单满射bijective function 对射函数; 只射函数billion 十亿bimodal distribution 双峰分布binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial distribution 二项分布binomial expression 二项式binomial series 二项级数binomial theorem 二项式定理bisect 平分；等分bisection method 分半法；分半方法bisector 等分线；平分线Boolean algebra 布尔代数boundary condition 边界条件boundary line 界（线）；边界bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号breadth 阔度broken line graph 折线图calculation 计算calculator 计算器；计算器calculus (1) 微积分学; (2) 演算cancel 消法；相消canellation law 消去律canonical 典型; 标准capacity 容量cardioid 心脏Cartesian coordinates 笛卡儿坐标Cartesian equation 笛卡儿方程Cartesian plane 笛卡儿平面Cartesian product 笛卡儿积category 类型；范畴catenary 悬链Cauchy sequence 柯西序列Cauchy's principal value 柯西主值Cauchy-Schwarz inequality 柯西 - 许瓦尔兹不等式central limit theorem 中心极限定理central line 中线central tendency 集中趋centre 中心；心centre of a circle 圆心centre of gravity 重心centre of mass 质量中心centrifugal force 离心力centripedal acceleration 向心加速度centripedal force force 向心力centroid 形心；距心certain event 必然事件chain rule 链式法则chance 机会change of axes 坐标轴的变换change of base 基的变换change of coordinates 坐标轴的变换change of subject 主项变换change of variable 换元；变量的换characteristic equation 特征(征)方程characteristic function 特征(征)函数characteristic of logarithm 对数的首数; 对数的定位部characteristic root 特征(征)根chart 图；图表check digit 检验数位checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circular motion 圆周运动circular permutation 环形排列; 圆形排列; 循环排列circumcentre 外心；外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆cissoid 蔓叶class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classical theory of probability 古典概率论classification 分类clnometer 测斜仪clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coaxial 共轴coaxial circles 共轴圆coaxial system 共轴系coded data 编码数据coding method 编码法co-domain 上域coefficient 系数coefficient of friction 摩擦系数coefficient of restitution 碰撞系数; 恢复系数coefficient of variation 变差系数cofactor 余因子; 余因式cofactor matrix 列矩阵coincide 迭合；重合collection of terms 并项collinear 共线collinear planes 共线面collision 碰撞column (1)列；纵行；(2) 柱column matrix 列矩阵column vector 列向量combination 组合common chord 公弦common denominator 同分母；公分母common difference 公差common divisor 公约数；公约common factor 公因子；公因子common logarithm 常用对数common multiple 公位数；公倍common ratio 公比common tangent 公切commutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图compatible 可相容的complement 余；补余complement law 补余律complementary angle 余角complementary equation 补充方程complementary event 互补事件complementary function 余函数complementary probability 互补概率complete oscillation 全振动completing the square 配方complex conjugate 复共轭complex number 复数complex unmber plane 复数平面complex root 复数根component 分量component of force 分力composite function 复合函数; 合成函数composite number 复合数；合成数composition of mappings 映射构合composition of relations 复合关系compound angle 复角compound angle formula 复角公式compound bar chart 综合棒形图compound discount 复折扣compound interest 复利；复利息compound probability 合成概率compound statement 复合命题; 复合叙述computation 计算computer 计算机；电子计算器concave 凹concave downward 凹向下的concave polygon 凹多边形concave upward 凹向上的concentric circles 同心圆concept 概念conclusion 结论concurrent 共点concyclic 共圆concyclic points 共圆点condition 条件conditional 条件句；条件式conditional identity 条件恒等式conditional inequality 条件不等式conditional probability 条件概率cone 锥；圆锥（体）confidence coefficient 置信系数confidence interval 置信区间confidence level 置信水平confidence limit 置信极限confocal section 共焦圆锥曲 congruence (1)全等；(2)同余congruence class 同余类congruent 全等congruent figures 全等图形congruent triangles 全等三角形conic 二次曲 ;圆锥曲conic section 二次曲 ;圆锥曲conical pendulum 圆锥摆conjecture 猜想conjugate 共轭conjugate axis 共轭conjugate diameters 共轭轴conjugate hyperbola 共轭(直)径conjugate imaginary / complex number 共轭双曲conjugate radical 共轭虚/复数conjugate surd 共轭根式; 共轭不尽根conjunction 合取connective 