sample variance

简明释义

样本方差

英英释义

例句

1.The sample variance 样本方差 helps researchers determine how much individual data points differ from the mean.

样本方差 样本方差帮助研究人员确定个别数据点与均值之间的差异程度。

2.In statistics, we often calculate the sample variance 样本方差 to understand the spread of a dataset.

在统计学中，我们经常计算样本方差 样本方差来理解数据集的分布。

3.The sample variance 样本方差 indicates how widely the data points are spread out in a sample.

样本方差 样本方差指示样本中数据点的分布范围有多广。

4.To compare two different groups, we can analyze their sample variance 样本方差.

为了比较两个不同的群体，我们可以分析它们的样本方差 样本方差。

5.When conducting a survey, calculating the sample variance 样本方差 is crucial for understanding variability.

进行调查时，计算样本方差 样本方差对于理解变异性至关重要。

作文

In the field of statistics, understanding the concept of sample variance is crucial for analyzing data sets. The sample variance is a measure that indicates how much individual data points in a sample differ from the sample mean. It provides insights into the spread and dispersion of data, which can be particularly important when making predictions or drawing conclusions based on a sample rather than an entire population. To calculate the sample variance, one begins by determining the mean of the sample. This is done by adding all the data points together and dividing by the number of points in the sample. Once the mean is established, the next step is to find the squared differences between each data point and the mean. These squared differences are then summed up and divided by the number of observations minus one (n-1). This adjustment, known as Bessel's correction, ensures that the sample variance provides an unbiased estimate of the population variance. For example, consider a sample consisting of the following five test scores: 82, 85, 87, 90, and 95. First, we calculate the mean: (82 + 85 + 87 + 90 + 95) / 5 = 87.8. Next, we find the squared differences: (82 - 87.8)² = 33.64, (85 - 87.8)² = 7.84, (87 - 87.8)² = 0.64, (90 - 87.8)² = 4.84, and (95 - 87.8)² = 51.84. Adding these squared differences together gives us 33.64 + 7.84 + 0.64 + 4.84 + 51.84 = 98.8. Finally, we divide this sum by (5 - 1), which equals 4, leading to a sample variance of 24.7. The significance of the sample variance extends beyond mere calculations; it plays a vital role in various statistical analyses, including hypothesis testing and confidence interval estimation. A higher sample variance indicates a greater degree of variability among the data points, while a lower sample variance suggests that the data points are more closely clustered around the mean. This information can help researchers and analysts make informed decisions based on the characteristics of the data they are studying. Moreover, understanding sample variance is essential for comparing different data sets. For instance, if two groups have similar means but significantly different sample variances, it may indicate that one group has more consistent results, while the other is more variable. Such insights can be pivotal in fields like quality control, psychology, and economics, where understanding variability can influence outcomes. In conclusion, the sample variance is a fundamental concept in statistics that helps quantify the spread of data within a sample. By calculating the sample variance, researchers can gain valuable insights into their data, facilitating better decision-making and analysis. As we continue to collect and analyze data in various fields, mastering the understanding of sample variance will undoubtedly enhance our ability to interpret and utilize statistical information effectively.

在统计学领域，理解样本方差的概念对于分析数据集至关重要。样本方差是一个衡量样本中各个数据点与样本均值之间差异的指标。它提供了关于数据的分散和扩展的见解，这在基于样本而非整个总体进行预测或得出结论时尤其重要。计算样本方差的第一步是确定样本的均值。这是通过将所有数据点相加并除以样本中的点数来完成的。一旦确定了均值，下一步是找到每个数据点与均值之间的平方差。这些平方差然后被求和，并除以观察次数减去一（n-1）。这种调整被称为贝塞尔修正，确保样本方差提供对总体方差的无偏估计。例如，考虑一个由以下五个测试分数组成的样本：82、85、87、90和95。首先，我们计算均值：（82 + 85 + 87 + 90 + 95）/ 5 = 87.8。接下来，我们找到平方差：（82 - 87.8）² = 33.64，（85 - 87.8）² = 7.84，（87 - 87.8）² = 0.64，（90 - 87.8）² = 4.84，以及（95 - 87.8）² = 51.84。将这些平方差相加得到33.64 + 7.84 + 0.64 + 4.84 + 51.84 = 98.8。最后，我们将这个总和除以（5 - 1），即4，得出样本方差为24.7。样本方差的重要性超越了简单的计算；它在各种统计分析中发挥着至关重要的作用，包括假设检验和置信区间估计。更高的样本方差表示数据点之间的变异程度较大，而较低的样本方差则表明数据点更紧密地聚集在均值附近。这些信息可以帮助研究人员和分析师根据他们所研究的数据特征做出明智的决策。此外，理解样本方差对于比较不同的数据集也至关重要。例如，如果两个组的均值相似但样本方差显著不同，这可能表明一个组的结果更一致，而另一个组则更加多变。这种见解在质量控制、心理学和经济学等领域可能具有关键影响，因为理解变异性可以影响结果。总之，样本方差是统计学中的一个基本概念，有助于量化样本内数据的分散程度。通过计算样本方差，研究人员可以获得对数据的有价值的见解，从而促进更好的决策和分析。随着我们在各个领域继续收集和分析数据，掌握对样本方差的理解无疑将增强我们有效解释和利用统计信息的能力。