Statistical Lab

• Background

  In July of 2010, two reporters writing for the Los Angeles Times broke a story about the city of Bell, one of the poorest and smallest cities in Los Angeles County. The two highest paid city officials, Manager Robert Rizzo and Assistant City Manager Angela Spaccia, pulled in salaries that seemed much higher than similar officials working in much larger, wealthier cities in the United States. Further investigation uncovered many instances of corruption among several of the city managers and city leaders, including instances of council members being paid thousands of dollars to attend meetings that lasted no longer than a few minutes.

  

  For the purposes of this lab, you are retracing the steps of an investigative reporter who broke the story by examining the salaries of public employees working for Bell and another city of comparable size and location.

• Guidelines

  In this lab, you will do the following.

  • Compute the mean and median to get a sense of how much a typical public employee earns in these cities.
  • Calculate the standard deviation, and determine how much variation there is in public employee salaries.
  • Look for any extreme outliers in public employee salaries, using the standard deviation.

• About the Data

  For this lab, you need to download the bellemployeesalaries.csv dataset. The data comes from the California State Controller's database, which contains information on the salary and other compensation benefits of public employees in the cities, counties, and special districts of California. The data you will be using shows the 2009 salaries of paid public employees (working more than 25 hours per week) for the cities of Bell and Duarte. Each row in the file represents a paid public employee. The file contains four columns:

  • cityName—the name of the city where the employee works; in this data file, the city will be either Bell or Duarte
  • department—the department name where the city employee worked
  • position—the job title of the city employee
  • wages—the total amount the employee earned in the year 2009 in US dollars, including their base pay and overtime

• Tech Guide

  You will need to use the Excel Tech Guide.

• Lab Questions

  Create and upload a histogram of the salary data for the city of Bell, where each bar width is about 50,000 US dollars. (Submit a file with a maximum size of 1 MB.)

  This answer has not been graded yet.

  (a)

  Is the distribution of the salaries symmetric?

  Yes No    

  (b)

  Without making any calculations, will the mean be larger or smaller than the median? Explain why.

  The mean will be ---Select--- larger smaller than the median, because the distribution is ---Select--- right skewed left skewed symmetric .

  For the city of Duarte, the median salary is 31,597.00 US dollars, the mean salary is 44,713.88 US dollars, and the standard deviation of the salaries is 36,448.59 US dollars (using the formula for the population standard deviation—recall that the data contains the salaries of all city employees). To ensure that your software tool is using the correct formulas, verify these results.

  (a)

  What is the population median, mean, and standard deviation for the salaries in Bell? (Round your answers to two decimal places.)

  Mean (μ) $ Median $ Standard Deviation (σ) $

  (b)

  Compare the mean salaries of Bell and Duarte, paying attention to the position titles and salaries in the two cities.

  The mean salary in Bell is ---Select--- smaller than the same as larger than the mean salary in Duarte.

  Does it pay to be a police officer in Bell?

  
  

  This answer has not been graded yet.

  In general, city managers earn the highest salaries in a city, and are paid well above a typical city employee. We want to find how far away the city manager salaries are from the mean for each city. Some cities have more variation in salaries than others, so we will compute how far the highest paid salaries are from the mean, and then divide that difference by the standard deviation of the city salaries, in order to make a fair comparison. In other words, we are going to calculate how many standard deviations the highest salaries are from their city means. Use the following formula.

  (Highest Salary − Mean Salary)

  Standard Deviation

  (a)

  For the city of Bell, how many standard deviations is the highest salary from the mean? (Round your answer to four decimal places.)

  (b)

  For the city of Duarte, how many standard deviations is the highest salary from the mean? (Round your answer to four decimal places.)

  (c)

  As an investigative reporter, you are used to seeing city manager salaries 4 or even 5 standard deviations away from the mean. What do you find curious about this data?

  
  

  This answer has not been graded yet.

• References

  1. Gottlieb, Jeff and Vives, Ruben, Los Angeles Times, "Is A City Manager Worth $800,000?," July 15, 2010, http://articles.latimes.com/2010/jul/15/local/la-me-bell-salary-20100715.
  2. Gottlieb, Jeff, Los Angeles Times, "Bell Sues Ex-Councilman, Foundation and Construction Firm Over Payouts," June 24, 2014, http://www.latimes.com/local/la-me-0625-bell-lawsuit-20140625-story.html.
  3. Knoll, Corina and Gottlieb, Jeff, Los Angeles Times, "Rizzo Gets 12 Years in Prison, Marking End to Scandal that Rocked Bell," April 16, 2014, http://www.latimes.com/local/lanow/la-me-ln-rizzo-set-to-be-sentenced--20140415-story.html.