harmonic mean

简明释义

调和平均值

英英释义

例句

1.The formula for the harmonic mean of two numbers is 2ab/(a+b).

两个数的调和平均数公式是 2ab/(a+b)。

2.The harmonic mean is often used in averaging rates, such as speed or efficiency.

在计算速度或效率等比率时，通常使用调和平均数。

3.To find the average speed of a round trip, we can use the harmonic mean of the speeds going and returning.

要找出往返旅行的平均速度，我们可以使用去程和回程速度的调和平均数。

4.When dealing with rates, the harmonic mean provides a more accurate average than the arithmetic mean.

在处理比率时，调和平均数提供的平均值比算术平均数更准确。

5.In finance, the harmonic mean can be useful for calculating average investment returns over time.

在金融领域，调和平均数可以用于计算投资回报的平均值。

作文

In mathematics, the concept of the harmonic mean (调和均值) plays a crucial role in various fields, including statistics, physics, and finance. The harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of a set of numbers. It is particularly useful when dealing with rates or ratios, making it an essential tool for many practical applications.To understand the harmonic mean, let's consider a simple example. Suppose we have two numbers: 4 and 6. The arithmetic mean of these two numbers is (4 + 6) / 2 = 5. However, if we want to calculate the harmonic mean, we first find the reciprocals of these numbers, which are 1/4 and 1/6. The average of these reciprocals is (1/4 + 1/6) / 2. To compute this, we need a common denominator, which is 12. Thus, we have:(3/12 + 2/12) / 2 = (5/12) / 2 = 5/24.Now, the harmonic mean is the reciprocal of this result:harmonic mean = 1 / (5/24) = 24/5 = 4.8. This value is different from the arithmetic mean, illustrating how the harmonic mean can provide a different perspective on the data.The harmonic mean is especially valuable in situations where the numbers represent rates. For instance, if a car travels at 60 kilometers per hour for one part of a journey and then at 90 kilometers per hour for another part, the average speed cannot simply be calculated using the arithmetic mean. Instead, we would use the harmonic mean to find a more accurate representation of the average speed over the entire journey.Another important aspect of the harmonic mean is its application in finance, particularly in calculating average rates of return. When evaluating investment performance, the harmonic mean provides a more realistic measure than the arithmetic mean, especially when dealing with percentages. For example, if an investment yields returns of 10% in one year and -20% in the next, the arithmetic mean would suggest a return of -5%, which does not accurately reflect the overall performance. By applying the harmonic mean, investors can better understand the true nature of their returns.In conclusion, the harmonic mean (调和均值) is a powerful mathematical tool that offers unique insights into the analysis of data, particularly when dealing with rates and ratios. Its application across various fields demonstrates its versatility and importance. Understanding the harmonic mean allows individuals to make more informed decisions based on a comprehensive analysis of their data. As we continue to encounter diverse datasets in our increasingly complex world, mastering concepts like the harmonic mean will undoubtedly enhance our analytical capabilities.

在数学中，调和均值（harmonic mean）这一概念在统计学、物理学和金融等多个领域中发挥着重要作用。调和均值的定义是某组数字的倒数的算术平均数的倒数。当处理比率或速率时，它尤其有用，因此成为许多实际应用中的重要工具。为了理解调和均值，我们来看一个简单的例子。假设我们有两个数字：4和6。这两个数字的算术平均数为(4 + 6) / 2 = 5。然而，如果我们想计算调和均值，我们首先要找到这两个数字的倒数，即1/4和1/6。这些倒数的平均值为(1/4 + 1/6) / 2。为了计算这个值，我们需要一个公分母，即12。因此，我们有：(3/12 + 2/12) / 2 = (5/12) / 2 = 5/24。现在，调和均值是这个结果的倒数：调和均值 = 1 / (5/24) = 24/5 = 4.8。这个值与算术平均数不同，说明了调和均值如何为数据提供不同的视角。调和均值在数字代表速率的情况下尤为重要。例如，如果一辆车在旅程的某一部分以每小时60公里的速度行驶，然后在另一部分以每小时90公里的速度行驶，那么平均速度不能简单地使用算术平均数来计算。相反，我们会使用调和均值来更准确地表示整个旅程的平均速度。调和均值的另一个重要方面是在金融中的应用，特别是在计算平均收益率时。在评估投资绩效时，调和均值提供了比算术平均数更现实的衡量标准，尤其是在处理百分比时。例如，如果一项投资在一年内收益为10%，而在下一年则为-20%，那么算术平均数将显示为-5%的回报，这并不能准确反映整体表现。通过应用调和均值，投资者可以更好地理解其回报的真实性质。总之，调和均值（harmonic mean）是一个强大的数学工具，能够为数据分析提供独特的见解，尤其是在处理速率和比率时。它在各个领域的应用展示了其多功能性和重要性。理解调和均值使个人能够根据对数据的全面分析做出更明智的决策。随着我们在日益复杂的世界中继续遇到多样化的数据集，掌握像调和均值这样的概念无疑将增强我们的分析能力。