As sample sizes increase, the sampling distributions approach a normal distribution. ... As the sample sizes increase, the variability of each sampling distribution decreases so that they become increasingly more leptokurtic.

Do larger samples have more variability?

However, the variability in the sample means will depend on the size of the samples, since larger samples are more likely to give estimated means that are closer to the true mean of the population.

What happens to variability as sample size increases?

In other words, as the sample size increases, the variability of sampling distribution decreases. Also, as the sample size increases the shape of the sampling distribution becomes more similar to a normal distribution regardless of the shape of the population.