Distribution of the Sample Mean (Jump to: Lecture | Video )

For example: A statistics class has six students, ages displayed below. Construct a sampling distribution of the mean of age for samples (n = 2).

Ages: 18, 18, 19, 20, 20, 21

First, we find the mean of every possible pairing where n = 2:

Figure 1.

Next, we create a frequency distribution for the new sample means:

Figure 2.

This is the distribution of our sample mean, where n = 2.

Figure 3.

As sample size increases, standard deviation decreases.

The standard deviation of the sampling distribution is also known as the standard error of the mean:

Figure 4.