Mean vs. Median in Training-Program Advertising
A GED graduate is comparing two medical-assistant training programs. Program X advertises an average starting salary of $38,000 and a 92% completion rate; its cohort had 25 students, and one graduate was hired at $70,000 by a specialty clinic. Program Y advertises a median starting salary of $34,500 and an 80% completion rate; its cohort had 120 students. Program X costs $9,800 and takes 9 months; Program Y costs $6,400 and takes 12 months. The graduate can borrow at 6% annual interest and wants to start earning within a year. Local job postings show most medical assistants start between $31,000 and $36,000. Program X's literature does not report median salary or the number of graduates who responded to the salary survey; Program Y reports that 85% of graduates responded. Which program's salary claim is more trustworthy, and which program is the better financial choice under her one-year constraint?
1. Explain why Program X's average salary is misleading. Use the cohort size and the $70,000 salary in your reasoning.
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Program X reports a mean, and a mean is sensitive to outliers. With only 25 students, one graduate at $70,000 can pull the average up substantially. For example, if the other 24 averaged about $36,700, the mean would be roughly (24 × 36,700 + 70,000) / 25 ≈ $38,000. That one salary is real but atypical; it does not describe what a typical graduate earns. The missing median and missing survey response rate make the $38,000 hard to interpret.
Program Y reports a median of $34,500, which is the middle graduate and is resistant to outliers. It also reports an 85% response rate, so the figure is based on most graduates. The local postings cluster at $31,000–$36,000, which is consistent with Y's median and makes X's $38,000 look inflated. Y's salary claim is more trustworthy, though a median still does not guarantee placement.
2. Calculate the difference in upfront tuition and the approximate interest cost if each loan is repaid one year after borrowing. Then recommend a program given the one-year start constraint.
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Upfront tuition: X = $9,800; Y = $6,400; difference = $3,400. Simple one-year interest at 6%: X = 9,800 × 0.06 = $588, total ≈ $10,388; Y = 6,400 × 0.06 = $384, total ≈ $6,784. X costs about $3,604 more in tuition plus interest for the first year.
But X finishes in 9 months, while Y takes 12. X gives three extra months of potential earnings and still meets the one-year start constraint with a buffer. At $34,500/year, three months gross is about $8,625-more than the $3,604 tuition gap, if she actually gets a job quickly. Y is cheaper and its salary figure is more credible, but it leaves no margin if the program runs long or job search takes time.
Judgment: Y is the lower-risk financial choice on cost and data quality; X can be better if she verifies placement rates and median salary and can start work promptly. The one-year constraint favors X's shorter timeline, but not enough to ignore X's weak salary evidence.
3. What additional information would you request from Program X before trusting its 92% completion and salary figures? Explain how each item changes the decision.
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Request from X: (1) median starting salary, not just mean; (2) salary-survey response rate and how non-responders were handled; (3) job placement rate within 6 months, defined clearly (full-time? in field?); (4) completion-rate definition and cohort size over several years, not one 25-student cohort; (5) total cost including supplies, exam fees, and retakes; (6) accreditation and loan-default or pass-rate data if available.
Each changes the decision. A median near $34,000 would erase X's advertised salary advantage. A low response rate would make even the median unreliable; a high placement rate could offset a lower salary. A 92% completion rate from one small cohort may not repeat. Total cost affects the loan comparison, and accreditation affects whether employers and certifications accept the training. If X cannot supply these, the safer choice is Y or delaying enrollment.