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3.5 Stem and Leaf Diagrams

GCSE Maths Foundation · Edexcel · Chapter 3: Graphs, tables and charts

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: drawing ordered stem and leaf diagrams and using them to find averages and range. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Draw an ordered stem and leaf diagram with a key
  • Read data values from a stem and leaf diagram, including decimals
  • Find the mode, median and range from a stem and leaf diagram
  • Compare two sets of data using a back-to-back stem and leaf diagram

Key words

  • Stem: The first digit (or digits) of each value, written once in a column.
  • Leaf: The last digit of each value, written in the row of its stem.
  • Key: Shows how to read the diagram, e.g. 3 | 4 means 34 seconds.
  • Ordered: The leaves in each row are written from smallest to largest.
  • Median: The middle value when the data is in order.
  • Range: Largest value − smallest value. It measures how spread out the data is.

Drawing a stem and leaf diagram

Split each value into a stem (tens) and a leaf (units). Write the stems in a column in order. Go through the data and put each leaf in its row. Then redraw with the leaves in order and add a key.

Worked example: times to solve a puzzle (seconds)

34 27 45 31 52 38 29 41 36 47 33 25 40 38
The values go from 25 to 52, so the stems are 2, 3, 4 and 5.
First draft (unordered), then put the leaves in each row in order.

Answer: see the ordered diagram on the right below, with its key

Key fact: Line the leaves up neatly in columns, and count them: there should be one leaf for every data value (here 14).

Finding the mode, median and range

Because the data is in order, you can count along the leaves. The median is the ((n + 1) ÷ 2)th value. The mode is the value that appears most often. The range is largest − smallest.

Worked example: using the ordered puzzle diagram

In order: 25, 27, 29, 31, 33, 34, 36, 38, 38, 40, 41, 45, 47, 52 (n = 14)
Median: (14 + 1) ÷ 2 = 7.5th value, halfway between the 7th (36) and 8th (38) = 37
Mode: 38 (it appears twice). Range: 52 − 25 = 27

Answer: median 37 s, mode 38 s, range 27 s

Key fact: Always write the value, not the leaf: the mode is 38, not 8.

Keys with decimals

The key tells you the place value. With the key 4 | 2 = 4.2 cm, the stem is the units and the leaf is the tenths.

Worked example: reading decimals

Smallest = 4.2 cm, largest = 7.5 cm. Range = 7.5 − 4.2 = 3.3 cm.
Mode: 6 | 6 appears three times, so 6.6 cm.
Median: 14 values, so halfway between the 7th (5.8) and 8th (6.1) = 5.95 cm.

Answer: range 3.3 cm, mode 6.6 cm, median 5.95 cm

Back-to-back stem and leaf diagrams

Two sets of data can share the stems. Leaves on the left are read from right to left, so the smallest leaf is still next to the stem.

Worked example: comparing two players

A: 16, 19, 21, 23, 25, 28, 30, 34, 37, 42. Median (25 + 28) ÷ 2 = 26.5, range 42 − 16 = 26
B: 24, 26, 29, 31, 33, 35, 35, 38, 40, 43. Median (33 + 35) ÷ 2 = 34, range 43 − 24 = 19

Answer: B scored more on average (median 34 > 26.5) and was more consistent (range 19 < 26)

Common mistakes

  • Forgetting the key, or leaving the leaves unordered.
  • Giving the leaf instead of the whole value, e.g. saying the mode is 8 instead of 38.
  • Finding the middle row of the diagram instead of the middle value.
  • Reading the left-hand side of a back-to-back diagram the wrong way round (it is 26, not 62).

Revision questions

Try these, then check your answers below each one.

Question 1. Here is a stem and leaf diagram.<br/>2 | 1 4 4 7<br/>3 | 0 2 5 5 5 8<br/>4 | 1 3 6<br/>5 | 0 2<br/>Key: 3 | 2 means 32<br/>How many values are shown?

Answer: 15

Working: 4 + 6 + 3 + 2 = 15 values.

Question 2. Here is a stem and leaf diagram.<br/>2 | 1 4 4 7<br/>3 | 0 2 5 5 5 8<br/>4 | 1 3 6<br/>5 | 0 2<br/>Key: 3 | 2 means 32<br/>What is the mode?

Answer: 35

Working: 35 appears three times.

Question 3. Here is a stem and leaf diagram.<br/>2 | 1 4 4 7<br/>3 | 0 2 5 5 5 8<br/>4 | 1 3 6<br/>5 | 0 2<br/>Key: 3 | 2 means 32<br/>What is the range?

Answer: 31

Working: 52 - 21 = 31.

Related lessons

Continue in the full course

This lesson is section 3.5 (EGCMF0305) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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