A University's 5.1% Salary Increase: Weighted Averages and Composition Effects
A university career office publishes: 'The average starting salary of our graduates rose from $52,000 in 2022 to $54,700 in 2024, an increase of 5.1% - more than double the increase in any single faculty.' The underlying table gives average starting salaries by faculty.
2022: Engineering $72,000; Business $56,000; Sciences $50,000; Arts $40,000. 2024: Engineering $74,232 (+3.1%); Business $57,344 (+2.4%); Sciences $51,400 (+2.8%); Arts $40,800 (+2.0%).
Shares of graduates: Engineering 18% → 22%; Business 24% → 24%; Sciences 24% → 24%; Arts 34% → 30%.
The survey response rate fell from 61% in 2022 to 44% in 2024, and response rates by faculty are not published. A prospective student's parent reads the 5.1% figure as evidence that every graduate is now doing better, and the career office is using it in recruitment material.
1. Reconcile the 5.1% overall increase with faculty increases of only 2.0–3.1%. Show the arithmetic.
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The overall figure is a weighted average, so it moves with both group averages and group shares.
2022: 0.18 × 72,000 + 0.24 × 56,000 + 0.24 × 50,000 + 0.34 × 40,000 = 12,960 + 13,440 + 12,000 + 13,600 = $52,000
2024: 0.22 × 74,232 + 0.24 × 57,344 + 0.24 × 51,400 + 0.30 × 40,800 = 16,331 + 13,763 + 12,336 + 12,240 = $54,670
Change = 2,670 ÷ 52,000 = 5.1%.
The decomposition: hold the 2022 shares constant and apply the 2024 salaries: 0.18 × 74,232 + 0.24 × 57,344 + 0.24 × 51,400 + 0.34 × 40,800 = 13,362 + 13,763 + 12,336 + 13,872 = $53,333, a rise of 2.6%.
So about 1,333 of the 2,670 increase - roughly half - comes from pay growth within faculties, and about 1,337 comes from the shift in mix: Engineering, the best-paid faculty, grew from 18% to 22%, while Arts, the lowest-paid, fell from 34% to 30%.
2. Is the parent's interpretation correct? What is the most defensible reading of the 5.1% figure?
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No. 'Every graduate is doing better' is a within-faculty claim, and the within-faculty numbers are the 2.0–3.1% figures.
Those increases are real and worth reporting, but they are about half the headline. The 5.1% largely describes a change in who graduated, not only a change in what graduates are paid: the university produced proportionally more engineers and fewer arts graduates. A graduate of the Arts faculty in 2024 earned 2.0% more than an Arts graduate in 2022 - nothing like 5.1%.
A second caveat: the figure is an average, not a median, and it covers respondents only. The response rate fell from 61% to 44%, and if employed graduates in high-paying roles are more likely to answer, the 2024 figure is biased upward. The shift toward Engineering may itself raise response propensity, so the direction of the bias is plausible but cannot be signed without per-faculty response rates.
Defensible wording: 'Reported average starting salaries rose 5.1%, of which about 2.6 points reflects pay growth within faculties and the remainder reflects a shift toward higher-paying disciplines.'
3. Which additional data would most change your confidence in the analysis, and which would not?
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What would change it: per-faculty response rates and per-faculty medians.
Response rates by faculty for both years would show whether the 2024 sample over-represents Engineering or high earners - the one gap that could overturn the decomposition, because it determines whether the observed mix shift is real or a sampling effect. Medians by faculty would show whether averages are being pulled by a thin tail of exceptional offers, which matters in cohorts of this size.
A third useful item is destination data by faculty (further study, unemployed, not seeking). A rising share entering postgraduate study removes low earners from the salary pool and inflates the average in exactly the same direction as the composition shift, so it could absorb part of the residual 2.5 points.
What would not change it: a larger total sample. The arithmetic of weighted averages is exact, so the composition effect is already quantified; more respondents reduce sampling noise but do not address the mix or the response bias. The open question is measurement, not sample size.