Question

B.38  

Average Size of a Performing Group in the Rock and Roll Hall of Fame

From its founding through 2015, the Rock and Roll Hall of Fame has inducted 303 groups or individuals, and 206 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 on StatKey. Some of the 206 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 206 values. Describe the shape, and identify the two groups with the largest number of people.

(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?

Answer 1

A) the mean size of the performer inductee groups (including individuals) is =

2.86407767

B) Use technology to create a graph of all 206 values. Describe the shape, and identify the two groups with the largest number of people:

we use bar chart to represent the graph of all 206 performer inductee groups with the frequencies

Two groups with largest people numbers are : 1 and 4

(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.

Here we randomly sample 10 samples from the given population of frequencies of 206 people 100000 times and plot the sampled distribution data as a bar chart to get the mean distribution.

It is to be noted that the population has a mean number of people (u) = 2.864078

And after 100000 simulation of random samples of size 10 from the population the sampling distribution has the mean (xbar ) = 2.8758

The bar plot of the sampling distribution is plotted below.

The sampling distribution has a high peak at value 1 and then at 4. Overall the sample data is a bit leptokurtic.

The center of the data is obviously located near 3 .

Standard error of the sample mean = = 2.233802