Using a random number generator from statistical software, create five sets (columns) of 50 random numbers between 0 and 9.

a. Create a frequency distribution and a histogram summarizing all 250 random numbers. What distribution best describes the histogram?

1. What is the mean of this distribution?

2. What is the standard deviation of this distribution?

b. Now, identify each row as a sample with five observations.

1. In a new column, compute the average of the first two observations in each row or sample. This is a sample size of 2, n = 2. In another column, compute the average of the first three observations (n = 3) in each row or sample. Continue this process for sample sizes of 4 (n = 4) and 5 (n = 5).

2. For each sample size, summarize the sample means with a frequency distribution and histogram.

3. For each sample size compute the mean of the means, the standard deviation of the means, and the range of the means.

4. Write a report that compares the population distribution to the sampling distributions of the means.

5. Write a report that compares the four sampling distributions of the mean.

6. What statistical principle does this exercise demonstrate? How does your analysis support this principle?