Step 1: Identify Stems and Leaves: Determine the appropriate place value for the stem based on the range of the data. For example, if data ranges from 105 to 150, the stems might be 10, 11, 12, 13, 14, and 15.
Step 2: Create an Unordered Diagram: Work through the raw data list and place each leaf next to its stem as it appears. This ensures no data points are missed during the initial sorting process.
Step 3: Create the Ordered Diagram: Rewrite the diagram, sorting the leaves in each row from smallest to largest. Ensure that the spacing between leaves is consistent so the visual 'bar' length accurately reflects the frequency.
Step 4: Add the Key and Totals: Provide a key to define the scale and, optionally, add the count of leaves in brackets at the end of each row to assist in finding the median position.
Purpose: These are used to compare two related datasets, such as test scores for two different classes or heights of two different species, using a single shared stem column.
Structure: The shared stems are placed in the center. One dataset's leaves extend to the right, while the other's extend to the left.
Ordering Rule: For the left-hand side, the leaves must increase in value as they move away from the center stem. This means the smallest values are closest to the vertical line, maintaining a mirror-image logic with the right-hand side.
| Feature | Stem & Leaf Diagram | Histogram |
|---|---|---|
| Data Type | Discrete or rounded continuous | Continuous grouped data |
| Raw Data | Fully visible and preserved | Hidden within frequency bars |
| Sample Size | Best for small to medium sets | Best for very large datasets |
| Ease of Use | Easy to find median/quartiles | Requires interpolation for estimates |
The 'Key' Requirement: Always check if a key is present; omitting the key is a frequent cause of lost marks even if the diagram is perfectly drawn. The key must include units if the data represents a physical measurement.
Median Calculation: To find the median of items, locate the position. Count through the ordered leaves from the smallest value until you reach that position.
Accuracy Check: Always count the total number of leaves in your final diagram to ensure it matches the number of data points in the original list. It is very easy to skip a number when transferring data.
Outlier Identification: Look for leaves that are significantly separated from the main body of data. These gaps are much easier to spot in a stem and leaf diagram than in a raw list.
