Data Collection | 数据收集

📚 Data Collection | 数据收集

Data collection is the foundation of statistical work. Before calculating averages, drawing graphs, or testing hypotheses, you must know how data were obtained. In Edexcel A-Level Mathematics, the Data Collection topic covers populations, samples, types of data, sampling methods, and sources of bias.

数据收集是统计工作的基础。在计算平均数、绘制图表或检验假设之前，你必须了解数据是如何获得的。在 Edexcel A-Level 数学中，数据收集主题涵盖总体、样本、数据类型、抽样方法以及偏差来源。

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1. Populations and Samples | 总体与样本

A population is the complete set of individuals, items, or measurements that a study aims to investigate. For example, if you want to know the average height of A-Level students in England, the population is all A-Level students in England.

总体是研究旨在调查的所有个体、对象或测量值的完整集合。例如，如果你想了解英格兰 A-Level 学生的平均身高，总体就是英格兰所有 A-Level 学生。

A census collects data from every member of the population. A sample is a subset of the population selected for study. In most situations, a sample is preferred because a census is costly, slow, and sometimes impossible.

普查从总体的每一个成员收集数据。样本是从总体中选出来用于研究的一个子集。在大多数情况下，人们优先选择样本，因为普查成本高、速度慢，有时甚至不可能。

A parameter is a numerical value that describes a population. A statistic is a value calculated from a sample and used to estimate a parameter.

参数是描述总体的数值。统计量是由样本计算出来、用于估计参数的值。

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2. Types of Data | 数据类型

Data can be classified as qualitative or quantitative. Qualitative data describe non-numerical characteristics such as colour, gender, or type of transport. Quantitative data are numerical and can be either discrete or continuous.

数据可以分为定性数据和定量数据。定性数据描述非数值特征，如颜色、性别或交通方式。定量数据是数值型的，可以是离散的或连续的。

Discrete data arise from counting. They can only take particular values, often integers, such as the number of students in a class or the number of goals scored in a match.

离散数据来自计数。它们只能取特定的值，通常是整数，例如班级学生人数或一场比赛中的进球数。

Continuous data arise from measuring. They can take any value within an interval, such as height, time, temperature, or mass.

连续数据来自测量。它们可以在一个区间内取任意值，例如身高、时间、温度或质量。

• Quantitative discrete: number of cars in a car park — 定量离散：停车场里的汽车数量
• Quantitative continuous: length of a leaf in cm — 定量连续：一片叶子的长度（cm）
• Qualitative: eye colour or type of pet — 定性：眼睛颜色或宠物类型

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3. Sampling Units and Sampling Frame | 抽样单位与抽样框

A sampling unit is an individual member of the population. For example, in a survey of school students, the sampling unit could be one student.

抽样单位是总体中的一个个体成员。例如，在一项针对学校学生的调查中，抽样单位可以是一名学生。

A sampling frame is a list of all sampling units from which a sample is selected. Ideally, the frame should cover the entire population with no duplicates or omissions.

抽样框是所有抽样单位的列表，样本从这个列表中抽取。理想情况下，抽样框应覆盖整个总体，没有重复或遗漏。

If a sampling frame is incomplete, undercoverage bias can occur because some members of the population cannot be selected. A clearly defined sampling frame is essential for random sampling methods.

如果抽样框不完整，就会产生覆盖不足偏差，因为总体中的一些成员无法被选中。对于随机抽样方法来说，清晰定义的抽样框至关重要。

In exam questions, you should be able to identify the sampling unit and the sampling frame from a real-life scenario, such as students from a school register or customers from a database.

在考试题目中，你应该能够从实际情景中识别抽样单位和抽样框，例如从学校注册表中选择学生或从数据库中选择顾客。

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4. Simple Random Sampling | 简单随机抽样

In simple random sampling, every possible sample of a given size has an equal chance of being selected. Each member of the population is equally likely to be chosen.

在简单随机抽样中，每个给定大小的可能样本被选中的机会相等。总体中的每个成员被选中的可能性相同。

To carry out simple random sampling, assign a unique number to each member of the sampling frame, then use a random number generator or lottery method to select the required number of members.

实施简单随机抽样时，给抽样框中的每个成员分配一个唯一编号，然后用随机数生成器或抽签法选出所需数量的成员。

A common way to carry out a simple random sample is to number every member from 1 to N, use a random number table or calculator, and ignore repeated or out-of-range numbers.

实施简单随机抽样的常用方法是给每个成员从 1 到 N 编号，使用随机数表或计算器，并忽略重复或超出范围的数字。

Advantages: it is unbiased and easy to understand. Disadvantages: it requires a complete sampling frame and may be inconvenient if the population is large or spread out.

优点：它无偏且易于理解。缺点：需要完整的抽样框，如果总体很大或分布很广，可能不太方便。

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5. Systematic Sampling | 系统抽样

Systematic sampling selects members at regular intervals from an ordered list. The first member is chosen at random, and then every kth member is selected, where k = N ÷ n.

系统抽样从有序列表中每隔固定间隔选取成员。第一个成员随机选择，然后每隔第 k 个成员选取，其中 k = N ÷ n。

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