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Quartiles and box plot

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

Eight children write a test. With the quartiles (die Quartile) and the box plot (der Boxplot) you see how the points are spread out.
📄 Open worksheet (PDF, German)

The video

In the video the box plot is drawn from five numbers: box, median line and two lines.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:18 The quartiles
  3. 0:50 The box plot
  4. 1:22 Reading box plots
  5. 1:51 Careful, mistake!
  6. 2:12 Try it yourself

The most important points

Quartiles

The median splits the ordered values \(4, 5, 5, 6, 7, 9, 9, 12\) into two halves. Median: \(6{,}5\). Lower quartile \(Q_1 = 5\), upper quartile \(Q_3 = 9\).

The median of each half is a quartile.
The median of each half is a quartile.

The box plot

Five numbers: smallest value, \(Q_1\), median, \(Q_3\), largest value. The box goes from \(Q_1\) to \(Q_3\), a line shows the median.

Box plot of the test points.
Box plot of the test points.
Each section has 25\,\% of the values. Interquartile range 9 - 5 = 4, range 12 - 4 = 8.
Each section has \(25\,\%\) of the values. Interquartile range \(9 - 5 = 4\), range \(12 - 4 = 8\).

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

Books read: \(3, 4, 4, 5, 6, 8, 8, 9\). Find the five numbers for the box plot.

Show solution

smallest value \(3\), \(Q_1 = 4\), median \(5{,}5\), \(Q_3 = 8\), largest value \(9\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Quartile und Boxplot (fünf Zahlen, Quartilsabstand, Boxplot lesen). 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.