统计入门指南：Rice University教程

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《基础统计学》是RISE大学出品的一本详尽介绍统计学原理的权威教材，由芭芭拉·阿里洛夫斯基和苏珊·迪恩两位资深作者共同编撰，由开放科学出版社（OpenStax）与 Rice University 联合出版。该书内容覆盖广泛，从抽样和数据出发，深入探讨描述性统计、概率论、离散随机变量、连续随机变量、正态分布、中心极限定理、置信区间以及单样本假设检验等多个关键领域，旨在为初学者提供全面而实用的统计知识。在第一部分“Sampling and Data”中，学生将学习如何设计有效的抽样方法和理解收集的数据类型，这对于后续分析的基础至关重要。第二部分“Descriptive Statistics”则涵盖了集中趋势度量（如均值、中位数和众数）、分散程度度量（如方差和标准差）以及数据可视化，帮助读者解读和呈现数据的基本特征。进入第三部分“Probability Topics”，读者将掌握概率的基本概念，包括事件的概率、条件概率、独立事件和全概率定理等，这些是理解和应用随机变量的基础。第四和第五部分深入讨论了离散随机变量和连续随机变量，分别涉及离散概率分布和连续概率密度函数，如二项分布、几何分布、泊松分布和正态分布等。第六章专门探讨正态分布，这是许多实际问题中常见的模型，理解其性质和应用对于很多统计分析至关重要。第七章的中心极限定理揭示了大量独立同分布随机变量的平均值如何趋向于正态分布，这对于理解样本均值的分布有着深远的影响。接着，第八章介绍了置信区间，它是推断统计的核心概念，通过置信区间的构建，可以估计总体参数的可能范围，为决策提供依据。第九章“Hypothesis Testing with One Sample”讲解了一样本假设检验，即在单个总体中测试特定假设，这是统计推断的重要组成部分，也是实验设计和数据解释中的常见工具。《基础统计学》这本书不仅适合统计学入门者，也对那些希望深入了解统计原理的专业人士具有参考价值。由于它遵循Creative Commons Attribution 4.0 International License (CC BY 4.0)协议，读者可以根据该许可协议自由下载、分享和使用，只需确保适当的署名。无论是数字版还是印刷版，都要求包含来源链接，体现了开放教育资源的共享理念。

Solution 1.1

The population is all first year students attending ABC College this term.

The sample could be all students enrolled in one section of a beginning statistics course at ABC College (although

this sample may not represent the entire population).

The parameter is the average (mean) amount of money spent (excluding books) by first year college students at

ABC College this term.

The statistic is the average (mean) amount of money spent (excluding books) by first year college students in the

sample.

The variable could be the amount of money spent (excluding books) by one first year student. Let X = the amount

of money spent (excluding books) by one first year student attending ABC College.

The data are the dollar amounts spent by the first year students. Examples of the data are $150, $200, and $225.

1.1 Determine what the key terms refer to in the following study. We want to know the average (mean) amount of

money spent on school uniforms each year by families with children at Knoll Academy. We randomly survey 100

families with children in the school. Three of the families spent $65, $75, and $95, respectively.

Example 1.2

Determine what the key terms refer to in the following study.

A study was conducted at a local college to analyze the average cumulative GPA’s of students who graduated last

year. Fill in the letter of the phrase that best describes each of the items below.

1._____ Population 2._____ Statistic 3._____ Parameter 4._____ Sample 5._____ Variable 6._____ Data

a) all students who attended the college last year

b) the cumulative GPA of one student who graduated from the college last year

c) 3.65, 2.80, 1.50, 3.90

d) a group of students who graduated from the college last year, randomly selected

e) the average cumulative GPA of students who graduated from the college last year

f) all students who graduated from the college last year

g) the average cumulative GPA of students in the study who graduated from the college last year

Solution 1.2

1. f; 2. g; 3. e; 4. d; 5. b; 6. c

8 Chapter 1 | Sampling and Data

This OpenStax book is available for free at http://cnx.org/content/col11562/1.17

Example 1.3

Determine what the key terms refer to in the following study.

As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected

and reviewed data about the effects of an automobile crash on test dummies. Here is the criterion they used:

Speed at which Cars Crashed Location of “drive” (i.e. dummies)

35 miles/hour Front Seat

Table 1.1

Cars with dummies in the front seats were crashed into a wall at a speed of 35 miles per hour. We want to know

the proportion of dummies in the driver’s seat that would have had head injuries, if they had been actual drivers.

We start with a simple random sample of 75 cars.

Solution 1.3

The population is all cars containing dummies in the front seat.

