在前面的学习中，我们涉及的都是原始数据的分布。一个总体中所有原始分数的分布就形成了总体分布（population distribution）。但是在实际的研究中，我们往往无法对总体分布进行直接考察，而是从这个总体中抽取出个体作为样本进行考察，抽取出来的样本的分数就形成了样本分布（sample distribution）。当然我们可以从同一总体中抽取出很多个样本。总体中抽取的所有可能的特定容量分布的统计量所形成的统计分布就是取样分布（sampling distribution）
取样分布的一个特例便是样本均值的分布（distribution of sample means）。它是指总体中可抽取的所有可能的特定容量（n）的随机样本的均值的集合。注意，样本均值的分布包含所有可能的样本，而且由于它是取样分布，在样本均值分布中，值不是分数，而是一个统计量。
样本均值的分布在形状上接近正态分布，而且在无偏估计下，样本均值分布的均值是等于总体均值的。当我们得到所有均值时，它们的均值就完全与总体相等了，因此所有样本均值的平均值叫做X bar 的期望值，且应该等于总体均值。样本均值分布用标准误（standar error of X bar，简称SE）来衡量分布的变异性。标准误就是样本均值分布的标准差。
In our previous studies, we covered distributions of raw data. The distributions of all the raw scores in an population form the population distribution.However, in actual research, we are often unable to examine the population distribution directly; instead, we examine individuals drawn from the population as samples. The scores of the drawn samples form the sample distribution.Certainly we can draw many samples from the same total. The statistical distribution formed by the statistics of all possible specific capacity distributions drawn from the population is the sampling distribution.
A special case of the sampling distribution is the distribution of sample means. It is the set of the means of all possible random samples of a particular capacity (n) that can be drawn from the population. Be aware that the distribution of sample means contains all possible samples. Since it is a sampling distribution, the value is not a fraction but a statistic in the sample mean distribution.