A university-wide salary figure may look like something you can reconstruct from the medians reported for its courses. Even if every course supplies its graduate count, that reconstruction generally does not work. Group medians summarize the middle of separate distributions; they do not preserve the order of all the salaries needed to find the middle of the combined distribution.

Establish what the reported median describes

The notes to the official 2024 SMU Graduate Employment Survey publication define the salary median in relation to full-time permanently employed graduates. Retain that population when reading its results. Do not substitute total annual awards, the entire graduating class or an enrollment headcount as weights for a salary statistic.

The experiments below are CollegeVerse's own arithmetic. They use invented individual monthly salaries in one fictional currency and make no claim about actual SMU graduates, courses or university-wide pay. For an even number of observations, each illustrative median is calculated as the average of the two middle observations.

First experiment: two course summaries

Imagine two disjoint course groups with complete observations for this exercise:

Group Ordered salaries in experiment 1 Number Median
A 3,000; 4,000; 9,000 3 4,000
B 3,500; 4,500; 5,000; 5,500; 6,000 5 5,000

The eight combined observations in order are 3,000; 3,500; 4,000; 4,500; 5,000; 5,500; 6,000; 9,000. The two central values are 4,500 and 5,000, giving a combined median of 4,750.

A simple average of the course medians gives 4,500. Weighting the two medians by three and five gives 4,625: the sum of 12,000 and 25,000 divided by eight. Neither reproduces the combined median, even though the group sizes and medians are correct.

Second experiment: preserve the summaries, change the distribution

Now keep exactly the same number of observations and the same median in each group, but change the salaries away from the group centers:

Group Ordered salaries in experiment 2 Number Median
A 3,900; 4,000; 4,100 3 4,000
B 1,000; 2,000; 5,000; 5,100; 5,200 5 5,000

The combined order is now 1,000; 2,000; 3,900; 4,000; 4,100; 5,000; 5,100; 5,200. Its median is 4,050, the midpoint of 4,000 and 4,100.

The published-looking summaries would be identical in the two experiments: group sizes of three and five, with medians of 4,000 and 5,000. Yet the combined medians differ by 700. That counterexample demonstrates why the summaries do not determine a unique pooled median. Adding more decimal places to a weighted average cannot recover information those summaries omit.

Means require a different calculation and different evidence

An arithmetic mean can be combined from group means using the correct observation counts when groups are disjoint, definitions align and coverage is complete. That property belongs to means, not medians. It also fails as a practical reconstruction when the supposed weights describe a different population or some groups are missing.

Do not respond by seeking private graduate salary records. For ordinary course research, use a pooled measure published by the responsible source, retain the separate course medians, or state that the combined measure is unavailable. Confidentiality and the source's release rules remain relevant; a missing combined figure is not an invitation to reconstruct protected observations.

Keep the comparison at the level the evidence supports

Record the course, survey year, salary definition, employment population and any published coverage caveat. If your decision concerns one course, its appropriately defined result may be more relevant than an improvised university-wide number. Read the salary-distribution guide for the separate question of what one median leaves out.

A supported conclusion might be: “These are the medians for these course populations; a pooled university median cannot be calculated from the supplied summaries.” That is a useful boundary on the analysis, not a reason to publish a misleading average.