Mittelwertrechner — Arithmetisches Mittel, Median & Modus berechnen
Berechnet den statistischen Durchschnitt, den zentralen Medianwert und den Modalwert aus beliebigen Zahlenreihen.
Formelherleitung & mathematische Grundlagen
Summiert alle Werte einer Stichprobe und teilt die Summe durch die Gesamtanzahl der Beobachtungen.
Variablendefinitionen & Maßeinheiten
Worked Statistical Summary Example
Consider a classroom quiz dataset containing 7 student scores: [12, 15, 15, 18, 20, 24, 36]:
When to Rely on Median Instead of Mean
While the arithmetic mean is the most common metric, it is vulnerable to distortion from extreme outliers. For instance, in national household income statistics, a tiny handful of billionaires drastically pulls the mean upward.
Economists utilize median household income rather than mean income because the median represents the true middle citizen, unaffected by extreme high or low tail events.
Häufig gestellte Fragen zu Mittelwertrechner (Mittelwert, Median, Modus)
What is the difference between Mean, Median, and Mode?
Mean is the mathematical average (sum divided by count). Median is the middle value when numbers are sorted in order. Mode is the number that appears most frequently in the dataset.
How do I calculate the median of an even number of data points?
When the count is even, take the arithmetic average of the two central numbers. For example, for [10, 20, 30, 40], the middle two numbers are 20 and 30, so the median is (20 + 30) ÷ 2 = 25.
Can a dataset have more than one mode?
Yes. If two values tie for the highest frequency, the dataset is bimodal. If three or more tie, it is multimodal. If no value repeats, there is no mode.
How is a weighted average calculated?
In a weighted average, each value is multiplied by its relative assigned weight (such as course credits in GPA). The products are summed and divided by the sum of all weights.
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