Read before calculating: use the key, list every observation and check the number of leaves against the number of data values.
- Translate each stem and leaf into the original data value.
- Construct an ordered plot that retains zeros and repeated observations.
- Find simple summaries from an ordered plot.
The idea
A stem-and-leaf plot keeps each original data value visible. The key tells you how a stem and leaf combine. With the key 1 | 2 = 12, the stem represents tens and each leaf represents ones. Put leaves in ascending order and write one leaf for every observation, including repeated values.
Before you begin: Read place value, order numbers and find the middle of an ordered list.
Worked examples
01 Start with the method
Use the key 1 | 2 = 12. Read the data and find its median.
Use the key to reconstruct each observation. Both 5 leaves in the first row must be retained.
There are six observations. The median is halfway between the third and fourth values of this ordered list.
The median need not be an observed value. Here it lies between the two middle observations.
A mistake to avoid
A leaf is not a frequency. Two leaves labelled 5 mean two observations ending in 5. Always read the key before interpreting any row.
02Find the mode and range
Use the key 4 | 1 = 41. Find the mode, range and median.
Read each leaf as a separate observation. The list contains four values.
The repeated value is the mode. Subtract the smallest observation from the largest to obtain the range.
For four values, average the second and third values to find the median.
03Keep zeros and repeated leaves
Construct a stem-and-leaf plot using tens as stems and ones as leaves.
Order the values so each row’s leaves will be written in ascending order.
Separate tens from ones. Retain both 20s and the zero leaf for 40.
State the key and count the leaves. Six leaves match the six original observations.
Practice questions with answers
Work these out first, then open each solution to compare your method. These questions are untimed.
Question 1
Use the key 2 | 1 = 21. What is the largest observation?
Show solution 1
The last leaf on the highest stem is 3 | 5. The key says this represents 35, not 3.5.
Question 2
Use key 1 | 8 = 18. Find the smallest observation.
Show solution 2
The first leaf on the lowest stem gives 1 | 8 = 18.
Question 3
Use key 3 | 0 = 30. How many observations equal 30?
Show solution 3
Each zero leaf on stem 3 represents one observation of 30. There are two such leaves.
Question 4
Use key 1 | 2 = 12. How many observations are in the plot?
Show solution 4
Count leaves, including repeated zeros: two leaves in the first row and three in the second.
Question 5
Use key 1 | 1 = 11. Find the median.
Show solution 5
The ordered values are 11, 14, 18, 23, 24. The third of five observations is 18.
Common questions
Why is the key essential?
The same stem and leaf can represent different scales. For example, 3 | 4 could mean 34 or 3.4 depending on the key. Read the stated key rather than assuming.
Do I write a repeated observation more than once?
Yes. Each observation needs its own leaf. Omitting repeated leaves changes the number of observations and can change summaries such as the median and mode.
Can a leaf be zero?
Yes. With tens as stems, 2 | 0 represents 20. A zero leaf is an observation and must be counted.