Median vs. mean (Median vs. Durchschnitt)
The median is the middle value once a list of numbers is sorted; the mean (average, Durchschnitt) is the sum divided by the count. Half of all values sit above the median and half below it, no matter how extreme the highest or lowest entries are. The mean has no such floor — one very large number pulls it upward, which is why it often overstates the "typical" case.
Why it matters
German salary, rent, and wealth statistics get quoted everywhere — job postings, city-comparison articles, news coverage of inequality. A mean moves whenever any single value moves, including a handful of directors, landlords, or heirs with unusually high numbers. A median barely reacts to the same outliers, because adding one more high earner to the list doesn't change which value sits in the middle.
For salary comparisons, rent per square meter (Miete pro Quadratmeter), and net wealth (Nettovermögen), the median usually describes the typical household more closely than the mean does. Reading only the mean can leave someone thinking their own salary or rent is below par when it's actually close to normal — the mean was just pulled up by a small group of very high values.
Worked example
Five coworkers' monthly net salaries: €2,200, €2,300, €2,400, €2,500, and €9,800 (one senior manager). Sorted, the middle value — the median — is €2,400. The mean is (2,200 + 2,300 + 2,400 + 2,500 + 9,800) / 5 = €3,840. Four of the five people earn less than the mean; only the median reflects what a "typical" coworker actually takes home. Someone earning €2,450 might read "average salary: €3,840" and wrongly conclude they're underpaid, when they're actually earning slightly above the middle of this group.
Rent listings in a neighborhood (illustrative numbers): eight apartments list for €10, €11, €11, €12, €12, €13, €14, and €40 per square meter — the last one a renovated penthouse. The mean is 123 / 8 ≈ €15.4/m². The median (the average of the two middle values, €12 and €12) is €12/m². Someone comparing a €12.50/m² apartment to the mean would conclude it's a bargain; comparing it to the median shows it's close to what most listings actually charge.
A real-world version of the same gap: German full-time employees had a median gross annual salary of €52,159 in 2024, while the mean gross annual salary was €62,235 — a roughly €10,000 gap the Statistisches Bundesamt (Destatis, Federal Statistical Office) attributes to particularly high earners pulling the average upward (2024) [1]. Whether a given salary is "typical for the country" is a question the median answers; the mean answers a different question — what everyone would earn if total pay were split evenly.
Check yourself
Five coworkers earn these monthly net salaries: €2,200, €2,300, €2,400, €2,500, and €9,800. What is the median salary, in euros?
Using the same five salaries (€2,200, €2,300, €2,400, €2,500, €9,800), what is the mean (average) salary, in euros?
A city's salary report leads with the mean salary. One very high-earning outlier is skewing that number upward. Which statistic better answers 'is my salary typical for this city?'
Which of these three datasets is LEAST likely to show a large gap between its mean and its median?
Sources
- Statistisches Bundesamt (Destatis) — 1 % der Vollzeitbeschäftigten verdiente im Jahr 2024 mehr als 213 286 Euro brutto (median and mean gross annual earnings, full-time employees, 2024), https://www.destatis.de/DE/Presse/Pressemitteilungen/2025/04/PD25_134_621.html (2025)