normal distribution

简明释义

正态分布

英英释义

例句

1.A key property of a normal distribution 正态分布 is that it is symmetric about the mean.

一个normal distribution 正态分布的关键特性是它关于均值是对称的。

2.The results of the standardized test were found to be in a normal distribution 正态分布.

标准化测试的结果被发现呈现出normal distribution 正态分布。

3.When analyzing errors in measurements, we often assume they follow a normal distribution 正态分布.

在分析测量误差时，我们通常假设它们遵循normal distribution 正态分布。

4.Many natural phenomena, such as heights of people, approximate a normal distribution 正态分布.

许多自然现象，例如人的身高，近似于normal distribution 正态分布。

5.In statistics, data that follows a bell curve is said to have a normal distribution 正态分布.

在统计学中，遵循钟形曲线的数据被称为具有normal distribution 正态分布。

作文

The concept of normal distribution is fundamental in statistics and plays a crucial role in various fields, including psychology, finance, and natural sciences. To understand normal distribution, we first need to recognize that it describes how data points are spread out in a dataset. A normal distribution is often represented graphically by a bell-shaped curve, where the majority of the data points cluster around the mean, or average, value, while fewer points lie at the extremes.One of the key characteristics of a normal distribution is its symmetry. This means that if you were to draw a vertical line through the center of the bell curve, both sides would mirror each other. The mean, median, and mode of a normal distribution all coincide at the center, which is a unique property that simplifies many statistical analyses.In practical terms, the normal distribution is significant because many natural phenomena tend to follow this pattern. For instance, when measuring human heights, test scores, or even errors in manufacturing processes, the results often approximate a normal distribution. This tendency allows researchers to make predictions and infer probabilities based on the properties of the distribution.Another important aspect of the normal distribution is the empirical rule, also known as the 68-95-99.7 rule. This rule states that 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 around 99.7% fall within three standard deviations. This provides a quick way to assess the spread and variability of the data, allowing for more informed decision-making.Moreover, the normal distribution serves as the foundation for many statistical tests and methodologies, such as t-tests and ANOVA. These tests assume that the data follows a normal distribution, which enables researchers to draw conclusions about populations from sample data. If the data deviates significantly from a normal distribution, alternative methods may need to be employed to analyze the data accurately.In conclusion, understanding the concept of normal distribution is vital for anyone involved in data analysis or research. Its prevalence in nature and its mathematical properties make it an essential tool for interpreting and predicting outcomes. By recognizing the characteristics and implications of a normal distribution, individuals can improve their analytical skills and enhance their ability to make data-driven decisions. As we continue to collect and analyze data in an increasingly complex world, the importance of grasping the normal distribution cannot be overstated. It not only aids in understanding the underlying patterns in data but also equips us with the tools necessary for effective problem-solving and decision-making in various domains.

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中发挥着至关重要的作用。要理解正态分布，我们首先需要认识到它描述了数据集中数据点的分布情况。正态分布通常通过一个钟形曲线来表示，其中大多数数据点聚集在均值或平均值附近，而较少的数据点位于极端。正态分布的一个关键特征是其对称性。这意味着如果你在钟形曲线的中心画一条垂直线，两侧将相互镜像。正态分布的均值、中位数和众数都在中心重合，这是一个独特的属性，使许多统计分析变得简单。在实际应用中，正态分布之所以重要，是因为许多自然现象往往遵循这种模式。例如，在测量人类身高、考试成绩或甚至制造过程中的误差时，结果往往接近正态分布。这种趋势使研究人员能够基于分布的特性进行预测和推断概率。另一个正态分布的重要方面是经验法则，也称为68-95-99.7法则。该法则指出，在正态分布中，大约68%的数据点落在均值的一个标准差内，约95%的数据点落在两个标准差内，约99.7%的数据点落在三个标准差内。这为评估数据的分布和变异性提供了一种快速的方法，从而可以做出更明智的决策。此外，正态分布为许多统计检验和方法论奠定了基础，例如t检验和方差分析（ANOVA）。这些检验假设数据遵循正态分布，这使得研究人员能够从样本数据中得出关于总体的结论。如果数据显著偏离正态分布，可能需要采用替代方法来准确分析数据。总之，理解正态分布的概念对任何参与数据分析或研究的人来说都是至关重要的。它在自然界中的普遍性及其数学特性使其成为解释和预测结果的重要工具。通过认识正态分布的特征和影响，个人可以提高分析能力，增强基于数据的决策能力。随着我们在日益复杂的世界中继续收集和分析数据，掌握正态分布的重要性不可低估。它不仅有助于理解数据中的潜在模式，还为我们提供了在各个领域有效解决问题和做出决策所需的工具。