normal distribution

简明释义

正态分布

英英释义

例句

1.The test scores of students in a large class typically exhibit a normal distribution 正态分布, with few students scoring very low or very high.

一大班学生的考试成绩通常表现出一个normal distribution 正态分布，很少有学生得分非常低或非常高。

2.In quality control, manufacturers often look for defects that fall outside the range of a normal distribution 正态分布 to ensure product reliability.

在质量控制中，制造商通常寻找超出normal distribution 正态分布范围的缺陷，以确保产品的可靠性。

3.In statistics, the heights of adult men in a given population often follow a normal distribution 正态分布, where most individuals are around the average height.

在统计学中，给定人群中成年男性的身高通常遵循一个normal distribution 正态分布，大多数个体的身高都接近平均值。

4.When analyzing the performance of a process, engineers often assume that the measurement errors are distributed according to a normal distribution 正态分布.

在分析过程性能时，工程师通常假设测量误差按照normal distribution 正态分布分布。

5.Many natural phenomena, such as blood pressure readings, tend to follow a normal distribution 正态分布, making it easier to analyze health data.

许多自然现象，如血压读数，往往遵循一个normal distribution 正态分布，这使得分析健康数据变得更容易。

作文

The concept of normal distribution is fundamental in the field of statistics and plays a crucial role in various disciplines, including psychology, finance, and natural sciences. A normal distribution, also known as Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. This bell-shaped curve represents how values are spread around the average, providing insights into the behavior of random variables.To understand normal distribution, one must first grasp its key characteristics. The first characteristic is its symmetry; the left side of the curve mirrors the right side. This means that half of the values lie below the mean and half above it. The second characteristic is the mean, median, and mode all coincide at the center of the distribution. This central point represents the highest peak of the curve, indicating the most common value in a dataset.Another important aspect of normal distribution is the standard deviation, which measures the dispersion of data points from the mean. In a normal distribution, approximately 68% of the data points fall within one standard deviation of the mean, about 95% fall within two standard deviations, and about 99.7% fall within three standard deviations. This property is often referred to as the empirical rule or the 68-95-99.7 rule, and it helps researchers understand the variability in their data.The significance of normal distribution extends beyond theoretical statistics; it has practical applications in real-world scenarios. For instance, in psychology, test scores are often assumed to follow a normal distribution. When researchers analyze the results of standardized tests, they can apply statistical methods based on this assumption to determine how students performed relative to one another. Similarly, in finance, the returns on investment are frequently modeled using a normal distribution, allowing investors to assess risk and make informed decisions.Moreover, the Central Limit Theorem (CLT) states that the sum of a large number of independent random variables will tend to be normally distributed, regardless of the original distribution of the variables. This theorem is pivotal because it justifies the use of normal distribution in many statistical tests and procedures, even when the underlying data does not follow a normal distribution itself. It allows statisticians to make predictions and inferences about populations based on sample data, which is invaluable in research.In conclusion, the normal distribution is a cornerstone of statistical analysis that provides a framework for understanding data patterns and making predictions. Its properties of symmetry, the relationship between mean and standard deviation, and its applications across various fields underscore its importance. Whether in academic research or practical decision-making, grasping the concept of normal distribution equips individuals with the analytical tools necessary to interpret data effectively and derive meaningful conclusions. As we continue to gather and analyze data in an increasingly data-driven world, the relevance of normal distribution remains paramount, guiding us in our quest to understand the complexities of the information around us.

正态分布的概念在统计学领域中是基础性的，并在心理学、金融和自然科学等多个学科中发挥着至关重要的作用。正态分布，也称为高斯分布，是一种概率分布，关于均值是对称的，显示出接近均值的数据比远离均值的数据更频繁地出现。这种钟形曲线表示了数值围绕平均值的分布情况，为随机变量的行为提供了洞察。要理解正态分布，首先必须掌握其关键特征。第一个特征是其对称性；曲线的左侧与右侧镜像相同。这意味着一半的值低于均值，而另一半高于均值。第二个特征是均值、中位数和众数都在分布的中心重合。这个中心点代表曲线的最高峰，表明数据集中最常见的值。正态分布的另一个重要方面是标准差，它衡量数据点与均值之间的离散程度。在正态分布中，大约68%的数据点落在均值的一个标准差内，大约95%落在两个标准差内，约99.7%落在三个标准差内。这一特性通常被称为经验法则或68-95-99.7规则，它帮助研究人员理解数据的变异性。正态分布的重要性不仅限于理论统计；它在现实世界的应用中也具有实际意义。例如，在心理学中，测试分数通常假设遵循正态分布。当研究人员分析标准化测试的结果时，他们可以基于这一假设应用统计方法，以确定学生之间的表现如何。类似地，在金融领域，投资回报率常常使用正态分布进行建模，使投资者能够评估风险并做出明智的决策。此外，中心极限定理（CLT）表明，许多独立随机变量的总和将趋向于正态分布，无论原始变量的分布如何。这个定理是关键的，因为它证明了在许多统计检验和程序中使用正态分布的合理性，即使底层数据本身并不遵循正态分布。这使得统计学家能够根据样本数据对总体进行预测和推断，这在研究中是无价的。总之，正态分布是统计分析的基石，为理解数据模式和做出预测提供了框架。它的对称性、均值与标准差之间的关系，以及在各个领域的应用，突显了其重要性。无论是在学术研究还是实际决策中，掌握正态分布的概念使个人具备了解释数据的分析工具，从而得出有意义的结论。随着我们在一个日益数据驱动的世界中继续收集和分析数据，正态分布的相关性仍然至关重要，引导我们理解周围信息的复杂性。