Stem & Leaf Diagrams (Edexcel GCSE Statistics)

Stem & Leaf Diagrams

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 longer numbers

  • two-digit data could be something like 23 but could also be 2.3

  • 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 36 would be split into a stem of 3 and a leaf of 6

• A stem can have more than one leaf

  • So the stems become our classes in our data

    • e.g. the stem of 3 becomes a class interval – covering values from 30 to 39

    • Any other values in the 30s would join the same stem/class as additional leaves

To draw a stem-and-leaf diagram

• STEP 1
  Draw a rough version first

  • Always draw a rough stem-and-leaf diagram first

    • Though you can skip this step if the data is given to you in order

  • Work through the data one value at a time,

    • Split each value into a stem and a leaf

    • Lightly cross out each data value as you use it (to ensure none are missed out or used twice)

  • This gets the data into the correct basic form

    • grouped into its stems

    • with the correct number of leaves

• STEP 2
  Draw a final diagram

  • Put 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

  • The key should explain how the values have been split into stems and leaves

    • e.g. does 3|6 mean 36 or 3.6?  

    • 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

    • the highest number will be at the end of the last stem

  • Continue crossing out the next lowest/highest numbers until you meet in the middle

    • if one number remains in the middle, then it is the median

    • if two numbers remain find the midpoint between them

    • (if the midpoint isn't obvious then add them together and divide by 2)

• For the lower quartile ...

  • Find the median first

    • Repeat the process for the median but on the lower half of the data

    • (i.e. 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

    • (i.e. from but not including the median)

• The interquartile range is the difference between the lower and upper quartiles

  • IQR = UQ - LQ

• Remember to put the number back into its original format

  • i.e. don't only use the leaf

  • This is a common mistake when finding the median and quartiles

    • e.g. writing Median = 6 instead of Median = 36

What else can I do with a stem-and-leaf diagram?

• Many things are easy to see in a stem-and-leaf diagram

  • The data is arranged into classes so it is easy to see the modal class

    • i.e. the stem with the greatest number of leaves

  • The data is arranged in order, so the maximum and minimum can be identified easily

    • This can be used to find the range (maximum value - minimum value)

  • Outliers can be easily identified (and removed if necessary)

• You can compare data sets

  • Remember to comment on a measure of central tendency ('average')

    • (use the median)

  • and a measure of dispersion ('spread')

    • (use the interquartile range)

• A box plot ('box and whisker diagram') can be drawn for the data

  • For this you need the median, upper and lower quartiles, and maximum and minimum values

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

• These are used when it is helpful for the data to be split into two comparable categories

  • e.g. boy/girl, child/adult, UK/non-UK, etc.

• This makes it easier to compare two data sets

  • i.e. instead of having two separate stem-and-leaf diagrams

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

  • i.e. from the centre to the left

• In all other respects back-to-back stem and leaf diagrams are the same as regular stem and leaf diagrams