Sampling Distribution

The sampling distribution is the distribution (分配) of a statistic — say the sample mean — that you would see if you drew the sample over and over again from the same population. It is the key idea that makes inference possible: it describes how much your estimate would jump around due to the luck of the draw.

You almost never observe it directly (you usually have just one sample), but theory and simulation tell you its shape. The central limit theorem (中央極限定理) is the gift here: for large samples the sampling distribution of the mean is approximately a normal (bell) curve centred on the true value, no matter what the raw data look like.