Stem & Leaf Diagrams | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What is a stem-and-leaf diagram?

• A stem-and-leaf diagram is a straightforward and efficient method of displaying data. 
  • The raw data remains accessible as the actual numbers construct the diagram.
• The diagram organizes data in order and into classes (groups).
• It facilitates the recognition of patterns within the data due to its ordered nature, making it useful for identifying the median and quartiles.
• Stem-and-leaf diagrams are especially beneficial for two-digit data but can be applied to larger numbers as well. 
  • For instance, two-digit data could represent numbers like 26 or 2.6. 
  • Therefore, a key is essential for interpreting a stem-and-leaf diagram correctly.

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

• The concept of stem-and-leaf diagrams involves splitting the digits from each value in the data into stems and leaves. 
  • For instance, a data value like 26 would be divided into a stem of 2 and a leaf of 6.
• In this representation, a stem can consist of more than one leaf, turning the stems into classes in our dataset. 
  • For example, the stem of 2 would form a class interval spanning values from 20 to 29. 
  • Any other values in the 20s would also belong to this stem/class, potentially resulting in a stem of 2 with multiple leaves.
• To create a stem-and-leaf diagram, follow these steps:
  • Step 1: If the data is not already in order, begin by sketching a rough stem-and-leaf diagram. Progress through each value in the data, breaking it down into a stem and a leaf. Mark off each data point as you utilize it to ensure none are overlooked. This process helps format the data correctly, grouping it into its respective stems with the appropriate 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. For example, does 2|6 mean 26 or 2.6? The key will provide clarity.

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

• For the median:
  • Begin by lightly eliminating the lowest and highest numbers. Be cautious with the highest number, which might be at the end of the dataset.
  • Continue eliminating the next lowest/highest numbers until you reach the middle. If two numbers are left, determine their midpoint. If unclear, add them together and divide by two.
• For the lower quartile:
  • First, find the median. Then, repeat the process similar to finding the median but on the lower half of the data, up to but excluding the median.
• For the upper quartile:
  • Start by finding the median. Then, repeat the process akin to finding the median but on the upper half of the data, from but excluding the median.
• Interquartile range (IQR) calculation:
  • Simply subtract the Lower Quartile (LQ) from the Upper Quartile (UQ): IQR = UQ - LQ
• Common mistake to avoid:
  • Ensure to put the number back into its original format when finding the median and quartiles. Do not solely rely on the leaf of the stem.
  • For Example, Median = 6 instead of Median = 26