Stem and Leaf Diagrams
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 twodigit data but can be used with threedigit 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
 Leaves would always be single digits
 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
 The first diagram should get the data into the right format
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‑andwhisker diagram (box plot)
 Outliers, once defined, can be easily identified and removed
What about backtoback 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/nonUK. Etc
 Note that the leaves on the lefthand 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 backtoback 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 boxandwhisker diagram
 Identify and remove outliers
 Compare data shown by stem and leaf diagrams (either separate or backtoback); 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
Worked Example
The following stem and leaf diagrams show the times taken by some children and adults to complete a level on a computer game.
2  3 represents a time of 23 seconds
(a)
Compare the times taken to complete the level between the children and the adults.
(b)
It is later discovered two of the adults’ times had been omitted from the diagram –times of 23 and 42 seconds.
Briefly explain whether adding these times would change the adults’ median time.
Briefly explain whether adding these times would change the adults’ median time.
(a)
Compare the times taken to complete the level between the children and the adults.
(b)
It is later discovered two of the adults’ times had been omitted from the diagram –times of 23 and 42 seconds.
Briefly explain whether adding these times would change the adults’ median time.
Briefly explain whether adding these times would change the adults’ median time.
Exam Tip
 Accuracy is important
 (Lightly) tick off values as you add them to a stem and leaf diagram
 Check you have the right number of data values in total on your diagram
 Other checks can include ensuring the median has the same number of values either side of it