infinite population

简明释义

无限总体

英英释义

例句

1.The concept of an infinite population (无限总体) is crucial in understanding the central limit theorem.

理解中心极限定理时，无限总体（无限总体）的概念至关重要。

2.When conducting a survey, researchers may treat the target group as an infinite population (无限总体) if the sample size is large enough.

在进行调查时，如果样本量足够大，研究人员可能会将目标群体视为无限总体（无限总体）。

3.For theoretical models, we often work with the assumption of an infinite population (无限总体) to derive formulas.

对于理论模型，我们通常在推导公式时假设存在一个无限总体（无限总体）。

4.In quality control, manufacturers might assume that defects occur in an infinite population (无限总体) of products.

在质量控制中，制造商可能假设缺陷发生在一个无限总体（无限总体）的产品中。

5.In statistical theory, we often assume an infinite population (无限总体) to simplify calculations.

在统计理论中，我们常常假设一个无限总体（无限总体）以简化计算。

作文

In the realm of statistics, the concept of an infinite population refers to a theoretical group of individuals or items that is limitless in size. This idea is particularly significant when conducting surveys or experiments where the total number of potential subjects is not practically countable. For instance, consider a scenario where a researcher is interested in studying the behavior of all possible consumers of a particular product. In reality, it would be impossible to survey every single consumer; thus, the researcher operates under the assumption of an infinite population. This allows them to utilize statistical methods that can provide insights based on a sample rather than requiring exhaustive data collection.The notion of an infinite population is crucial in many fields, including sociology, psychology, and marketing. It enables researchers to draw conclusions from finite samples while acknowledging that their findings may apply broadly to a larger context. For example, when assessing public opinion on a political issue, pollsters often rely on a sample that represents the views of an infinite population of voters. By using statistical techniques such as confidence intervals and hypothesis testing, they can make inferences about the entire voting population based on the opinions of a smaller group.Moreover, the concept of an infinite population also plays a vital role in probability theory. In certain probabilistic models, it is assumed that the number of trials can be infinite, which simplifies calculations and predictions. For instance, when flipping a coin, the outcomes can be viewed as part of an infinite population of potential flips. Each flip is independent, and the probabilities remain constant regardless of how many times the coin is flipped. This characteristic is essential for understanding concepts like the law of large numbers, which states that as the number of trials increases, the sample average will converge to the expected value.Despite its theoretical nature, the idea of an infinite population provides a framework for researchers to think about their work in broader terms. It encourages them to consider the implications of their findings beyond the immediate sample they are studying. This perspective is particularly important in an increasingly interconnected world where the behaviors and preferences of individuals can have far-reaching effects.In practical applications, researchers must still be cautious when generalizing their results from a sample to an infinite population. Factors such as sampling bias, non-response rates, and the representativeness of the sample can significantly affect the validity of their conclusions. Therefore, while the concept of an infinite population is useful, it is essential to approach the interpretation of results with a critical eye.In conclusion, the term infinite population serves as a fundamental concept in statistics and research methodologies. It allows researchers to utilize finite samples to make inferences about larger groups, facilitating the study of complex phenomena in various fields. By understanding the implications and limitations of working with an infinite population, researchers can enhance the reliability of their findings and contribute valuable insights to their respective disciplines.

在统计学领域，无限人口的概念指的是一个理论上的个体或物品组，其规模是无限的。这个想法在进行调查或实验时尤为重要，因为潜在受试者的总数是无法实际计算的。例如，考虑一个研究者希望研究某一特定产品的所有潜在消费者行为的场景。实际上，对每一个消费者进行调查是不可能的；因此，研究者在假设有一个无限人口的前提下进行操作。这使得他们能够利用统计方法，通过样本而不是需要详尽的数据收集来提供见解。无限人口的概念在社会学、心理学和市场营销等多个领域至关重要。它使研究人员能够从有限的样本中得出结论，同时承认他们的发现可能适用于更广泛的背景。例如，在评估公众对某一政治问题的看法时，民调机构通常依赖于一个代表无限人口选民观点的样本。通过使用置信区间和假设检验等统计技术，他们可以根据较小群体的意见推断整个投票人群。此外，无限人口的概念在概率论中也扮演着重要角色。在某些概率模型中，假设试验次数可以是无限的，这简化了计算和预测。例如，在掷硬币时，结果可以被视为潜在掷硬币结果的无限人口的一部分。每次掷硬币都是独立的，概率保持不变，无论掷了多少次。这一特性对于理解大数法则等概念至关重要，该法则指出，随着试验次数的增加，样本平均值将收敛于期望值。尽管其理论性质，无限人口的想法为研究人员提供了更广泛地思考其工作的框架。它鼓励他们考虑其发现对他们所研究的即时样本之外的影响。在一个日益互联的世界中，个体的行为和偏好可能会产生深远的影响，这一视角尤其重要。在实际应用中，研究人员在将其结果从样本推广到无限人口时仍需谨慎。抽样偏差、非响应率和样本的代表性等因素可能会显著影响他们结论的有效性。因此，尽管无限人口的概念是有用的，但在解释结果时必须以批判的眼光来看待。总之，无限人口这一术语在统计学和研究方法论中是一个基本概念。它允许研究人员利用有限样本对更大群体进行推断，从而促进各个领域复杂现象的研究。通过理解与处理无限人口相关的影响和局限性，研究人员可以增强其发现的可靠性，并为各自学科贡献有价值的见解。