targas-edu.de
DE ☾ A+

Mean, median and range

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

Five children need \(10, 15, 20, 10\) and \(25\) minutes to get to school. Three values describe such data: the mean (der Mittelwert), the median (der Median) and the range (die Spannweite).
📄 Open worksheet (PDF, German)

The video

In the video you see why an outlier (der Ausreißer) changes the mean a lot but the median hardly at all.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:24 The mean
  3. 0:53 The median
  4. 1:19 The range
  5. 1:38 The outlier
  6. 2:01 Careful, mistake!
  7. 2:22 Try it yourself

The most important points

Mean

Add all values, divide by the number of values: \((10 + 15 + 20 + 10 + 25) : 5 = 16\).

The mean is 16 minutes.
The mean is \(16\) minutes.

Median

First put in order, then take the value in the middle: \(10, 10, \mathbf{15}, 20, 25\). With an even number of values: the mean of the two middle values.

Median = 15; for 15 and 20: (15 + 20) : 2 = 17{,}5.
Median \(= 15\); for \(15\) and \(20\): \((15 + 20) : 2 = 17{,}5\).

Range and outlier

Range = largest value \(-\) smallest value \(= 25 - 10 = 15\). A very large value (outlier) changes the mean a lot, the median hardly.

Emil needs 95 minutes: mean 30, median 15.
Emil needs \(95\) minutes: mean \(30\), median \(15\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/4
The worksheet – Page 2
Page 2/4
The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Pocket money per week: \(5, 8, 4, 10, 8\) euros. Calculate a) the mean b) the median c) the range.

Show solution

a) \(35 : 5 = 7\) € b) in order \(4, 5, 8, 8, 10\): \(8\) € c) \(10 - 4 = 6\) €

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Mittelwert, Median und Spannweite (auch mit Ausreißer). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.