Stem & Leaf Diagrams (CIE IGCSE Maths: Extended)

What is a stem-and-leaf diagram?

• A stem-and-leaf diagram is a simple but effective way of showing data
  • the raw data is still available as the numbers themselves create the diagram
• A stem-and-leaf diagram
  • puts data into order
  • puts data into classes (groups)
• A stem-and-leaf diagram makes patterns in the data easy to see
  • as the data is in order it is useful for finding the median and quartiles
• Stem-and-leaf diagrams are particularly useful for two-digit data but can be used for bigger numbers
  • two-digit data could be something like 26 but could also be 2.6
  • due to this, it is essential a stem-and-leaf diagram has a key

How do I draw a stem-and-leaf diagram?

• The digits from each value in the data are split into two – stems and leaves
  • e.g. the data value 26 would be split into a stem of 2 and a leaf of 6
• As in nature though, a stem can have more than one leaf, so the stems become our classes in our data
  • e.g. the stem of 2 becomes a class interval – covering values from 20 to 29
  • Any other values in the 20’s would join the same stem/class – so a stem of 2 could end up having two or more leaves
• To draw a stem-and-leaf diagram ...

STEP 1

Unless the data is in order, always draw a rough stem-and-leaf diagram first
Work through the data one value at a time, splitting each into a stem and a leaf
Lightly cross each data value out as you use it - this will help to ensure none are missed out
This gets the data into the right format, grouped into its stems, with the correct number of leaves

STEP 2

Draw a final diagram with the stems in (ascending) order
For each stem, rearrange the leaves into (ascending) order
Ensure your leaves are lined up in neat columns (so the size of each stem/class can be easily seen)

STEP 3

Add a key to your diagram to explain how the two digits have been split into stems and leaves
e.g. does 2|6 mean 26 or 2.6?  The key will let us know!

How do I find the median and quartiles from a stem-and-leaf diagram?

• For the median ...
  • Lightly cross out numbers from the beginning and end
    • i.e. - cross out the lowest number and the highest number
    • be careful with the highest number - it will be at the end of the last stem
  • Continue crossing out the next lowest/highest numbers until you meet in the middle
    • if two numbers remain in the middle, find the midpoint between them
    • if the midpoint isn't obvious then add them together and halve
• For the lower quartile ...
  • Find the median first
    • Repeat the process for the median but on the lower half of the data
      (up to but not including the median)
• For the upper quartile ...
  • Find the median first
    • Repeat the process for the median but on the upper half of the data
      (from but not including the median)
• Since the interquartile range is the difference between the lower and upper quartiles, it can be easily calculated
  • IQR = UQ - LQ
• A common mistake when finding the median and quartiles is to not put the number back into its original format and to only use the leaf
  • e.g. Median = 6 instead of Median = 26