Question

Describe the terms sampling variability and sampling distributions. Provide an example of each.

Answer 1

We know that,

That difference between the sample statistics and the parameter is called sampling variability. There is always variability in a measure. Variability comes from the fact that not every participant in the sample is the same. For example, the average height of American males is 5'10” but I am 6'3″.

And

The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size {\displaystyle n}. It may be considered as the distribution of the statistic for all possible samples from the same population of a given sample size.

For example,

The sampling distribution of the sample mean approaches a normal distribution with a mean of μ and a variance of σ²/N as N, the sample size, increases.

Thank you.