limit of error

简明释义

误差极限

英英释义

例句

1.In statistics, the limit of error helps determine how closely a sample reflects the population.

在统计学中，误差限有助于确定样本与总体的相似程度。

2.The survey results were adjusted for a limit of error of ±3%, indicating potential variations.

调查结果经过调整，误差限为±3%，表明可能存在变化。

3.When conducting experiments, it's crucial to understand the limit of error to evaluate the reliability of your results.

在进行实验时，了解误差限对于评估结果的可靠性至关重要。

4.The engineer stated that the limit of error for the calibration process should not exceed 1%.

工程师表示，校准过程的误差限不应超过1%。

5.The measurement device has a limit of error of ±0.5mm, meaning it can only be accurate within that range.

该测量设备的误差限为±0.5毫米，这意味着它只能在该范围内准确。

作文

In the world of science and mathematics, precision is paramount. However, it is impossible to achieve absolute accuracy in measurements and calculations. This is where the concept of the limit of error (误差限) comes into play. The limit of error refers to the maximum amount by which a measured or calculated value can deviate from the true value. Understanding this concept is crucial for researchers, engineers, and anyone involved in quantitative analysis.To illustrate the importance of the limit of error, consider a simple example involving the measurement of a length. Imagine a scientist measuring the length of a table with a ruler. If the ruler has a smallest division of 1 millimeter, then the scientist can only be certain about the measurement to within half of that smallest division, which is 0.5 millimeters. Therefore, if the scientist measures the length of the table as 100 centimeters, the true length could actually be anywhere between 99.95 centimeters and 100.05 centimeters. In this case, the limit of error is ±0.05 centimeters.The limit of error is not just a theoretical concept; it has practical implications in various fields. For instance, in engineering, knowing the limit of error helps in designing components that must fit together accurately. If the tolerances are too loose, parts may not function properly, leading to failures. Conversely, if the tolerances are too tight, manufacturing costs may increase significantly due to the need for more precise machinery and processes.Moreover, the limit of error is also essential in statistics. When conducting surveys or experiments, researchers must account for potential errors in their data. The limit of error helps in determining the reliability of the results. For example, if a poll indicates that 60% of people support a particular policy with a limit of error of ±3%, it means that the true level of support could be as low as 57% or as high as 63%. This information is vital for policymakers who rely on such data to make informed decisions.In addition, the limit of error is closely related to the concept of confidence intervals in statistics. A confidence interval provides a range of values within which we expect the true parameter to lie, considering the limit of error. For instance, if a researcher reports a 95% confidence interval for a mean measurement as 10 ± 2, it implies that the researcher is 95% confident that the true mean lies between 8 and 12. This relationship underscores the importance of the limit of error in conveying the uncertainty associated with statistical estimates.In conclusion, the limit of error is a fundamental concept that permeates various domains, from scientific research to engineering and statistics. It provides a framework for understanding the inherent uncertainties in measurements and calculations. By recognizing the limit of error, professionals can make better-informed decisions, improve designs, and communicate findings more effectively. Ultimately, acknowledging and accounting for the limit of error enhances the credibility and reliability of any quantitative analysis, which is essential in our increasingly data-driven world.

在科学和数学的世界中，精确性至关重要。然而，在测量和计算中实现绝对准确是不可能的。这就是误差限的概念发挥作用的地方。误差限指的是测量或计算值与真实值之间可能偏离的最大量。理解这个概念对研究人员、工程师以及任何参与定量分析的人来说都是至关重要的。为了说明误差限的重要性，考虑一个简单的例子，涉及长度的测量。想象一下，一个科学家用尺子测量一张桌子的长度。如果尺子的最小刻度为1毫米，那么科学家只能确定测量到最小刻度的一半，即0.5毫米。因此，如果科学家测量到桌子的长度为100厘米，真实长度实际上可能在99.95厘米到100.05厘米之间。在这种情况下，误差限为±0.05厘米。误差限不仅是一个理论概念，它在各个领域都有实际意义。例如，在工程中，了解误差限有助于设计必须准确配合的组件。如果公差过松，部件可能无法正常工作，从而导致故障。相反，如果公差过紧，制造成本可能会显著增加，因为需要更精确的机械和工艺。此外，误差限在统计学中也至关重要。在进行调查或实验时，研究人员必须考虑数据中的潜在错误。误差限有助于确定结果的可靠性。例如，如果一项民调显示60%的人支持某项政策，误差限为±3%，这意味着真实的支持水平可能低至57%或高达63%。这一信息对于依赖这些数据做出明智决策的政策制定者至关重要。此外，误差限与统计学中的置信区间概念密切相关。置信区间提供了一个范围，在此范围内，我们期望真实参数位于该范围内，同时考虑到误差限。例如，如果研究人员报告某均值测量的95%置信区间为10 ± 2，这意味着研究人员有95%的信心真实均值在8到12之间。这种关系强调了误差限在传达与统计估计相关的不确定性方面的重要性。总之，误差限是一个基本概念，渗透到各个领域，从科学研究到工程和统计。它提供了一个框架，用于理解测量和计算中固有的不确定性。通过认识到误差限，专业人士可以做出更明智的决策，改善设计，更有效地沟通研究结果。最终，承认和考虑误差限提高了任何定量分析的可信度和可靠性，这在我们日益数据驱动的世界中是至关重要的。