normal distribution

简明释义

正态分布

英英释义

例句

1.The test scores of students often exhibit a normal distribution (正态分布), with most students scoring around the average.

学生的考试成绩通常呈现出正态分布（normal distribution），大多数学生的分数集中在平均值附近。

2.In statistics, many natural phenomena follow a normal distribution (正态分布), such as heights and weights of individuals.

在统计学中，许多自然现象遵循正态分布（normal distribution），例如个体的身高和体重。

3.The errors in measurement can often be assumed to follow a normal distribution (正态分布), which helps in error analysis.

测量中的误差通常可以假定遵循正态分布（normal distribution），这有助于进行误差分析。

4.When analyzing data, it's important to check if it follows a normal distribution (正态分布) before applying certain statistical tests.

在分析数据时，检查数据是否遵循正态分布（normal distribution）是很重要的，这样才能在应用某些统计检验之前做出正确判断。

5.Many quality control processes rely on the assumption that defects are normally distributed, i.e., they follow a normal distribution (正态分布).

许多质量控制过程依赖于缺陷呈正态分布的假设，即它们遵循正态分布（normal distribution）。

作文

The concept of normal distribution is fundamental in statistics and plays a crucial role in various fields such as psychology, finance, and natural sciences. To understand normal distribution, we first need to recognize that it describes how the values of a variable are distributed. In a normal distribution, most of the observations cluster around the central peak, and the probabilities for values further away from the mean taper off equally in both directions. This creates a bell-shaped curve, which is symmetric about the mean.One of the key characteristics of a normal distribution is that it is defined by two parameters: the mean (average) and the standard deviation (a measure of variability). The mean determines the center of the distribution, while the standard deviation indicates how spread out the values are around the mean. For instance, in a classroom setting, if we were to measure the heights of students, we might find that most students are around a certain height (the mean), with fewer students being much shorter or taller than this average.In practical applications, the normal distribution can be observed in numerous real-world phenomena. For example, in standardized testing, the scores often follow a normal distribution. This means that most students will score near the average, while fewer students will achieve extremely high or low scores. Understanding this distribution allows educators to set benchmarks and identify outliers effectively.Another important aspect of normal distribution is the empirical rule, which states that approximately 68% of the data points fall within one standard deviation of the mean, about 95% fall within two standard deviations, and around 99.7% fall within three standard deviations. This rule is extremely useful for predicting outcomes and understanding the likelihood of certain events occurring.Moreover, the normal distribution is essential in inferential statistics, where it enables researchers to make generalizations about populations based on sample data. Many statistical tests, including t-tests and ANOVA, assume that the data follows a normal distribution. If the data deviates significantly from this distribution, it may lead to incorrect conclusions.Despite its importance, it is crucial to remember that not all datasets follow a normal distribution. In real-life scenarios, data can be skewed or have outliers that affect the distribution's shape. Therefore, before applying statistical methods that rely on the assumption of normal distribution, it is essential to conduct tests for normality, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test.In conclusion, understanding normal distribution is vital for anyone working with data. Its properties provide insights into the behavior of data and allow for effective analysis and decision-making. By recognizing when data follows a normal distribution and when it does not, researchers can apply appropriate statistical methods, ensuring their findings are valid and reliable. As we continue to collect and analyze data in various disciplines, the significance of normal distribution will undoubtedly remain a cornerstone of statistical practice.

正态分布的概念在统计学中是基础性的，并在心理学、金融和自然科学等多个领域发挥着关键作用。要理解normal distribution，我们首先需要认识到它描述了一个变量的值是如何分布的。在normal distribution中，大多数观察值聚集在中心峰附近，而远离平均值的值的概率在两个方向上均匀递减。这形成了一个钟形曲线，该曲线关于均值是对称的。normal distribution的一个关键特征是它由两个参数定义：均值（平均值）和标准差（变异性度量）。均值决定了分布的中心，而标准差表示值围绕均值的分散程度。例如，在课堂环境中，如果我们测量学生的身高，我们可能会发现大多数学生的身高接近某个高度（均值），而极少数学生的身高则远低于或高于这个平均值。在实际应用中，normal distribution可以在许多现实世界现象中观察到。例如，在标准化测试中，得分通常遵循normal distribution。这意味着大多数学生的得分接近平均值，而极少数学生会获得非常高或非常低的分数。理解这种分布使教育工作者能够有效地设定基准并识别异常值。normal distribution的另一个重要方面是经验法则，该法则指出，约68%的数据点落在均值一个标准差范围内，约95%落在两个标准差范围内，约99.7%落在三个标准差范围内。这个规则对于预测结果和理解某些事件发生的可能性非常有用。此外，normal distribution在推论统计中至关重要，它使研究人员能够根据样本数据对总体进行概括。许多统计测试，包括t检验和方差分析，假设数据遵循normal distribution。如果数据显著偏离这种分布，可能会导致错误的结论。尽管它的重要性，但必须记住并非所有数据集都遵循normal distribution。在现实生活场景中，数据可能会偏斜或存在影响分布形状的异常值。因此，在应用依赖于normal distribution假设的统计方法之前，进行正态性检验是至关重要的，例如Shapiro-Wilk检验或Kolmogorov-Smirnov检验。总之，理解normal distribution对于任何处理数据的人来说都是至关重要的。它的属性提供了对数据行为的洞察，使有效的分析和决策成为可能。通过识别数据何时遵循normal distribution以及何时不遵循，研究人员可以应用适当的统计方法，确保他们的发现是有效和可靠的。随着我们继续在各个学科中收集和分析数据，normal distribution的重要性无疑将继续成为统计实践的基石。