Measures of the Spread of the Data · Exercise 26

A survey of enrollment at 35 community colleges across the United States yielded the following figures:
6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622

(a) Organize the data into a chart with six intervals of equal width from 0 to 30,000. Label the two columns "Enrollment" and "Frequency."
(b) Construct a histogram of the data.
(c) If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
(d) Calculate the sample mean.
(e) Calculate the sample standard deviation.
(f) A school with an enrollment of 8000 would be how many standard deviations away from the mean?

This is an open-ended exercise: its source gives no single answer.

OpenStax, Introductory Statistics 2e · §2.7 Measures of the Spread of the Data · Exercise 26