Quantitative Reasoning

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Module 4 – Case


Assignment Overview

Signature Assignment: Quantitative Reasoning, Emphasized Level

In this assignment, your quantitative reasoning skills will be assessed. The Quantitative Reasoning rubric will be useful for this purpose. In MGT511 quantitative reasoning skills were assessed at the “introduced” level. In HRM520 they were assessed at the “reinforced” level. Finally, in this course your skills will be assessed at the “emphasized” level.

The math that we learned in high school and perhaps relearned in college has applications in nearly all fields including human resource management. In this case assignment we will look at something as simple as straight lines, as in linear equations.

Straight lines play an important role in a wide variety of applications, in many fields including business.

An equation with two variables is a linear equation. Many relationships are linear or almost linear, so that they can be approximated by linear equations.

If you need a refresher on solving equations, watch the Khan Academy, level 2 video retrieved from  https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/algebra-linear-equations-2


The following linear equation is useful to make a future projection:

In 1970, there were 37,000 shopping malls in the United States.

Even with the growth of online shopping, in 2017 there were 116,000 shopping malls.

If this growth continues, how many shopping malls will there be in 2030?

Let’s use two variables:

y = number of shopping centers

x = number of years after 1970

So, to put this in an equation:

y = 116,000−37,000×1970−2017 +37,000 {“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mi>y</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mfrac><mrow><mn>116</mn><mo>,</mo><mn>000</mn><mo>-</mo><mn>37</mn><mo>,</mo><mn>000</mn><mi>x</mi></mrow><mrow><mn>1970</mn><mo>-</mo><mn>2017</mn></mrow></mfrac><mo>&#xA0;</mo><mo>+</mo><mn>37</mn><mo>,</mo><mn>000</mn><mo>&#xA0;</mo></math>”}

79,00047 = 1,681{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mfrac><mrow><mn>79</mn><mo>,</mo><mn>000</mn></mrow><mn>47</mn></mfrac><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mn>1</mn><mo>,</mo><mn>681</mn></math>”}

So, the linear equation is y = 1681x + 37,000

Now, assuming that this equation remains valid in the future, we can predict how many shopping malls there will be in 2030:

There are 60 years between 1970 and 2030.

y = 1681(60) + 37,000 y = 100,860 + 37,000 or 137,860 shopping malls in 2030.

This example probably reminds you that there might be other factors going on that will not make this equation valid in the future. But, for our purposes, it shows if all things stay the same, we can make future predictions.

There are many different examples of ways linear equations are used in real life—for example, distance traveled by a bus compared with distance traveled by a bicycle. Which one will get to work on time? Or, production rates—will employees who are slow producers make as many products over time as employees who are only speedy during the first part of the shift? This type of linear application can also be applied, of course, to pricing, dimensions, and mixing raw products. For example, if we have two semi-trucks of products moving toward each other at different speeds to reach the same point, which one will reach the dock sooner? Another example is estimating how much a box of 60 safety glasses on sale for $120 and marked down by 35 percent cost before the sale.

Yet another example of a real-life linear equation is estimating the dimensions of office shelving whose width needs to be four times its height, given that the wood available for use is 72 feet. Or, estimating how much a company pays a vendor for raw material that was priced yesterday for $800, but today has been marked up 25 percent.

Case Assignment

Now it is your turn. For the Module 4 Case Assignment, solve the following three problems, completing a, b, and c for each problem. In “b” for each, explain step by step how you arrived at the answer. And in “c” for each, conduct research to arrive at a strong (informative) paragraph, being sure to cite sources.

Problem #1: According to the U. S. Bureau of Labor Statistics, there were about 16.3 million union workers in 2000 and 14.7 million union workers in 2018.

  1. If the change in the number of union workers is considered to be linear, write an equation expressing the number y of union workers in terms of the number x of years since 2000.
  2. Assuming that the equation in part “a” remains accurate, use it to predict the number of union workers in 2050.
  3. Is the number that you came up with in 1b realistic? Why or why not? What can interfere with the future number of union workers that the equation does not account for?

Problem #2: According to the U.S. Bureau of Labor Statistics, in 1990, 529,000 people worked in the air transportation industry. In 2018, the number was 498,780.

