empirical rule

简明释义

经验定则

英英释义

例句

1.Using the empirical rule, we can predict that 95% of the population will fall within two standard deviations.

使用经验法则，我们可以预测95%的人口将落在两个标准差范围内。

2.The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean.

根据经验法则，对于正态分布，大约68%的数据位于均值的一个标准差范围内。

3.In our statistics class, we learned how to apply the empirical rule to analyze test scores.

在我们的统计课上，我们学习了如何应用经验法则来分析考试成绩。

4.The empirical rule is particularly useful when dealing with large datasets in data analysis.

在数据分析中，经验法则在处理大型数据集时特别有用。

5.As a quality control manager, I rely on the empirical rule to ensure product consistency.

作为质量控制经理，我依靠经验法则来确保产品的一致性。

作文

The concept of the empirical rule is fundamental in statistics and plays a crucial role in understanding the distribution of data. This rule, often referred to as the 68-95-99.7 rule, provides a simple way to interpret the standard deviation and the normal distribution. According to the empirical rule, in a normal distribution, approximately 68% of the data points fall within one standard deviation from the mean, about 95% fall within two standard deviations, and around 99.7% fall within three standard deviations. This statistical insight allows researchers, analysts, and students to make educated guesses about the likelihood of certain outcomes based on a given dataset.To illustrate the significance of the empirical rule, consider a scenario where a teacher records the test scores of her students. If the scores are normally distributed with a mean of 75 and a standard deviation of 10, the empirical rule indicates that approximately 68% of the students scored between 65 and 85 (one standard deviation from the mean). Furthermore, about 95% of the students scored between 55 and 95 (two standard deviations), while nearly all students scored between 45 and 105 (three standard deviations). This information helps the teacher understand how her students performed relative to one another and identify any outliers or exceptional performers.The empirical rule is not only useful in educational settings but also has practical applications in various fields such as finance, healthcare, and quality control. For instance, in finance, investors can use the empirical rule to assess the risk associated with certain investments. By examining historical returns and their distribution, they can estimate the probability of extreme losses or gains, helping them make informed decisions.In healthcare, the empirical rule can assist in analyzing patient data. For example, if the blood pressure readings of a group of patients are normally distributed, doctors can quickly determine how many patients fall within a healthy range versus those who may be at risk of hypertension. This application of the empirical rule can lead to timely interventions and better health outcomes.Moreover, the empirical rule serves as a foundational concept for more advanced statistical methods. Understanding this rule equips individuals with the knowledge to tackle more complex analyses, such as hypothesis testing and regression analysis. It fosters a deeper comprehension of how data behaves and the inherent variability within datasets.In conclusion, the empirical rule is an essential principle in the realm of statistics that aids in interpreting data distributions. Its simplicity and effectiveness make it a valuable tool across various disciplines. By grasping the empirical rule, individuals can enhance their analytical skills, leading to better decision-making processes in both professional and personal contexts. Whether in education, finance, or healthcare, the applications of the empirical rule are vast and impactful, highlighting its significance in our data-driven world.

“经验法则”（empirical rule）的概念在统计学中是基础性的，并在理解数据分布方面发挥着至关重要的作用。这个规则通常被称为68-95-99.7法则，提供了一种简单的方法来解释标准差和正态分布。根据经验法则，在正态分布中，约68%的数据点落在均值的一标准差范围内，约95%落在两标准差范围内，而大约99.7%落在三标准差范围内。这一统计洞察使研究人员、分析师和学生能够根据给定数据集对某些结果的可能性做出有根据的猜测。为了说明经验法则的重要性，考虑一个场景：一位老师记录她学生的考试成绩。如果这些成绩呈正态分布，均值为75，标准差为10，那么经验法则表明，约68%的学生成绩在65到85之间（均值的一标准差）。此外，大约95%的学生成绩在55到95之间（均值的两标准差），而几乎所有学生的成绩在45到105之间（均值的三标准差）。这些信息帮助老师了解她的学生相对于彼此的表现，并识别任何异常值或表现突出的学生。经验法则不仅在教育领域有用，还在金融、医疗和质量控制等多个领域具有实际应用。例如，在金融领域，投资者可以利用经验法则来评估某些投资相关的风险。通过检查历史回报及其分布，他们可以估计极端损失或收益的概率，从而帮助他们做出明智的决策。在医疗领域，经验法则可以帮助分析患者数据。例如，如果一组患者的血压读数呈正态分布，医生可以快速确定有多少患者处于健康范围内，以及有多少患者可能面临高血压风险。经验法则的这种应用可以导致及时干预和更好的健康结果。此外，经验法则作为更高级统计方法的基础概念，理解这一规则使个人能够应对更复杂的分析，例如假设检验和回归分析。它促进了对数据行为及数据集中固有变异性的更深入理解。总之，经验法则是统计学领域中的一个基本原则，有助于解释数据分布。它的简单性和有效性使其成为各个学科的宝贵工具。通过掌握经验法则，个人可以增强他们的分析能力，从而在职业和个人环境中做出更好的决策。无论是在教育、金融还是医疗领域，经验法则的应用都是广泛而深远的，突显了其在我们数据驱动的世界中的重要性。