The sample is the 75 cars, selected by a simple random sample.

The parameter is the proportion of driver dummies (if they had been real people) who would have suffered head

injuries in the population.

The statistic is proportion of driver dummies (if they had been real people) who would have suffered head injuries

in the sample.

The variable X = the number of driver dummies (if they had been real people) who would have suffered head

injuries.

The data are either: yes, had head injury, or no, did not.

Example 1.4

Determine what the key terms refer to in the following study.

An insurance company would like to determine the proportion of all medical doctors who have been involved in

one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and

determines the number in the sample who have been involved in a malpractice lawsuit.

Solution 1.4

The population is all medical doctors listed in the professional directory.

The parameter is the proportion of medical doctors who have been involved in one or more malpractice suits in

the population.

The sample is the 500 doctors selected at random from the professional directory.

The statistic is the proportion of medical doctors who have been involved in one or more malpractice suits in the

sample.

The variable X = the number of medical doctors who have been involved in one or more malpractice suits.

The data are either: yes, was involved in one or more malpractice lawsuits, or no, was not.

Chapter 1 | Sampling and Data 9

Do the following exercise collaboratively with up to four people per group. Find a population, a sample, the parameter,

the statistic, a variable, and data for the following study: You want to determine the average (mean) number of glasses

of milk college students drink per day. Suppose yesterday, in your English class, you asked five students how many

glasses of milk they drank the day before. The answers were 1, 0, 1, 3, and 4 glasses of milk.

1.2 | Data, Sampling, and Variation in Data and Sampling

Data may come from a population or from a sample. Small letters like

generally are used to represent data values.

Most data can be put into the following categories:

• Qualitative

• Quantitative

Qualitative data are the result of categorizing or describing attributes of a population. Hair color, blood type, ethnic group,

the car a person drives, and the street a person lives on are examples of qualitative data. Qualitative data are generally

described by words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Blood

type might be AB+, O-, or B+. Researchers often prefer to use quantitative data over qualitative data because it lends itself

more easily to mathematical analysis. For example, it does not make sense to find an average hair color or blood type.

Quantitative data are always numbers. Quantitative data are the result of counting or measuring attributes of a population.

Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics are

examples of quantitative data. Quantitative data may be either discrete or continuous.

All data that are the result of counting are called quantitative discrete data. These data take on only certain numerical

values. If you count the number of phone calls you receive for each day of the week, you might get values such as zero, one,

two, or three.

All data that are the result of measuring are quantitative continuous data assuming that we can measure accurately.

Measuring angles in radians might result in such numbers as

3π

, and so on. If you and your friends carry

backpacks with books in them to school, the numbers of books in the backpacks are discrete data and the weights of the

backpacks are continuous data.

10 Chapter 1 | Sampling and Data

This OpenStax book is available for free at http://cnx.org/content/col11562/1.17

Example 1.5 Data Sample of Quantitative Discrete Data

The data are the number of books students carry in their backpacks. You sample five students. Two students carry

three books, one student carries four books, one student carries two books, and one student carries one book. The

numbers of books (three, four, two, and one) are the quantitative discrete data.

1.5 The data are the number of machines in a gym. You sample five gyms. One gym has 12 machines, one gym has

15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 machines. What type of

data is this?

Example 1.6 Data Sample of Quantitative Continuous Data

The data are the weights of backpacks with books in them. You sample the same five students. The weights (in

pounds) of their backpacks are 6.2, 7, 6.8, 9.1, 4.3. Notice that backpacks carrying three books can have different

weights. Weights are quantitative continuous data because weights are measured.

1.6 The data are the areas of lawns in square feet. You sample five houses. The areas of the lawns are 144 sq. feet,

160 sq. feet, 190 sq. feet, 180 sq. feet, and 210 sq. feet. What type of data is this?

Example 1.7

You go to the supermarket and purchase three cans of soup (19 ounces) tomato bisque, 14.1 ounces lentil, and 19

ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli,

cauliflower, spinach, and carrots), and two desserts (16 ounces Cherry Garcia ice cream and two pounds (32

ounces chocolate chip cookies).

Name data sets that are quantitative discrete, quantitative continuous, and qualitative.

Solution 1.7

One Possible Solution:

• The three cans of soup, two packages of nuts, four kinds of vegetables and two desserts are quantitative

discrete data because you count them.

• The weights of the soups (19 ounces, 14.1 ounces, 19 ounces) are quantitative continuous data because you

measure weights as precisely as possible.

• Types of soups, nuts, vegetables and desserts are qualitative data because they are categorical.

Try to identify additional data sets in this example.

Chapter 1 | Sampling and Data 11

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