Suppose That in a Group of Six Athletes There Are $\frac{1}{2}$

Essay

Suppose that in a group of six athletes there are three jockeys whose heights are 60,65 , and 55 inches, and three basketball players whose heights are 80,75 , and 85 inches.
-Suppose that the six athletes are divided into clusters according to their sports, each cluster is assigned a probability of $\frac{1}{2}$ , and a random sample of size 2 is taken from one of the randomly chosen clusters. List all possible samples, calculate their means, and calculate $\sigma_{\bar{x}}$ .