The idea

Stem-and-leaf diagrams (including back-to-back)

A stem-and-leaf diagram keeps every value and shows the shape of the data at once. How to draw an ordered diagram with a key, how to read the mode, median and range (and the quartiles) by counting leaves, and how to compare two groups on a back-to-back diagram with an average and a spread, in context.

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Statistics · Data representation

Stem-and-leaf diagrams (including back-to-back)

Why it works

Every value kept, and the shape on view

Mia works in a café. She times how long, in seconds,

19

customers wait for their coffee:

46

35

62

28

41

50

35

24

57

39

43

30

68

35

48

27

54

32

46

What is a typical wait? Are most waits short? The list hides the answers. A stem-and-leaf diagram sorts the numbers into rows, so you see their shape, and it keeps every number, so none is lost. Each number splits in two. For

46

, the stem is the tens digit,

4

, and the leaf is the units digit,

6

4 \mid 6 \;\text{ represents }\; 46 \text{ seconds}

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