本书根据经济管理类专业的特点，贯彻“学以致用”的原则，侧重于统计思维的培养和社会经济问题中统计方法的应用，培养学生运用基本统计方法解决实际经济管理问题的能力，不涉及较深的数学知识。为帮助学生更好地理解各章的理论知识，本书还编写了很多真实案例加以说明。本书内容包括绪论、统计数据的搜集和整理、总量指标与相对指标、平均指标与变异指标、抽样估计与假设检验、相关分析与回归分析、时间序列分析、统计指数。每章后附有二维码，扫描可阅读趣味小资料。本书的附录中还给出了常用统计表。为方便教学，本书免费提供电子课件、习题参考答案，读者可登录华信教育资源网www.hxedu.com.cn下载使用。本书可作为高等院校经济学类、工商管理类专业，以及职业技术学院财经类专业的教学用书，也可作为人文、社会科学等专业学生的教材或参考书，还可作为从事经济管理、企业管理工作以及科研工作的有关人员的参考书。

前 言 这个星球未来的主人会是什么样的？这完全取决于今后拥有数据的人。控制数据的人， 不仅控制了未来，也控制了生命的未来，因为数据会是未来世界上最宝贵的资产。 —尤瓦尔·赫拉利（《人类简史》作者） 网络信息技术的飞速发展催生了以几何级数增加的数据量，同时也丰富了数据类型， 使我们进入了大数据时代。数字地球、智慧城市、电子商务、互联网金融、社交网络、云 计算技术等得到了广泛应用，它们渗透到人们生活的每一个角落，影响着我们每一个人。 大数据时代的到来虽然解决了信息匮乏问题，但又带来了信息泛滥问题，这使人们面对海 量、复杂的信息时难以快速、有效地甄别出有用的内容。因此，如何有效应对大数据带来 的挑战、使数据的价值得到有效的开发与利用，已成为当今世界各行各业最为关心的、企 业界和学术界全力探索的问题之一。 数据是一座资源宝藏，是一种资产。大数据已经成为一种战略性资源，成为重塑国家 竞争优势的新机遇，因此在很多国家都引起了高度重视，比如，美国已形成“数据就是石 油”的新理念。数据本身并没有价值，它的价值在于隐藏在其深处的有用知识。如何拨开 数据的面纱，发现这些隐而不见的有用知识，使数据成为提升企业和国家竞争力的重要资 源，已成为各国政府当今的重要任务。大数据开发与应用已上升为国家战略，很多国家都 制订了大数据研究与开发计划。目前，大数据在教育、医疗、汽车、交通、材料、传媒、 金融、商业和服务等行业都得到了较好的应用，并彰显出巨大的能量。大数据在给企业运 营、政府管理和媒体传播等创造有效机制的同时，也将给人们的生活、工作与决策、思维 等带来颠覆性的变革。因此，在大数据时代，统计学显得尤为重要，统计学专业也成为本 科的热门专业，这些都验证了英国科幻小说作家H.G.威尔斯的预言：统计思维总有一天会 像读写能力一样，成为一个有效率公民的必备能力。 在现实生活中，统计无处不在，统计无处不有，统计无处不用。特别是在大数据时代， 我们面对的是繁杂的海量数据，虽然统计数字不会说谎，但别有用心者却可以利用数字达 到说谎的目的。因此，学习统计知识、获得数据分析能力、掌握数据分析方法、借用“统 计慧眼”识别真假数据，就显得非常重要，这也应该成为每个人的必修课。在大数据时代， 统计学是读懂、听懂和看懂事情真相的基础，数据挖掘与统计分析已成为现代人必不可少 的技能，因为统计学是人们把握不确定世界的基本规律，把客观数据转化为有用信息和 知识的一把钥匙，有助于人们以更加智慧的方法进行各种决策。正如美国著名统计学家 C.R.劳在《统计与真理：怎样运用偶然性》一书中所说：“对统计学的一知半解常常造成不 必要的上当受骗，对统计学的一概排斥往往造成不必要的愚昧无知。” 统计学是一门关于数据搜集、整理、显示、分析和解释的方法论学科。对经济管理类 统计学 IV 专业学生来说，在日常学习和今后的工作中，都会涉及很多社会经济方面的数据和一些大 数据分析，因此，经济统计学一直是经济管理类本科专业的核心课程和必修学科之一。但 在高校中，对于统计学课程开设的必要性和重要性，学校和师生都存在着认识不足的问题， 这种现象需要引起高度重视。由于统计学与数学，特别是概率和数理统计理论的关系密切， 抽象性较强，因此有些学生感到统计学难学，教师也感到统计学教学效果不太理想。如何 提高经济管理类本科专业的统计学教学效果，提高学生应用统计学的理论知识与方法解决 实际经济问题的能力，是许多统计学教师一直在思考的问题。从数据处理流程来看，大数 据处理与统计学是相通的，都包括搜集、预处理、分析、显示和解释数据。我们认为，在 大数据时代，强调统计学教学的必要性和重要性尤为重要。 统计学是一门方法论学科，在长期的发展过程中形成了很多各具特色的统计思维，如 平均思维、变异思维、概率思维、推断思维、检验思维、普遍联系思维、相关思维、动态 思维等，这些统计思维对处理不确定现象、分析数据和解释数据都曾经产生过巨大的影响， 因此成为统计学的核心内容。在大数据时代，由于数据的复杂性和混杂性，统计学人还需 要建立新的思维模式。只有培养和提高统计思维能力，才能更好地学习统计学，发挥统计 学的应用价值。 统计学的学科性质决定了其理论和方法应用的广泛性，使之成为认识社会与自然的有 力武器，并推动了人类社会的发展。可以毫不夸张地说，统计改变了世界，统计改变了生 活，统计改变了人的思想。正如我国当代著名学者马寅初所说：“学者不能离开统计而究学， 实业家不能离开统计而执业，政治家不能离开统计而施政。” 统计学是公认的“社会科学的女王”。已故著名经济学家保罗·萨缪尔森在其经典教科 书《经济学》中特别提到：“在许多与经济学有关的学科中，统计学是特别重要的。”据统 计，在诺贝尔经济学奖的获奖者中，三分之二以上获奖者的研究成果与统计和定量分析有 关。经济管理类专业课程的学习过程中所涉及的现象基本都具有随机性、不确定性的特点， 因此，学好统计学、用好统计方法对经济管理类本科专业的学习具有特别重要的意义。从 学科性质方面来看，统计学是一门关于一切学问的学问，当代著名统计学家C.R.劳在《统 计与真理：怎样运用偶然性》一书中说：“与其说统计学是通过搜集整理数据来引出答案的 一组规则，不如说它是一种思考或推理的方法。”因此，在统计学的教学过程中，应以培养 学生的统计思维能力为重点，并结合经济管理类专业所涉及的实质性学科的具体研究对象 来选择和应用统计方法。在大数据时代，统计学的教与学不应要求死记有关概念、定理和 计算公式，而应加强基础性原理与知识的教学，突出统计学理论与方法的应用性，建立起 大数据统计思维。学习统计学是为了应用和解决实际问题，因此，对教师来说，教好统计 学的标志是教会学生运用统计思维思考问题和选择合适的统计方法解决实际社会经济问 题。对学生来说，学好统计学的标志是虽然记不住公式，但能够在统计思想的引导下，选 择合适或最优的统计方法，或者通过创新统计方法有效地解决实际问题。 为了帮助学生学好、用好统计知识，培养统计思维，我们编写了本教材。我们根据经 济管理类专业的特点，努力贯彻“学以致用”的原则，在保证统计学知识结构比较完整的 前 言 V 前提下，尽量精简比较繁琐的数学推导方面的内容，对推断统计学的内容也进行了适当的 选择。因此，本教材注重实用，并不需要很深的数学知识，大部分内容只需要中学的数学 知识。为了帮助学生更好地理解各章的理论知识，编者除应用举例外，还编写了很多真实 案例加以说明。本书虽然是专门为学习经济管理类专业的学生编写的，但也是一本介绍统 计学基本原理、基本方法及其在经济管理领域的基本应用的教科书，因此，本书对学习统 计学课程、应用统计学知识的其他人士也有重要的参考价值。 参加本书编写的有杜德权（负责第二章、第六章的编写工作）、袁春梅（负责第三章的 编写工作）、赵志红（负责第七章的编写工作）、张志伟（负责第八章的编写工作）和姚寿 福（负责第一章、第四章、第五章的编写工作）。姚寿福负责全书的设计、修改和定稿工作。 本书是“四川省教育厅精品课”建设的成果之一，也是在各位编写者多年的教学基础 上编写的。在本书编写过程中，我们对经济管理类专业的特点、知识学习的连续性、继承 性及教学时长等方面进行了综合考虑，在体系设计和内容安排上做了一些调整，使教材能 更好地满足经济管理类专业的教学要求。 首先，经济管理类专业的统计学教学目的是，使学生掌握基本的统计原理、形成基本 的统计思想、学会基本的统计分析方法，培养学生运用基本统计方法解决实际经济管理问 题的能力。因此，本书侧重于统计思维的培养和社会经济问题中统计方法的应用，而未涉 及较深的数学知识。 其次，由于经济管理类本科生一般都要学习“概率论与数理统计”这门先修的数学课 程和“计量经济学”等课程，因此，本书把抽样调查、参数估计、假设检验和方差分析放 在一章中进行介绍，以避免课程内容重复。对相关与回归分析也只介绍了一元线性回归模 型的参数估计、统计检验和基本应用，而未涉及多元线性回归模型的知识，目的就是使同 学们能够更好地形成基本的回归分析思维。 尽管我们一直努力编写一本高质量的教材，但由于水平有限，书中难免存在疏漏或错 误之处，在此恳请同行和读者不吝赐教，以便我们今后加以改进和完善，反馈请发邮件至 364515068@qq.com。 姚寿福 2020 年3 月于西华大学

