What is a stem and leaf diagram?

• A?stem?and?leaf?diagram shows?ALL?RAW?data and groups it into?class?intervals
• Stem and leaf diagrams lend themselves to two-digit data but can be used with three-digit data, rarely more

• The numbers in?brackets?indicate how many values are in that class interval
  • These are not always included but can be useful when there is a large amount of data to display

How do I draw a stem and leaf diagram?

• Identify the?stems?and the?leaves
  • Leaves?would always be?single?digits
    • the number?2?would be represented by?12 | 2
• If starting from?unordered?data draw?two?diagrams
  • The?first?diagram should get the data into the right?format
    • • i.e.? ? ?a list of stems with their corresponding leaves
  • The?second?diagram should have stems and leaves in?order, with a?key
  • This helps?accuracy?as values are less likely to be missed out

What are stem and leaf diagrams used for?

• The data is arranged into?classes?so at a glance it is possible to see the?modal?class?interval
• As the data is in order the?median,?quartiles,?maximum?and?minimum?can be identified easily
  • Check you can do this – find the minimum, maximum, median and upper and lower quartiles from the stem and leaf diagram at the start of this revision note
  • Note that these five values are those needed in order to construct a?box?and-whisker?diagram?(box plot)
• Outliers, once defined, can be easily identified and removed

What about back-to-back stem and leaf diagrams?

• These are used when it is helpful for the data to be split into two comparable categories such as boy/girl, child/adult, UK/non-UK. Etc

• Note that the leaves on the left-hand side of the stems (Boys) increase from the centre outwards

Are there any variations on stem and leaf diagrams?

• There are a few minor variations on stem and leaf diagrams that you may see online or in different textbooks

• Some or all the different/extra features in the diagram above may appear
• These differences can be applied to back-to-back stem and leaf diagrams
• With large amounts of data, the stems may be split into?two?rows
  • Every stem will be listed?twice
  • The?first?row for a?stem?will contain?leaves?0 - 4
  • The?second?row will contain?leaves 5 - 9

What might I be asked to do with a stem and leaf diagram?

• You may be asked to?draw?or?complete?a stem and leaf diagram
• Find?statistical?measures?–?median,?quartiles?and interquartile range in particular
  • From which you may be required to draw a?box-and-whisker?diagram
• Identify and remove?outliers
• Compare?data shown by stem and leaf diagrams (either separate or back-to-back); comment on two things and each should be in both terms of the maths and the context of the question
  • a comment about?average?(use median)

e.g. the girls’?median?of 88% was higher than the boys’ median of 65% so on average the girls performed better on the test

• • a comment about?variation?(spread) (use interquartile range)

e.g. the girls’?interquartile?range?of 30% was greater than the boys’ 15% so the boys had more consistent scores on the test

• Analyse?what would happen to statistical measures such as the median and quartiles if a?value?changed?or a?new?value?were to be added to the data