连词connector box 捙接框consecutive integers 连续整数consecutive numbers 连续数；相邻数consequence 结论；推论consequent 条件；后项conservation of energy 能量守恒conservation of momentum 动量守恒conserved 守恒consistency condition 相容条件consistent 一贯的；相容的consistent estimator 相容估计量constant 常数constant acceleration 恒加速度constant force 恒力constant of integration 积分常数constant speed 恒速率constant term 常项constant velocity 怛速度constraint 约束；约束条件construct 作construction 作图construction of equation 方程的设立continued proportion 连比例continued ratio 连比continuity 连续性continuity correction 连续校正continuous 连续的continuous data 连续数据continuous function 连续函数continuous proportion 连续比例continuous random variable 连续随机变量contradiction 矛盾converge 收敛convergence 收敛性convergent 收敛的convergent iteration 收敛的迭代convergent sequence 收敛序列convergent series 收敛级数converse 逆(定理)converse of a relation 逆关系converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形convexity 凸性coordinate 坐标coordinate geometry 解析几何；坐标几何coordinate system 坐标系系定理；系；推论coplanar 共面coplanar forces 共面力coplanar lines 共面co-prime 互质; 互素corollary 系定理; 系; 推论correct to 准确至；取值至correlation 相关correlation coefficient 相关系数correspondence 对应corresponding angles (1)同位角；(2)对应角corresponding element 对应边corresponding sides 对应边cosecant 余割cosine 余弦cosine formula 余弦公式cost price 成本cotangent 余切countable 可数countable set 可数集countably infinite 可数无限counter clockwise direction 逆时针方向；返时针方向counter example 反例counting 数数；计数couple 力偶Carmer's rule 克莱玛法则criterion 准则critical point 临界点critical region 临界域cirtical value 临界值cross-multiplication 交叉相乘cross-section 横切面；横截面；截痕cube 正方体；立方；立方体cube root 立方根cubic 三次方；立方；三次(的)cubic equation 三次方程cubic roots of unity 单位的立方根cuboid 长方体；矩体cumulative 累积的cumulative distribution function 累积分布函数cumulative frequecy 累积频数；累积频率cumulative frequency curve 累积频数曲cumulative frequcncy distribution 累积频数分布cumulative frequency polygon 累积频数多边形；累积频率直方图curvature of a curve 曲线的曲率curve 曲线curve sketching 曲线描绘(法)curve tracing 曲线描迹(法)curved line 曲线curved surface 曲面curved surface area 曲面面积cyclic expression 输换式cyclic permutation 圆形排列cyclic quadrilateral 圆内接四边形cycloid 旋输线; 摆线cylinder 柱；圆柱体cylindrical 圆柱形的damped oscillation 阻尼振动data 数据De Moivre's theorem 棣美弗定理De Morgan's law 德摩根律decagon 十边形decay 衰变decay factor 衰变因子decelerate 减速decelaration 减速度decile 十分位数decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制decision box 判定框declarative sentence 说明语句declarative statement 说明命题decoding 译码decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列decreasing series 递减级数；下降级数decrement 减量deduce 演绎deduction 推论deductive reasoning 演绎推理definite 确定的；定的definite integral 定积分definition 定义degenerated conic section 降级锥曲线degree (1) 度; (2) 次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of confidence 置信度degree of freedom 自由度degree of ODE 常微分方程次数degree of precision 精确度delete 删除; 删去denary number 十进数denominator 分母dependence (1)相关; (2)应变dependent event(s) 相关事件; 相依事件; 从属事件dependent variable 应变量; 应变数depreciation 折旧derivable 可导derivative 导数derived curve 导函数曲线derived function 导函数derived statistics 推算统计资料; 派生统计资料descending order 递降序descending powers of x x的降序descriptive statistics 描述统计学detached coefficients 分离系数(法)determinant 行列式deviation 偏差; 变差deviation from the mean 离均差diagonal 对角线diagonal matrix 对角矩阵diagram 图; 图表diameter 直径diameter of a conic 二次曲线的直径difference 差difference equation 差分方程difference of sets 差集differentiable 可微differential 微分differential coefficient 微商; 微分系数differential equation 微分方程differential mean value theorem 微分中值定理differentiate 求...