Constructing and reading stem plots
The key, ordered rows and individual leaves together preserve the recorded numerical data
- Key State a stem-and-leaf example with its value and units. Never assume the stem means tens
- Leaves Keep one final digit for every record, including repeated digits and zeroes
- Gaps Show interior empty stems so the numerical gaps remain visible
- Split rows Use the stated split convention. Here L holds 0–4 and H holds 5–9.
- Summaries Count individual leaves to locate the median; subtract smallest from largest for the range
Worked example
Construct an ordered stem plot for 2.4, 1.8, 3.1, 2.4, 4.0, 3.6, 1.5 and 4.0 cm
- \(\displaystyle 1\mid5\ 8\)Stem 1 contains the lengths 1.5 and 1.8 cm
- \(\displaystyle 2\mid4\ 4\)Keep two leaves for the repeated length 2.4 cm
- \(\displaystyle 3\mid1\ 6\)Place 3.1 before 3.6
- \(\displaystyle 4\mid0\ 0\)Both zero leaves represent measured values of 4.0 cm
- \(\displaystyle 2\mid4\text{ means }2.4\)Include centimetres in the key; count eight leaves
Common mistakes
Difficulty levels
Questions about this topic
Can a stem plot show continuous measurements?+
Yes, at their recorded precision. State the key and units so each leaf can be decoded
Why keep zero leaves?+
A zero is a real final digit. For example, 4 | 0 can mean 4.0 cm
Why keep an empty stem?+
It preserves a gap between occupied stems. An empty row is different from a zero leaf
What do L and H mean?+
In these split plots, L holds leaves 0–4 and H holds leaves 5–9. Other conventions must be explicitly stated
Can the stem have two digits?+
Yes. With a whole-number key, 12 | 8 means 128.
Can the median be absent from the plot?+
Yes. With an even number of observations, the average of the two middle values may not be recorded
Is a stem plot suitable for every data set?+
No. It suits manageable numerical data sets. Very large lists can become crowded; categories need a different display
Does it preserve the unrounded measurements?+
It preserves the recorded values only. Rounding before plotting can discard information
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 5: Statistics