arithmetical mean

简明释义

算术平均

英英释义

例句

1.In statistics, the arithmetical mean 算术平均数 is often used to summarize a set of data points.

在统计学中，算术平均数常用于总结一组数据点。

2.To improve our project outcomes, we should regularly calculate the arithmetical mean 算术平均数 of our key performance indicators.

为了改善我们的项目成果，我们应定期计算关键绩效指标的算术平均数。

3.When analyzing sales figures, the arithmetical mean 算术平均数 helps businesses understand their performance.

在分析销售数据时，算术平均数帮助企业了解其业绩。

4.The arithmetical mean 算术平均数 of the temperatures recorded over the week gives us a good estimate of the overall climate.

一周内记录的温度的算术平均数可以很好地估计整体气候。

5.To find the average score of the students, we need to calculate the arithmetical mean 算术平均数 of their test results.

为了找出学生的平均分，我们需要计算他们考试成绩的算术平均数。

作文

In the realm of mathematics, one of the most fundamental concepts is that of the average. When we talk about the average in a statistical context, we often refer to the arithmetical mean, which is a method used to summarize a set of numbers with a single value. The arithmetical mean is calculated by adding all the values in a dataset and then dividing that sum by the total number of values. This simple yet effective calculation helps us understand the central tendency of data, making it easier to interpret and analyze information.For instance, consider a scenario where a teacher wants to determine the average score of her students on a recent exam. If the scores are 70, 80, 90, and 100, the teacher would first add these scores together: 70 + 80 + 90 + 100 = 340. Next, she would divide this sum by the number of students, which is 4. Thus, the arithmetical mean score would be 340 ÷ 4 = 85. This average score provides the teacher with a clear picture of how her class performed overall, allowing her to make informed decisions about future lessons and areas that may need improvement.The importance of the arithmetical mean extends beyond academic settings; it is widely used in various fields such as economics, psychology, and even sports. For example, economists often use the arithmetical mean to analyze consumer spending patterns or to gauge the performance of different sectors within the economy. By calculating the average income or expenditure in a given area, they can draw conclusions about economic health and trends.Moreover, in the field of sports, statistics play a crucial role in evaluating player performance. Coaches and analysts frequently rely on the arithmetical mean to assess players' scoring averages, assists, rebounds, and other key performance indicators. By understanding the average performance of individual players, teams can strategize more effectively and make decisions about trades, drafts, and training.However, while the arithmetical mean is a useful tool, it is essential to recognize its limitations. One significant drawback is that it can be heavily influenced by outliers—values that are significantly higher or lower than the rest of the dataset. For instance, if one student scored 30 on the same exam mentioned earlier, the new total would be 70 + 80 + 90 + 100 + 30 = 370, leading to an arithmetical mean of 370 ÷ 5 = 74. This drastic drop in the average highlights how sensitive the mean is to extreme values, which may not accurately represent the majority of the data.To address this issue, statisticians often complement the arithmetical mean with other measures of central tendency, such as the median and mode. The median, for example, represents the middle value when a dataset is ordered from least to greatest, providing a more robust measure when outliers are present. Thus, while the arithmetical mean is a valuable metric, it should be used in conjunction with other statistical tools to provide a more comprehensive analysis.In conclusion, the arithmetical mean serves as a vital concept in mathematics and statistics, enabling us to distill complex datasets into understandable figures. Whether in education, economics, or sports, the ability to calculate and interpret the arithmetical mean empowers individuals and organizations to make informed decisions based on data. Understanding both its applications and limitations is crucial for anyone looking to work with statistics effectively. The arithmetical mean not only simplifies data analysis but also enhances our ability to communicate findings clearly and concisely.

在数学领域，最基本的概念之一就是平均数。当我们在统计上下文中谈论平均数时，我们通常指的是算术平均数，这是一种用于用单一值来总结一组数字的方法。算术平均数是通过将数据集中所有值相加，然后将该总和除以值的总数来计算的。这种简单而有效的计算帮助我们理解数据的集中趋势，使得信息的解释和分析变得更加容易。例如，考虑一个场景，一位老师想要确定她的学生在最近一次考试中的平均分。如果分数是70、80、90和100，老师首先会将这些分数加在一起：70 + 80 + 90 + 100 = 340。接下来，她会将这个总和除以学生的数量，即4。因此，算术平均数分数将是340 ÷ 4 = 85。这个平均分数为老师提供了她的班级整体表现的清晰图景，使她能够对未来的课程和可能需要改进的领域做出明智的决策。算术平均数的重要性不仅限于学术环境；它在经济学、心理学甚至体育等多个领域广泛应用。例如，经济学家常常使用算术平均数来分析消费者支出模式或评估经济中不同部门的表现。通过计算特定区域的平均收入或支出，他们可以得出有关经济健康和趋势的结论。此外，在体育领域，统计数据在评估球员表现方面发挥着至关重要的作用。教练和分析师经常依赖算术平均数来评估球员的得分平均、助攻、篮板和其他关键表现指标。通过了解个别球员的平均表现，球队可以更有效地制定策略并做出关于交易、选秀和训练的决策。然而，尽管算术平均数是一个有用的工具，但认识到它的局限性也至关重要。一个显著的缺点是，它可能受到极端值的严重影响——即远高于或低于其余数据集的值。例如，如果一名学生在同一考试中得了30分，那么新的总分将是70 + 80 + 90 + 100 + 30 = 370，这导致新的算术平均数为370 ÷ 5 = 74。这个平均数的急剧下降突显了均值对极端值的敏感性，这可能无法准确代表大多数数据。为了应对这个问题，统计学家通常会用其他集中趋势的衡量标准来补充算术平均数，例如中位数和众数。中位数，例如，表示当数据集按从小到大的顺序排列时的中间值，当存在极端值时，提供了更稳健的衡量标准。因此，虽然算术平均数是一个有价值的指标，但它应该与其他统计工具结合使用，以提供更全面的分析。总之，算术平均数作为数学和统计学中的一个重要概念，使我们能够将复杂的数据集简化为可理解的数字。无论是在教育、经济还是体育领域，计算和解释算术平均数的能力使个人和组织能够基于数据做出明智的决策。理解它的应用和局限性对于任何希望有效处理统计数据的人来说都是至关重要的。算术平均数不仅简化了数据分析，还增强了我们清晰而简洁地传达发现的能力。