的导数differentiate from first principle 从基本原理求导数differentiation 微分法digit 数字dimension 量; 量网; 维(数)direct impact 直接碰撞direct image 直接像direct proportion 正比例direct tax, direct taxation 直接税direct variation 正变(分)directed angle 有向角directed line 有向直线directed line segment 有向线段directed number 有向数direction 方向; 方位direction angle 方向角direction cosine 方向余弦direction number 方向数direction ratio 方向比directrix 准线Dirichlet function 狄利克来函数discontinuity 不连续性discontinuous 间断(的);连续(的); 不连续(的)discontinuous point 不连续点discount 折扣discrete 分立; 离散discrete data 离散数据; 间断数据discrete random variable 间断随机变数discrete uniform distribution 离散均匀分布discriminant 判别式disjoint 不相交的disjoint sets 不相交的集disjunction 析取dispersion 离差displacement 位移disprove 反证distance 距离distance formula 距离公式distinct roots 相异根distincr solution 相异解distribution 公布distributive law 分配律diverge 发散divergence 发散(性)divergent 发散的divergent iteration 发散性迭代divergent sequence 发散序列divergent series 发散级数divide 除dividend (1)被除数；(2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor of zero 零因子dodecagon 十二边形domain 定义域dot 点dot product 点积double angle 二倍角double angle formula 二倍角公式double root 二重根dual 对偶duality (1)对偶性; (2) 双重性due east/ south/ west /north 向东/ 南/ 西/ 北dynamics 动力学eccentric angle 离心角eccentric circles 离心圆eccentricity 离心率echelon form 梯阵式echelon matrix 梯矩阵edge 棱；边efficient estimator 有效估计量effort 施力eigenvalue 本征值eigenvector 本征向量elastic body 弹性体elastic collision 弹性碰撞elastic constant 弹性常数elastic force 弹力elasticity 弹性element 元素elementary event 基本事件elementary function 初等函数elementary row operation 基本行运算elimination 消法elimination method 消去法；消元法ellipse 椭圆ellipsiod 椭球体elliptic function 椭圆函数elongation 伸张；展empirical data 实验数据empirical formula 实验公式empirical probability 实验概率；经验概率empty set 空集encoding 编码enclosure 界限end point 端点energy 能; 能量entire surd 整方根epicycloid 外摆线equal 相等equal ratios theorem 等比定理equal roots 等根equal sets 等集equality 等(式)equality sign 等号equation 方程equation in one unknown 一元方程equation in two unknowns (variables) 二元方程equation of a straight line 直线方程equation of locus 轨迹方程equiangular 等角(的)equidistant 等距(的)equilateral 等边(的)equilateral polygon 等边多边形equilateral triangle 等边三角形equilibrium 平衡equiprobable 等概率的equiprobable space 等概率空间equivalence 等价equivalence class 等价类equivalence relation 等价关系equivalent 等价(的)error 误差error allowance 误差宽容度error estimate 误差估计error term 误差项error tolerance 误差宽容度escribed circle 旁切圆estimate 估计；估计量estimator 估计量Euclidean algorithm 欧几里德算法Euclidean geometry 欧几里德几何Euler's formula 尤拉公式；欧拉公式evaluate 计值even function 偶函数even number 偶数evenly distributed 均匀分布的event 事件exact 真确exact differential form 恰当微分形式exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解example 例excentre 外心exception 例外excess 起exclusive 不包含exclusive disjunction 不包含性析取exclusive events 互斥事件exercise 练习exhaustive event(s) 彻底事件existential quantifier 存在量词expand 展开expand form 展开式expansion 展式expectation 期望expectation value, expected value 期望值；预期值experiment 实验；试验experimental 试验的experimental probability 实验概率explicit function 显函数exponent 指数exponential function 指数函数exponential order 指数阶; 指数级express…in terms of…以………表达expression 式；数式extension 外延；延长；扩张；扩充extension of a function 函数的扩张exterior angle 外角external angle bisector 外分角external point of division 外分点extreme point 极值点extreme value 极值extremum 极值face 面factor 因子；因式；商factor method 因式分解法factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式分解factorization of polynomial 多项式因式分解fallacy 谬误FALSE 假(的)falsehood 假值family 族family of circles 圆族family of concentric circles 同心圆族family of straight lines 直线族feasible solution 可行解；容许解Fermat's last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数figure (1)图(形)；(2)数字final velocity 末速度finite 有限finite dimensional vector space 有限维向量空间finite population 有限总体finite probability space 有限概率空间finite sequence 有限序列finite series 有限级数finite set 有限集first approximation 首近似值first derivative 一阶导数first order differential equation 一阶微分方程first projection 第一投影; 第一射影first quartile 第一四分位数first term 首项fixed deposit 定期存款fixed point 定点fixed