计算精确的合并方差

摘要：

提出了一种计算合并数据集方差的精确方法。与其他方法相比，它的主要优点是简单，易于推导和记忆，并且不需要任何假设。结果可以简明地总结如下：“精确合并方差是方差的均值加上分量数据集均值的方差。“证明是如此简单，以前肯定做过很多次，但在教科书中没有。讨论了其现实意义。

英文摘要：

An exact method of calculating the variance of a pooled data set is presented. Its major advantages over the many other methods are that it is simple, is easily derived and remembered, and requires no assumptions. The result can be concisely summarized as follows: "The Exact pooled variance is the mean of the variances plus the variance of the means of the component data sets." The proof is so simple that it has certainly been done many times before, but it is absent in the textbooks. Its practical significance is discussed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。