weighted mean; weighted average

简明释义

加权平均数

英英释义

例句

1.The teacher explained that the class participation would count for 20% of the total grade, making it part of the weighted average 加权平均数 calculation.

老师解释说，课堂参与将占总成绩的20%，这使得它成为加权平均数 weighted average计算的一部分。

2.When analyzing survey results, researchers often use a weighted mean 加权平均数 to account for different group sizes.

在分析调查结果时，研究人员通常使用加权平均数 weighted mean来考虑不同组的大小。

3.The weighted average 加权平均数 of prices helps consumers compare the cost of products more effectively.

价格的加权平均数 weighted average帮助消费者更有效地比较产品的成本。

4.To calculate the final grade for the course, we used a weighted average 加权平均数 based on homework, exams, and projects.

为了计算课程的最终成绩，我们使用了一个加权平均数 weighted average，它基于作业、考试和项目的分数。

5.In finance, the weighted mean 加权平均数 of a portfolio's returns helps investors understand performance better.

在金融中，投资组合回报的加权平均数 weighted mean帮助投资者更好地理解绩效。

作文

In the realm of statistics and data analysis, the concept of weighted mean or weighted average plays a critical role in accurately representing data sets that have varying levels of significance. Unlike a simple arithmetic mean, which treats all values equally, the weighted mean assigns different weights to different values based on their importance or frequency. This is particularly useful in scenarios where certain data points are more representative or relevant than others. For instance, in academic grading, a student's final score may be calculated using a weighted average where exams count for more than quizzes. To illustrate this concept, consider a student who has completed three assignments with the following scores: Assignment 1 (80 points), Assignment 2 (90 points), and Assignment 3 (70 points). If we assume that Assignment 1 is worth 50% of the final grade, Assignment 2 is worth 30%, and Assignment 3 is worth 20%, we can calculate the weighted average as follows: First, we multiply each score by its corresponding weight: - Assignment 1: 80 * 0.5 = 40 - Assignment 2: 90 * 0.3 = 27 - Assignment 3: 70 * 0.2 = 14 Next, we sum these weighted scores: 40 + 27 + 14 = 81 Finally, the weighted mean or weighted average score for the student is 81. This method provides a more accurate reflection of the student's performance, especially when some assignments are deemed more critical to the overall assessment. The application of weighted means extends beyond education into various fields such as finance, economics, and research. In finance, for example, investors often use weighted averages to determine the average cost of shares in a portfolio, taking into account the number of shares purchased at different prices. This approach helps in assessing the overall performance of investments more effectively than simply averaging the prices. Moreover, in economic studies, researchers might apply weighted averages to calculate indices like the Consumer Price Index (CPI), where different categories of goods and services contribute differently to inflation rates. By applying appropriate weights, economists can gain insights into the true cost of living changes experienced by consumers. In conclusion, the concept of weighted mean or weighted average is an invaluable tool in data analysis, providing a nuanced understanding of data sets where not all values hold equal weight. Whether in education, finance, or economics, employing weighted averages allows for more informed decisions and analyses. Thus, mastering the use of weighted means is essential for anyone seeking to engage deeply with quantitative data.

在统计和数据分析领域，加权平均数或加权平均的概念在准确表示具有不同重要性的数据集方面起着至关重要的作用。与简单的算术平均数不同，简单算术平均数对所有值一视同仁，而加权平均数根据各个值的重要性或频率赋予不同的权重。这在某些数据点比其他数据点更具代表性或相关性的情况下尤其有用。例如，在学术评分中，学生的最终分数可能使用加权平均来计算，其中考试的权重高于测验。为了说明这一概念，考虑一个学生完成了三项作业，得分如下：作业1（80分）、作业2（90分）和作业3（70分）。如果我们假设作业1占最终成绩的50%，作业2占30%，作业3占20%，我们可以按如下方式计算加权平均：首先，我们将每个分数乘以其对应的权重：- 作业1：80 * 0.5 = 40- 作业2：90 * 0.3 = 27- 作业3：70 * 0.2 = 14接下来，我们将这些加权分数相加：40 + 27 + 14 = 81最后，学生的加权平均数或加权平均分数为81。这种方法提供了学生表现的更准确反映，特别是在某些作业被视为对整体评估更为关键时。加权平均数的应用不仅限于教育，还扩展到金融、经济和研究等多个领域。例如，在金融领域，投资者通常使用加权平均来确定投资组合中股票的平均成本，同时考虑在不同价格下购买的股票数量。这种方法在评估投资的整体表现时，比简单地平均价格更有效。此外，在经济研究中，研究人员可能会应用加权平均来计算消费者物价指数（CPI）等指数，其中不同类别的商品和服务对通货膨胀率的贡献不同。通过应用适当的权重，经济学家可以深入了解消费者所经历的生活成本变化。总之，加权平均数或加权平均的概念是数据分析中的一项宝贵工具，提供了对数据集中各值不等权重的细致理解。无论是在教育、金融还是经济领域，使用加权平均都可以做出更明智的决策和分析。因此，掌握加权平均数的使用对于任何希望深入参与定量数据的人来说都是必不可少的。