point iteration method 定点迭代法fixed pulley 定滑轮flow chart 流程图focal axis 焦轴focal chord 焦弦focal length 焦距focus(foci) 焦点folium of Descartes 笛卡儿叶形线foot of perpendicular 垂足for all X 对所有Xfor each /every X 对每一Xforce 力forced oscillation 受迫振动form 形式；型formal proof 形式化的证明format 格式；规格formula(formulae) 公式four leaved rose curve 四瓣玫瑰线four rules 四则four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程fractional index 分数指数fractional inequality 分式不等式free fall 自由下坠free vector 自由向量; 自由矢量frequency 频数；频率frequency distribution 频数分布；频率分布frequency distribution table 频数分布表frequency polygon 频数多边形；频率多边形friction 摩擦; 摩擦力frictionless motion 无摩擦运动frustum 平截头体fulcrum 支点function 函数function of function 复合函数；迭函数functional notation 函数记号fundamental theorem of algebra 代数基本定理fundamental theorem of calculus 微积分基本定理gain 增益；赚；盈利gain perent 赚率；增益率；盈利百分率game （1）对策；（2）博奕Gaussian distribution 高斯分布Gaussian elimination 高斯消去法general form 一般式；通式general solution 通解；一般解general term 通项generating function 母函数; 生成函数generator (1)母线; (2)生成元geoborad 几何板geometric distribution 几何分布geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列geometric series 等比级数geometry 几何；几何学given 给定；已知global 全局; 整体global maximum 全局极大值; 整体极大值global minimum 全局极小值; 整体极小值golden section 黄金分割grade 等级gradient (1)斜率；倾斜率；(2)梯度grand total 总计graph 图像；图形；图表graph paper 图表纸graphical method 图解法graphical representation 图示；以图样表达graphical solution 图解gravitational acceleration 重力加速度gravity 重力greatest term 最大项greatest value 最大值grid lines 网网格线group 组；grouped data 分组数据；分类数据grouping terms 并项；集项growth 增长growth factor 增长因子half angle 半角half angle formula 半角公式half closed interval 半闭区间half open interval 半开区间harmonic mean (1) 调和平均数; (2) 调和中项harmonic progression 调和级数head 正面（钱币）height 高（度）helix 螺旋线hemisphere 半球体；半球heptagon 七边形Heron's formula 希罗公式heterogeneous (1)参差的; (2)不纯一的hexagon 六边形higher order derivative 高阶导数highest common factor(H.C.F) 最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图Holder's Inequality 赫耳德不等式homogeneous 齐次的homogeneous equation 齐次方程Hooke's law 虎克定律horizontal 水平的；水平horizontal asymptote 水平渐近线horizontal component 水平分量horizontal line 横线；水平线horizontal range 水平射程hyperbola 双曲线hyperbolic function 双曲函数hypergeometric distribution 超几何分布hypocycloid 内摆线hypotenuse 斜边hypothesis 假设hypothesis testing 假设检验hypothetical syllogism 假设三段论hypotrochoid 次内摆线idempotent 全幂等的identical 全等；恒等identity 等（式）identity element 单位元identity law 同一律identity mapping 恒等映射identity matrix 恒等矩阵identity relation 恒等关系式if and only if/iff 当且仅当；若且仅若if…, then 若….则；如果…..则illustration 例证；说明image 像点；像image axis 虚轴imaginary circle 虚圆imaginary number 虚数imaginary part 虚部imaginary root 虚根imaginary unit 虚数单位impact 碰撞implication 蕴涵式；蕴含式implicit definition 隐定义implicit function 隐函数imply 蕴涵；蕴含impossible event 不可能事件improper fraction 假分数improper integral 广义积分; 非正常积分impulse 冲量impulsive force 冲力incentre 内力incircle 内切圆inclination 倾角；斜角inclined plane 斜面included angle 夹角included side 夹边inclusion mapping 包含映射。

CH2NUMERICAL SUMMARY STATISTICS(商务统计,英文版)

μ
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Divide by the number of values
BEO1106 - Week 2
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Properties of the mean:
+ Each quantitative data set has one and only one mean; + It is the most comprehensive measure of central location
original unit of measurement; – It does not exist when the mean is zero, and can be misleading when some of the values are positive and some others are negative.
largest
•
Quartiles:
the 25th (Q1), 50th (Q2 or median) and 75th (Q3) percentiles.
Properties of the percentiles:
+ They measure non-central location (unless p=50); – They are really useful for only large data sets.
• Variance: ‘average’ of the squared deviations from the mean.