Ordered stem-and-leaf plots
Keep one leaf per observation and let the key determine its place value
- Use the key 4 | 6 can mean 46 or 4.6, depending on the key
- Order and repeat Order each row and keep every repeated leaf and zero
- Keep gaps Retain empty stems between the minimum and maximum
- Split when stated L holds 0–4 and H holds 5–9. Count leaves, not stem headings
- Check the result Decode all leaves, match the raw data and count the observations
Worked example
Construct an ordered stem plot for 24, 31, 27, 35, 22, 38, 31, 29 and 34 seconds
22 4 7 9
31 1 4 5 8
Key: 3 | 4 means 34 seconds
\[n=9\]
- \(\displaystyle 2\mid 2\ 4\ 7\ 9\)Stem 2 holds four values, in order
- \(\displaystyle 3\mid 1\ 1\ 4\ 5\ 8\)Stem 3 holds five values. Keep both observations of 31
- \(\displaystyle 3\mid4\text{ means }34\)Use seconds in the key. Four plus five leaves account for all nine observations
Common mistakes
Dropping repeated leaves
✕\(\displaystyle 5\mid1\ 5\ 9\)✓\(\displaystyle 5\mid1\ 5\ 5\ 9\)
For 51, 55, 55, 59, both copies of 55 need leavesIgnoring a tenths key
✕\(\displaystyle 4\mid6\text{ means }46\)✓\(\displaystyle 4\mid6\text{ means }4.6\)
These examples use the stated key 4 |0=4.0. Apply that key throughoutConfusing range with maximum
✕\(\displaystyle \text{range}=7.8\)✓\(\displaystyle 7.8-3.6=4.2\)
Range is largest minus smallest, with the original unitsDifficulty levels
introComplete selected rows for whole-number data
standardConstruct rows or recover counts and ordered values
challengeUse decimal or split stems and calculate a follow-on statistic or shape
examChoose a correct plot or read values from it
Questions about this topic
Why keep zero leaves?+
A zero is a real final digit, such as 40 or 4.0. Removing it removes an observation
Why keep empty stems?+
They show gaps without compressing the scale
Which way do single-plot leaves go?+
From smallest to largest as you move right from the stem
What do split stems mean?+
The same stem has low 0–4 and high 5–9 rows. The key still applies
Must I draw the entire plot?+
Draw a complete plot when asked. Practice may grade only explicitly named rows; use the full data to check your construction
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 9: Probability and statistics
In this chapter
Finite events, probability assignments and complementsDescribe and order probability values9B Venn diagrams and tables: Venn diagrams, two-way tables and set notation for two eventsComplete and use a two-way probability tableCompound events, the addition rule and mutual exclusivity9C Set notation: Event notation and shaded regionsFinite sets and set operationsBuild two-step sample spaces with and without replacementUse two-step probability treesExperimental probability from observed frequenciesDesign and interpret a probability simulationFind the mean and the median, and choose between themWork backwards from a mean or medianMode, bimodal and no-mode data, and the effect of an outlierConstruct an ordered stem plot from raw dataConstruct and read back-to-back stem-and-leaf plotsDescribe the shape of a distributionGroup numerical data into class intervalsConstruct a histogram from a frequency tableRead values from a histogramFind the range, the quartiles and the IQRProduce a five-number summary and construct a boxplotRead values and percentages from a boxplotCompare a numerical variable across groupsSurveys and statistical investigations