harmonic mean

简明释义

调和中项

英英释义

例句

1.The harmonic mean is particularly useful in averaging rates, such as speed or efficiency.

在平均速率（如速度或效率）的计算中，调和平均数特别有用。

2.When evaluating the performance of a machine over different cycles, the harmonic mean provides a more accurate measure.

在评估机器在不同周期内的性能时，调和平均数提供了更准确的衡量标准。

3.In finance, the harmonic mean can be used to calculate average prices when dealing with different quantities.

在金融中，当处理不同数量时，可以使用调和平均数来计算平均价格。

4.The formula for the harmonic mean of n numbers is 1 divided by the average of their reciprocals.

调和平均数的公式是n个数的倒数平均值的倒数。

5.To find the average of multiple speeds, you should use the harmonic mean instead of the arithmetic mean.

要计算多个速度的平均值，应该使用调和平均数而不是算术平均数。

作文

The concept of the harmonic mean is often overlooked in everyday mathematics, yet it plays a crucial role in various fields, including statistics, finance, and even in our daily decision-making processes. To understand the harmonic mean, we must first distinguish it from other types of means, such as the arithmetic mean and geometric mean. While the arithmetic mean is simply the sum of a set of numbers divided by the count of those numbers, the harmonic mean offers a different perspective, particularly useful when dealing with rates or ratios. For example, consider a scenario where a car travels a certain distance at different speeds. If a car travels 60 miles at an hour and then 30 miles at another hour, calculating the average speed using the arithmetic mean would yield 45 miles per hour. However, this does not accurately represent the car's overall speed for the entire journey. Instead, applying the harmonic mean provides a more precise measure of the average speed over the entire distance, which in this case would be 40 miles per hour. This highlights the importance of using the harmonic mean when dealing with quantities that are inversely related to the average rate.In finance, the harmonic mean can be particularly useful in calculating average prices. Suppose an investor buys shares of a stock at different prices. The harmonic mean allows the investor to determine the average cost per share more accurately than the arithmetic mean, especially when the number of shares purchased varies with each price. This can lead to better investment decisions and a clearer understanding of the overall cost basis.Moreover, the harmonic mean is also applied in the field of physics, particularly in situations involving wave frequencies and sound waves. When combining multiple frequencies, the harmonic mean can help in determining the overall frequency of the resultant wave. This application showcases how the harmonic mean extends beyond simple numerical calculations into complex real-world scenarios.Understanding the harmonic mean also enriches our grasp of mathematical relationships. It emphasizes the significance of context when interpreting data. For instance, in social sciences, researchers often deal with averages to summarize data sets. Recognizing when to apply the harmonic mean instead of the arithmetic mean can lead to more accurate representations of societal trends and behaviors.In conclusion, the harmonic mean is a powerful mathematical tool that offers unique insights into averages, particularly in cases involving rates, ratios, and varying quantities. Its applications span across several disciplines, making it an essential concept for anyone engaged in analytical thinking. By incorporating the harmonic mean into our calculations and analyses, we can achieve a deeper understanding of the relationships between numbers and make more informed decisions based on accurate data interpretation.

“调和均值”这一概念在日常数学中常常被忽视，但它在统计学、金融以及我们的日常决策过程中扮演着至关重要的角色。要理解“调和均值”，我们首先必须将其与其他类型的均值（如算术均值和几何均值）区分开来。算术均值是将一组数字相加后除以数字的个数，而“调和均值”则提供了不同的视角，特别是在处理比率或速率时尤为有用。例如，考虑一个场景，一辆车以不同的速度行驶一定距离。如果一辆车以每小时60英里行驶，然后以每小时30英里行驶，使用算术均值计算平均速度将得出每小时45英里。然而，这并不能准确代表整段旅程的汽车总速度。相反，应用“调和均值”可以更精确地测量整个距离的平均速度，在这种情况下为每小时40英里。这突显了在处理与平均速率成反比的量时使用“调和均值”的重要性。在金融领域，“调和均值”在计算平均价格时特别有用。假设投资者以不同的价格购买股票的股份。“调和均值”使投资者能够更准确地确定每股的平均成本，而不是算术均值，特别是当每个价格购买的股份数量不同时。这可以导致更好的投资决策，并更清晰地理解整体成本基础。此外，“调和均值”也应用于物理学，特别是在涉及波频率和声波的情况下。当组合多个频率时，“调和均值”可以帮助确定结果波的整体频率。这种应用展示了“调和均值”如何超越简单的数字计算，进入复杂的现实场景。理解“调和均值”还丰富了我们对数学关系的理解。它强调了在解释数据时背景的重要性。例如，在社会科学中，研究人员经常处理均值来总结数据集。认识到何时应用“调和均值”而非算术均值，可以导致对社会趋势和行为的更准确表示。总之，“调和均值”是一种强大的数学工具，提供了对平均值独特的见解，特别是在涉及速率、比率和变化量的情况下。它的应用跨越多个学科，使其成为任何参与分析思维的人的基本概念。通过将“调和均值”纳入我们的计算和分析中，我们可以更深入地理解数字之间的关系，并基于准确的数据解释做出更明智的决策。