  1. Find a linear equation giving the number of employees in the air transportation industry in terms of x, the number of years since 1990.
  2. Assuming the equation remains valid in the future, in what year will there be 400,000 employees in the air transportation industry?
  3. Is the number you came up with in 2b realistic? Why or why not? What can interfere with the future number of employees working in the air transportation industry that the equation does not account for?

Problem #3: The U.S. Bureau of Labor Statistics estimated that in 1990, 1.1 million people worked in the truck transportation industry. In 2018, the number was 1.5 million.

  1. Find a linear equation giving the number of employees in the truck transportation industry in terms of x, the number of years since 1990.
  2. Assuming the equation remains valid in the future, in what year will there be 2.5 million employees in the truck transportation industry?
  3. Is the number you came up with in 3b realistic? Why or why not? What can interfere with the future number of employees working in the trucking industry that the equation does not account for?

Source: U.S. Bureau of Labor Statistics. Occupational employment statistics. Retrieved from https://www.bls.gov/oes/current/naics4_484000.htm#00-0000.

Assignment Expectations
  • Critical Thinking: Expresses quantitative analysis of data to support the discussion showing what evidence is used and how it is contextualized.
  • Interpretation: explains information presented in mathematical terms (e.g., equations, graphs, diagrams, tables, and/or words).
  • Presentation: Able to convert relevant information into various mathematical terms (e.g., equations, graphs, diagrams, tables, and/or words).
  • Conclusions: Draws appropriate conclusions based on the analysis of factual information/data.
  • Timeliness: Submits assignment on time or with professor’s pre-approved assignment extension.

Module 4 – Background


Required Materials

Morgan, J. (2016). People analytics: A new way to make decisions in the workplace. Retrieved from  https://www.youtube.com/watch?v=EZqKsOoA8tw.  Standard YouTube license.

KnowledgeAtWharton. (2015). What’s behind the surge of interest in people analytics? Retrieved from  https://www.youtube.com/watch?v=9Xyd2gnQaP8

HR Metrics

More and more organizations are collecting data about employees and analyzing the data in an effort to make better employee-related decisions.

HR metrics and the use of balanced scorecards and other performance measurement systems provide the decision-making capacity to influence business strategy, which in turn transforms HR into strategic partners with the business.

The Society for Human Resource Management (SHRM) has identified key human capital measurements that are critical to evaluating HR performance:

Revenue Factor:

Revenue/Total Full-Time Employees

Human Capital Value Added:

(Revenue – Operating Expense – Compensation & Benefit Cost)/Compensation & Benefit Cost

Total Compensation Revenue Ratio:

Compensation & Benefit Cost/Revenue

Labor Cost Revenue Ratio:

(Compensation & Benefit Cost + Other Personnel Cost)/Revenue

Training Investment Factor:

Total Training Cost/Headcount

Cost per Hire:

(Advertising + Agency Fees + Recruiter’s Salary/Benefits + Relocation + Other Expenses)/ Operating Expenses

Health Care Costs per Employee:

Total Health Care Costs/Total Employees

Turnover Costs:

Termination Costs + Hiring Costs + Training Costs + Other Costs

These measurements then can be compared to the same organization’s past performance as well as to the performance of other companies.

HR professionals sometimes also track:

  • How satisfied are employees with their jobs?
  • How satisfied are employees with their supervisors?
  • What is the time to fill job openings (the period from job requisition approval to new-hire start date)?
  • What is the length of employment (by job title, department; from employment start date to employment end date)?
  • What is the number of days the positions were vacant (vacant period)?
  • What is the new-hire performance level (average performance appraisal of new hires, compared to previous period)?
  • What is the manager satisfaction level (survey of hiring managers, compared to previous period)?
  • What is the turnover rate of new hires (during a specified period)?
  • What is the financial impact of bad hires (comparing turnover cost and cost per hire)?
  • What is the preventable turnover (the reasons the employee left and what measures may be taken to prevent it)?
  • What Is the diversity turnover (turnover rate in professional, managerial, and technical positions)?
  • Learning and Growing Opportunities (percentage of employees who are satisfied with the learning and growth opportunities in the organization).
  • On-the job learning (percentage of employees who are satisfied with on-the-job learning, projects assignments for growth, and development and job rotation).

