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Jingdong book

AP统计学基础教程

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Jingdong book

AP统计学基础教程

Name: AP统计学基础教程
Brand: Jingdong book
SKU: 3101012311
Price: 42.26 USD
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Content Description

《AP统计学基础教程》全面介绍AP统计学的相关考点，涵盖描述性统计与推论性统计两大内容，详细阐述了数据描述、数据采集、概率基础、随机变量、抽样分布、区间估计和假设检验的相关内容。正文使用中英双语进行讲解，围绕AP考试的风格与要求详解每一知识点，每章后附有丰富的AP式英文习题以检测学生的掌握情况。同时，为配合AP考试的要求，《AP统计学基础教程》以TI－84计算器为例讲解相关的计算器操作，以提高考生的计算效率与应试技能。同时，全书最后配有全真AP模拟试题一套，以便考生在考前检测自己的应试水平。

Author Description

吕小康，博士，多年从事ACT、SAT、AP、GRE、GMAT等留美考试中的数学类课程的教学与研究工作。他同时也是中国人大学出版社出版的《AP统计学基础教程》的作者。每年受富臣教育委托赴美参加AP官方年会及在国内举办的各类AP研讨班，近距离接触AP资深阅卷者与命题专家，参与AP课程的教学研讨与试题分析，全面吸取原汁原味的AP教学理念，准确把握最新的考试动态与应试趋势。教学风格严谨清晰又不失轻松活泼，已帮助多名富臣学子获得各类美国考试中的数学满分成绩。但与获得高分相比，他更感兴趣的是如何激励学生领略数学这一人类理性思维结晶的无穷魅力与深远影响。

Catalogue

Chapter 1 Data description
第1章数据描述
1.1 数据的基本类型
1.2 数据的图表呈现
1.3 数据的数字特征
1.4 习题检测

Chapter 2 Data collection
第2章数据采集
2.1 抽样方式
2.2 实验设计
2.3 习题检测

Chapter 3 Essentials of probability
第3章概率基础
3.1 随机事件及其运算
3.2 概率的定义及其运算
3.3 计数技巧
3.4 习题检测

Chapter 4 Random variables
第4章随机变量
4.1 随机变量的定义与类型
4.2 随机变量的数字特征
4.3 常见离散型分布
4.4 常见连续型分布
4.5 大数定理与中心极限定理
4.6 习题检测

Chapter 5 Parameter estimation
第5章参数估计
5.1 基本术语
5.2 样本均值与样本比例的抽样分布
5.3 点估计与区间估计
5.4 习题检测

Chapter 6 Hypothesis testing
第6章假设检验
6.1 假设检验的基本思想
6.2 假设检验的类型与公式
6.3 相关系数与线性回归的假设检验
6.4 卡方检验
6.5 习题检测

Chapter 7 Simulation test and answers
第7章 AP考试全真模拟试题及详解
7.1 试题
7.2 详解

Appendix 1 AP statistics fomula
附录一 AP统计学公式
Appendix 2 Probability tables
附录二概率分布表
Appendix 3 Random digit table
附录三随机数表
Appendix 4 Teminology for AP statistics
附录四统计术语中英对照表
Appendix 5 TI-84 statistics operation guide
附录五 TI-84统计操作指南
Appendix 6 Greek alphabet
附录六希腊字母表

Book Abstract

正文精彩页：
Chapter 1 Data description
第1章数据描述

资料的简化是统计方法的目标.
——［英］费希尔
Statistics: The only science that enables different experts using the same figures to draw different conclusions.
——［America］ Evan Esar

统计学 (statistics) 是现代人在实际生活中最需要的一门数学学科. 从物理、生物、医学、通信、人工智能等传统所谓的理工科, 到经济、金融、保险、精算等商科类学科, 以及政治学、社会学、心理学等社会科学, 都有统计学的用武之地, 它在工商业决策、政府情报、信息安全、系统检测以及日常生活的基本判断等领域扮演着不可或缺的角色. 序言中已经提过描述性统计 (descriptive statistics) 与推论性统计 (inferential statistics, 又称statistical inference). 描述性统计是关于数据的收集、组织和呈现的工作, 主要表现为制作图表并解释图表的意义, 以及概括数据的数字特征上. 推论性统计则研究如何通过局部资料 (样本信息) 来推论全局特征 (总体特征), 需要较强的概率论基础. 在一些人的眼中, “统计即是图表”. 这一说法虽并不准确, 却也道出统计学一大部分的内容: 描述性统计. 它负责对统计数据的采集和描述, 并且通常采用图表的方式呈现. 本章将主要讨论数据的基本图表处理方式和数字概括方式.

