Dotplots & Stemplots

Constructing a Stemplot

• Step 1: Identify the range of the data to determine appropriate stems (e.g., the tens digits).
• Step 2: List the stems vertically in a column and draw a vertical line to their right.
• Step 3: For each data point, record the leaf (the next digit) in the row corresponding to its stem.
• Step 4: Reorder the leaves in each row so they are in ascending order from left to right.
• Step 5: Provide a key that defines the units for the stem and leaf.

Finding the Median

• Since the data in a stemplot is already ordered, the median can be found by counting into the middle of the total number of observations ($n$). If $n$ is odd, the median is the $(\frac{n+1}{2})^{th}$ value; if $n$ is even, it is the average of the two middle values.

Unlike histograms, which group data into bins and lose individual values, stemplots allow the user to see every specific number in the set while still perceiving the 'bins' created by the stems.

• Always check the Key: Examiners often use keys to change the scale (e.g., $1 | 2$ could mean $1.2$ or $1200$). Never assume the units are standard integers.

• Visualizing Shape: To determine the skew of a stemplot, mentally rotate the graph 90 degrees counter-clockwise. If the 'tail' of the leaves extends toward the higher numbers (bottom of the original plot), it is skewed to the right (positive skew).

• Median Calculation: When finding the median, always include the stem value. A common mistake is identifying the middle leaf (e.g., '6') but forgetting to attach it to its stem (e.g., '2'), resulting in an incorrect answer (6 instead of 26).