The above metrics will help managers make better decisions concerning:

  • Types of training, for which segments of the workforce will yield the best results.
  • Actions to take to help reduce absenteeism.
  • Actions to take to reduce turnover and what retention efforts to implement.
  • Optimal mix of reward programs to boost employee engagement to help drive stronger financial performance.
  • Opportunities for New Hires (percentage of employees who report training opportunities among the top three reasons they accepted the job).

Source for the above: Suman, B. Metrics for human resource management. (2011). Education, Business, Technology. Slideshare.net presentation.

PeopleMatttersOnline. (2016). Top trends in HR analytics. Retrieved from  https://www.youtube.com/watch?v=NV9GIB5JwDM.

Firing Line with Bill Kutik. (2016). Top analyst Holger Mueller predicts the future of predictive analytics for HR. Retrieved from  https://www.insidehr.com.au/what-percentage-people-create-most-value/

Required Reading

Brockbank, W. (2017). What percentage of your people create 90 percent of the value? Inside HR. Retrieved from  https://www.insidehr.com.au/what-percentage-people-create-most-value/

Lawler, E. E. (2017). Reinventing talent management: principles and practices for the new world of work. Retrieved from ProQuest, Ebook Central in the Trident Online Library.

Ward, D. (2017). Big data helps workers thrive: A Q & A with Jenny Dearborn. HR Magazine. Retrieved from  https://www.shrm.org/hr-today/news/hr-magazine/1117/Pages/big-data-helps-workers-thrive-jenny-dearborn.aspx

Optional Reading

Albrecht, C., Gardner, T., Allred, S., Winn, B., & Condie, A. (2016). To sit at the table, you have to know the language: Important financial metrics for HR directors. Strategic HR Review, 15(3), 123-128. Retrieved from ProQuest in the Trident online library.

Du Plessis, A.,J., & Fourie, L. D. W. (2016). Big data and HRIS used by HR practitioners: empirical evidence from a longitudinal study. Journal of Global Business and Technology, 12(2), 44-55. Retrieved from ProQuest in the Trident Online Library.

Feffer, M. (2014). HR moves toward wider use of predictive analytics. Retrieved from  https://www.shrm.org/ResourcesAndTools/hr-topics/technology/Pages/More-HR-Pros-Using-Predictive-Analytics.aspx

hiQ People Analytics Podcast (2016). Retrieved from  https://player.fm/series/hiq-people-analytics-podcast

HR Happy Hour (2017). We’re Only Human 13–Calculating the ROI of Human Resources. Podcast retrieved from  https://player.fm/series/hr-happy-hour/were-only-human-13-calculating-the-roi-of-human-resources  (also visit  https://www.h3hrhappyhour.net/  and/or  https://player.fm/podcasts/Human-Resources  for other topics related to HR)


If you have an interest in learning more about Human Resource Information Systems (HRIS) please review the following optional materials:

Anitha, J., & Aruna, M. (2013). Adoption of Human Resource Information System in Organizations. SDMIMD Journal Of Management, 4(2), 5-15. Retrieved from EBSCO in the Trident online library.

Gregg Learning. (2016). Introduction to HRIS. Retrieved from  https://www.youtube.com/watch?v=GP9DKNtcDOs. 

PcC. (2017). What’s now and what’s next in human resources technology? Download from  https://www.pwc.com/us/en/hr-management/technology/global-hr-technology-survey.html.

Sabrina Jahan, S. (2014) Human Resources Information System (HRIS): A Theoretical Perspective. Journal of Human Resource and Sustainability Studies, 2, 33-39. Retrieved from the Trident online library.

Sadiq, U., Khan, A. F., Ikhlaq, K., & Mujtaba, B. G. (2012). The impact of information systems on the performance of human resources department. Journal of Business Studies Quarterly, 3(4), 77-91. Retrieved from ProQuest in the Trident Online Library.

WorldatWorkTV. (2015). Implementing a New HRIS System: Challenges and Benefits Retrieved from  https://www.youtube.com/watch?v=RxoUj6HiNbY.  Standard YouTube license.

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