circular probable error

简明释义

圆概率误差圆概率误差(在二维误差分布中

英英释义

例句

1.The engineer calculated the circular probable error to ensure the precision of the measurements.

工程师计算了圆形可能误差以确保测量的精确性。

2.In navigation, understanding the circular probable error is crucial for accurate positioning.

在导航中，理解圆形可能误差对于准确定位至关重要。

3.To improve the reliability of the data, we need to minimize the circular probable error.

为了提高数据的可靠性，我们需要最小化圆形可能误差。

4.The circular probable error can significantly affect the results of the experiment.

这项实验的结果可能会受到圆形可能误差的显著影响。

5.The surveyor reported a circular probable error of 5 meters in his findings.

测量员在他的报告中指出了5米的圆形可能误差。

作文

In the realm of statistics and measurement, precision is paramount. One concept that often arises in discussions about measurement accuracy is the term circular probable error. This term refers to a specific statistical measure that quantifies the uncertainty associated with a measurement. It is particularly significant in fields such as engineering, physics, and various branches of science where accurate measurements are crucial. Understanding circular probable error can help researchers and practitioners better interpret their data and make informed decisions based on their findings.The circular probable error is essentially a way of expressing the variability of a set of measurements. It is defined as the radius of a circle within which a certain percentage of the measurements will fall. For instance, if a researcher states that the circular probable error of a measurement is 2 centimeters, this implies that there is a high probability (often around 50%) that the true value lies within a circle of 2 centimeters radius centered around the measured value. This concept is vital for understanding how much confidence one can have in a particular measurement and what the potential range of error might be.One practical application of the circular probable error can be seen in navigation systems. When determining a location using GPS, the system provides a reading that includes an error margin. This error margin can be represented as a circle around the reported location, indicating the area where the actual position is likely to be found. By applying the concept of circular probable error, navigators can better understand the limitations of their equipment and plan accordingly, ensuring they account for any potential inaccuracies in their positioning.Moreover, the significance of circular probable error extends beyond just individual measurements. In research studies, especially those involving large data sets or complex variables, understanding the aggregate error can lead to more robust conclusions. For example, when analyzing experimental results, researchers might use the circular probable error to assess the reliability of their findings. If the measurements consistently fall within a small circular probable error, it suggests a high level of precision and reliability in the data collected.However, it is also important to recognize the limitations of relying solely on circular probable error. While it provides valuable insights into measurement uncertainty, it does not account for systematic errors that may skew results. Therefore, it should be used in conjunction with other statistical tools and methods to provide a comprehensive view of the data. By combining circular probable error with techniques such as regression analysis or hypothesis testing, researchers can gain a deeper understanding of their data and its implications.In conclusion, the concept of circular probable error is an essential component of statistical analysis and measurement. It allows for a clearer understanding of the uncertainties inherent in data collection and provides a framework for interpreting results. Whether in scientific research, engineering applications, or everyday measurements, recognizing and applying the principles of circular probable error can lead to more informed decision-making and a greater appreciation for the complexities of measurement accuracy. As we continue to advance in our understanding of statistics and measurement theory, the importance of concepts like circular probable error will only grow, reinforcing the need for precision and reliability in all areas of inquiry.

在统计学和测量领域，精确性至关重要。一个常常在讨论测量准确性时出现的概念是圆形概率误差。这个术语指的是一种特定的统计测量，它量化了与测量相关的不确定性。在工程、物理学以及各个科学分支中，这一概念尤为重要，因为准确的测量是至关重要的。理解圆形概率误差可以帮助研究人员和从业者更好地解读数据，并根据他们的发现做出明智的决策。圆形概率误差本质上是一种表达一组测量变异性的方式。它被定义为一个圆的半径，在这个圆内某个百分比的测量值将会落入。例如，如果一位研究者声明某项测量的圆形概率误差是2厘米，这意味着有很高的概率（通常约为50%）真实值位于以测量值为中心的2厘米半径的圆内。这个概念对于理解对某项测量的信心程度及潜在误差范围至关重要。圆形概率误差的一个实际应用可以在导航系统中看到。在使用GPS确定位置时，系统提供的读数包括一个误差边际。这个误差边际可以表示为一个围绕报告位置的圆，指示实际位置可能被发现的区域。通过应用圆形概率误差的概念，导航员可以更好地理解其设备的局限性并相应地进行规划，确保他们考虑到定位中的任何潜在不准确性。此外，圆形概率误差的重要性不仅仅局限于单个测量。在研究中，尤其是涉及大型数据集或复杂变量的研究，理解聚合误差可以导致更稳健的结论。例如，在分析实验结果时，研究人员可能会使用圆形概率误差来评估其发现的可靠性。如果测量值始终落在较小的圆形概率误差之内，这表明所收集数据的精确性和可靠性较高。然而，也必须认识到，仅依赖圆形概率误差的局限性。尽管它提供了关于测量不确定性的宝贵见解，但它并未考虑可能扭曲结果的系统性误差。因此，它应与其他统计工具和方法结合使用，以提供数据的全面视角。通过将圆形概率误差与回归分析或假设检验等技术结合，研究人员可以更深入地理解其数据及其含义。总之，圆形概率误差的概念是统计分析和测量的重要组成部分。它允许更清晰地理解数据收集中固有的不确定性，并提供了解释结果的框架。无论是在科学研究、工程应用还是日常测量中，识别和应用圆形概率误差的原则都可以导致更明智的决策，并对测量准确性的复杂性有更大的欣赏。随着我们在统计学和测量理论理解上的不断进步，像圆形概率误差这样的概念的重要性只会增加，强化了在所有研究领域对精确性和可靠性的需求。