1. 1数据的基本类型
统计学的处理对象主要就是数据(data, 单数datum). 数据可以分为单变量数据(univariate data)、双变量数据(bivariate data) 和多变量数据(multivariate data), AP考试仅考查前两种. 所谓单变量数据, 是指仅包含单一特征值的变量, 如单独的身高、体重、兴趣、爱好; 双变量数据, 是指数据包含双重特征值, 如研究同一组人群时, 同时收集身高和体重, 并以有序数对的方式呈现 (170, 60), 前面为身高 (单位: 厘米), 后面为体重 (单位: 千克). 多变量数据的定义可以依次类推.

1.1.1定性数据
更具体的, 单变量数据又可以分为两种类型: 定性数据 (qualitative data) 和定量数据(quantitative data). 从表现形式上, 这两种数据的区别是显而易见的: 定性数据通常以文字、图形、录音、录像等非数字形式表现, 而定量数据通常是以数字形式表现. 由于定性数据通常无法通过数字量度进行区别, 我们通常将它们进行归类总结, 如天气状况 (下雨、晴天、阴天等)、性别 (男、女)、民族 (汉、回、蒙)、兴趣爱好 (足球、篮球、戏剧、音乐) 等. 我们只能知道, 班级里有多少人是汉族、多少人是回族, 但是不能说 “这个班级的平均民族是……”. 这种类型的定性数据也称为类型数据 (categorical data). 另外一种定性数据是顺序数据 (rank data), 即不仅可以分类, 还可以进行排序, 如教育程度 (小学、中学、大学)、对某事的态度 (十分赞同、较为赞同、中立、较不赞同、非常不赞同). 当然, 顺序数据也可以看成是一种特殊的类型数据, 两者就AP阶段的统计学处理而言, 可以不必做细分, 仅认为是定性数据即可. 要特别注意的是, 像球衣号码、门牌号码、车牌号码这类虽然在表面上似乎是用数字呈现, 但实际上仅表示一个标志和类别的数据, 只能认为是定性数据, 而不能认为是定量数据, 因为这里的数字没有任何计算性的特征, 仅仅是表示一个标志而已. 对于这类问题, 一个有效的判定方式是考虑这些数字的平均数有没有实际意义, 如果有实际意义, 一般就是下面介绍的定量数据; 如果平均数没有实际意义, 则一般为定性数据. 例如, 平均车牌号、平均球衣号、平均门牌号等完全不符合实际逻辑, 因此它们只能是定性数据.

1.1.2定量数据
定量数据在生活中也非常普遍, 如大家普遍关心的学习成绩、身高、体重、大学学费, 以及奔跑速度、汽车油耗、细菌数量, 等等, 它们可以用非常精确的数字进行刻画, 也是大家印象中数学类学科所最经常处理的对象. 同时还可以将定量数据划分为离散数据 (discrete data) 和连续数据 (continuous data). 离散数据的数值只能是有限个或可列个取值 (总数无穷但可一一列举, 如整数的数目), 一般用自然数或整数单位 (但不完全如此, 如鞋的尺码, 可能有半码的情况) 计算, 如家庭子女数、班级人数、设备台数, 这种数据的数值一般用计数 (counting) 的方式取得. 连续数据的取值却有很大不同. 它在一定区间内可以任意取值, 其可能数值是连续不断地充满整个区间, 相邻两个数值之间可作无限分割, 即可取无限个数值. 例如, 人的身高、体重、胸围、腰围, 容器的容积、物体的体积, 等等, 其数值只能通过测量 (measuring) 取得.
以后大家在统计学中可能会学到稍微不同的数据类型分类, 如最为普遍的是将数据根据其测量属性划分为定类 (nominal)、定序 (ordinal)、定距 (interval)、定比 (ratio) 四个层次, 其中, 前两者相当于这里的定性数据, 后两者就是定量数据. 四个层次的数据, 会涉及不同的统计学处理模式. 但就AP考试而言, 能理解categorical、 discrete和continuous三种性质的数据, 就已经足够了.

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