Properties of Sampling Distributions Explained in Statistics

We’ve been saying that the sampling distribution has some interesting properties that will later help you estimate the error in your samples. Let’s finally see what these properties are.

Again, to recap, let’s see what the notations and formulas are for populations, samples and sampling distributions.

So, there are two important properties of a sampling distribution of the mean:

1. Sampling distribution’s mean (${\mu }_{\overline{X}}$) = Population mean (μ)

2. Sampling distribution’s standard deviation (Standard error) = $\frac{\sigma }{\sqrt{n}}$, where σ is the population’s standard deviation and n is the sample size

Recall that in the last video, we created a sampling distribution and found the values of its mean and standard deviation as 2.348 and 0.4248, respectively. These values were very close to the values suggested by the formula, i.e., 2.385 and 0.44.