Stem and Leaf Diagrams (CIE A Level Maths: Probability & Statistics 1)

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