目 录 第一章 绪论 ································································································.1 第一节 统计学的概念 ··············································································.1 第二节 统计学的研究对象、理论基础和方法 ················································.2 一、统计学的研究对象 ························································································.2 二、统计学的理论基础 ························································································.2 三、统计学的研究方法 ························································································.3 第三节 统计学的几个基本概念 ··································································.4 一、总体、总体单位与样本 ··················································································.4 二、统计标志和标志表现 ·····················································································.5 三、变异和变量 ·································································································.5 四、统计指标和指标体系 ·····················································································.6 思考与练习 ·····························································································.8 第二章 统计数据的搜集和整理 ········································································.9 第一节 统计数据的搜集 ··········································································.10 一、统计调查的概念和类型 ·················································································.10 二、统计调查方案 ·····························································································.11 三、统计调查方法 ·····························································································.14 四、统计资料的间接来源 ····················································································.19 第二节 统计整理 ···················································································.19 一、统计整理的意义和内容 ·················································································.19 二、统计分组法 ································································································.20 三、分配数列 ···································································································.23 四、统计表 ······································································································.28 思考与练习 ····························································································.31 第三章 总量指标与相对指标 ··········································································.33 第一节 总量指标 ···················································································.33 一、总量指标的概念与意义 ·················································································.33 二、总量指标的种类 ··························································································.34 三、计算总量指标应注意的问题 ···········································································.35 第二节 相对指标 ···················································································.35 一、相对指标的概念和意义 ·················································································.35 二、计划完成程度相对指标 ·················································································.36 三、结构相对指标 ·····························································································.38 四、比较相对指标 ·····························································································.39 五、比例相对指标 ·····························································································.40 六、强度相对指标 ·····························································································.40 七、动态相对指标 ·····························································································.41 八、计算和应用相对指标应注意的问题 ··································································.41 思考与练习 ····························································································.42 第四章 平均指标与变异指标 ··········································································.44 第一节 集中趋势指标—平均指标 ···························································.44 一、平均指标的基本概念与特点 ···········································································.44 二、平均指标的作用 ··························································································.45 三、平均指标的度量 ··························································································.46 第二节 集中趋势指标—位置平均数 ························································.54 一、众数 ·········································································································.54 二、中位数 ······································································································.56 三、众数、中位数和算术平均数的比较 ··································································.59 第三节 离中趋势指标—变异指标 ···························································.60 一、变异指标的概念与作用 ·················································································.60 二、全距 ·········································································································.60 三、平均差 ······································································································.61 四、异众比率 ···································································································.62 五、四分位数差 ································································································.62 六、方差与标准差 ·····························································································.63 七、变异系数 ···································································································.65 八、数据的标准化处理 ·······················································································.66 第四节 数据分布的偏态与峰度 ·································································.67 一、矩的概念 ···································································································.67 二、偏态 ·········································································································.67 三、峰度 ·········································································································.68 思考与练习 ····························································································.69 第五章 抽样估计与假设检验 ··········································································.73 第一节 抽样调查与抽样估计 ····································································.73 一、概率抽样与非概率抽样 ·················································································.73 二、抽样误差及其测度 ·······················································································.76 三、样本统计量 ································································································.79 四、抽样分布 ···································································································.80 五、参数估计的一般问题 ····················································································.84 六、一个总体参数的区间估计 ··············································································.86 七、样本量的确定 ·····························································································.91 第二节 假设检验 ···················································································.93 一、假设检验的基本思想 ····················································································.94 二、假设检验的步骤 ··························································································.94 三、假设检验中的两类错误 ·················································································.96 四、一个总体参数的假设检验 ··············································································.97 第三节 方差分析 ·················································································.101 一、方差分析的基本问题 ··················································································.102 二、单因素方差分析 ························································································.104 三、方差分析中的多重比较 ···············································································.108 思考与练习 ··························································································.109 第六章 相关分析与回归分析 ··········································································114 第一节 相关分析与回归分析的概念 ···························································114 一、相关分析的概念与类型 ···············································································.114 二、回归分析的概念与类型 ···············································································.116 三、相关分析与回归分析的关系 ·········································································.117 第二节 相关表、相关图与相关系数 ···························································118 一、相关表 ····································································································.118 二、相关图 ····································································································.119 三、相关系数 ·································································································.119 第三节 一元线性回归模型 ·····································································.122 一、一元线性回归模型 ·····················································································.122 二、一元线性回归模型参数的估计 ······································································.124 三、一元线性回归模型的统计检验 ······································································.131 四、一元线性回归模型的应用 ············································································.137 第四节 可线性化的曲线回归 ··································································.141 一、非线性相关与回归的含义 ············································································.141 二、非线性回归模型的估计 ···············································································.141 思考与练习 ··························································································.145 第七章 时间序列分析 ·················································································.150 第一节 时间序列及分析方法概述 ····························································.150 一、时间序列的概念及分类 ···············································································.150 二、时间序列分析方法 ·····················································································.153 第二节 时间序列的水平指标分析 ····························································.154 一、发展水平 ·································································································.154 二、平均发展水平 ···························································································.154 三、增减量 ····································································································.159 四、平均增减量 ······························································································.160 第三节 时间序列的速度指标分析 ····························································.160 一、发展速度 ·································································································.160 二、增减速度 ·································································································.161 三、平均发展速度 ···························································································.162 四、平均增减速度 ···························································································.163 五、速度指标的分析与应用 ···············································································.163 第四节 时间序列的成分分析 ··································································.164 一、时间序列的构成成分和分析模型 ···································································.164 二、长期趋势的测定 ························································································.165 三、季节变动分析 ···························································································.180 四、循环变动的测定 ························································································.187 思考与练习 ··························································································.188 第八章 统计指数 ·······················································································.194 第一节 统计指数的概念和分类 ·······························································.194 一、指数的概念和性质 ·····················································································.194 二、统计指数作用 ···························································································.195 三、统计指数的分类 ························································································.196 第二节 总指数的编制方法 ·····································································.198 一、简单指数 ·································································································.198 二、加权指数 ·································································································.200 第三节 指数体系和因素分析 ··································································.207 一、指数体系及其作用 ·····················································································.207 二、复杂总体总量变动的因素分析 ······································································.208 三、平均指标指数的因素分析 ············································································.213 第四节 几种常用的经济指数 ··································································.216 一、消费者价格指数和零售物价指数 ···································································.216 二、工业生产指数 ···························································································.218 三、股票价格指数 ···························································································.219 四、产品成本指数 ···························································································.222 五、空间价格指数 ···························································································.223 思考与练习 ··························································································.224 附录A 常用统计表 ·······················································································.228 参考文献 ···································································································.242

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