From its founding through 2012, the Rock and Roll Hall of Fame has inducted 273 groups or individuals, and 181 of the inductees have been performers while the rest have been related to the world of music in some way other than as a performer. The full dataset is available at RockandRoll. Some of the 181 performer inductees have been solo artists while some are groups with a large number of members. We are interested in the average number of members across all groups or individuals inducted as performers.

(a) What is the mean size of the performer inductee groups (including individuals)? Use the correct notation with your answer.

(b) Use technology to create a graph of all 181 values. Describe the shape, and identify the two groups with the largest numbers.

(c) Use technology to generate a sampling distribution for the mean size of the group using samples of size n = 10. Give the shape and center of the sampling distribution and give the standard error.

(d) What does one dot on the sampling distribution represent?