empirical sample mean

简明释义

经验样本均值

英英释义

例句

1.The empirical sample mean 经验样本均值 of daily sales data provided insights into seasonal trends for the business.

每日销售数据的经验样本均值 empirical sample mean为企业提供了季节性趋势的见解。

2.In a clinical trial, researchers calculated the empirical sample mean 经验样本均值 of patient recovery times to assess treatment effectiveness.

在一项临床试验中，研究人员计算了患者恢复时间的经验样本均值 empirical sample mean以评估治疗效果。

3.The empirical sample mean 经验样本均值 of test scores helped the school determine the overall performance of its students.

测试分数的经验样本均值 empirical sample mean帮助学校确定学生的整体表现。

4.To better understand consumer preferences, the marketing team analyzed the empirical sample mean 经验样本均值 of survey responses.

为了更好地理解消费者偏好，市场团队分析了调查反馈的经验样本均值 empirical sample mean。

5.By calculating the empirical sample mean 经验样本均值, the researchers were able to make predictions about future outcomes.

通过计算经验样本均值 empirical sample mean，研究人员能够对未来结果做出预测。

作文

In the field of statistics, the concept of the empirical sample mean plays a crucial role in data analysis and interpretation. The empirical sample mean refers to the average value calculated from a set of observed data points, providing a measure of central tendency that is essential for understanding the underlying patterns within a dataset. This statistical measure is particularly important when researchers aim to draw conclusions about a larger population based on a smaller subset of data, known as a sample.To illustrate the significance of the empirical sample mean, consider a scenario in which a researcher is studying the average height of adult males in a city. Instead of measuring the height of every adult male, which would be impractical, the researcher selects a random sample of 100 men. By measuring their heights and calculating the empirical sample mean, the researcher can make informed estimates about the average height of all adult males in that city. This method allows for efficient data collection while still providing valuable insights.The calculation of the empirical sample mean is straightforward. It involves summing all the individual data points in the sample and then dividing that sum by the number of observations. Mathematically, it can be expressed as:Empirical Sample Mean = (X1 + X2 + ... + Xn) / nwhere X1, X2, ..., Xn represent the individual data points, and n is the total number of observations in the sample. This formula highlights how each data point contributes to the overall average, reinforcing the importance of each observation in the calculation.One critical aspect of the empirical sample mean is its sensitivity to outliers. An outlier is a data point that significantly deviates from the other observations in the dataset. For example, if one individual in the sample of 100 men is exceptionally tall or short, their height could skew the empirical sample mean, leading to potentially misleading conclusions. Therefore, researchers must carefully analyze their data for outliers and consider using alternative measures of central tendency, such as the median, when necessary.Furthermore, the empirical sample mean serves as a foundation for various statistical analyses, including hypothesis testing and confidence intervals. By utilizing the empirical sample mean, researchers can assess whether their findings are statistically significant and can estimate the range within which the true population mean is likely to fall. This application is particularly valuable in fields such as medicine, psychology, and social sciences, where understanding population characteristics is essential for making informed decisions.In conclusion, the empirical sample mean is a fundamental concept in statistics that provides a simple yet powerful tool for data analysis. By calculating the average of a sample, researchers can gain insights into larger populations, identify trends, and make predictions. However, it is essential to be aware of the limitations of the empirical sample mean, especially regarding the influence of outliers. Overall, mastering the concept of the empirical sample mean is vital for anyone engaged in research and data analysis, as it lays the groundwork for more complex statistical methodologies and interpretations.

在统计学领域，经验样本均值的概念在数据分析和解释中发挥着至关重要的作用。经验样本均值是指从一组观察数据点中计算出的平均值，它提供了一个中心趋势的衡量标准，这对于理解数据集中潜在模式至关重要。当研究人员希望根据较小的数据子集（称为样本）得出关于更大总体的结论时，这一统计测量尤为重要。为了说明经验样本均值的重要性，考虑一个场景：研究者正在研究一个城市成年男性的平均身高。研究者并不打算测量每一位成年男性的身高，这样做既不切实际也不必要，而是随机选择100名男性作为样本。通过测量他们的身高并计算出经验样本均值，研究者可以对该城市所有成年男性的平均身高进行有根据的估计。这种方法使数据收集变得高效，同时仍能提供有价值的见解。计算经验样本均值是相对简单的。它涉及将样本中的所有个体数据点相加，然后将该总和除以观察值的数量。从数学上讲，可以表示为：经验样本均值 = (X1 + X2 + ... + Xn) / n其中X1、X2、...、Xn代表个体数据点，n是样本中的观察总数。这个公式突显了每个数据点如何对整体平均值产生影响，从而强调了在计算中的每个观察值的重要性。经验样本均值的一个关键方面是其对离群值的敏感性。离群值是指在数据集中显著偏离其他观察值的数据点。例如，如果在100名男性的样本中，有一位个体的身高异常高或低，那么他们的身高可能会扭曲经验样本均值，导致可能误导性的结论。因此，研究人员必须仔细分析数据以寻找离群值，并在必要时考虑使用其他中心趋势的测量方式，如中位数。此外，经验样本均值作为各种统计分析的基础，包括假设检验和置信区间。通过利用经验样本均值，研究人员可以评估他们的发现是否具有统计显著性，并可以估计真实总体均值可能落入的范围。这种应用在医学、心理学和社会科学等领域尤为重要，因为了解总体特征对于做出明智的决策至关重要。总之，经验样本均值是统计学中的一个基本概念，为数据分析提供了一种简单而强大的工具。通过计算样本的平均值，研究人员可以获得对更大总体的洞察，识别趋势并进行预测。然而，必须意识到经验样本均值的局限性，尤其是关于离群值的影响。总的来说，掌握经验样本均值的概念对从事研究和数据分析的任何人来说都是至关重要的，因为它为更复杂的统计方法和解释奠定了基础。