Stem & Leaf Diagrams (Edexcel GCSE Statistics)
Revision Note
Written by: Roger B
Reviewed by: Dan Finlay
Stem & Leaf Diagrams
What is a stem-and-leaf diagram?
A stem-and-leaf diagram is a simple but effective way of showing data
the raw data is still available as the numbers themselves create the diagram
A stem-and-leaf diagram
puts data into order
puts data into classes (groups)
A stem-and-leaf diagram makes patterns in the data easy to see
as the data is in order it is useful for finding the median and quartiles
Stem-and-leaf diagrams are particularly useful for two-digit data but can be used for longer numbers
two-digit data could be something like 23 but could also be 2.3
due to this, it is essential a stem-and-leaf diagram has a key
How do I draw a stem-and-leaf diagram?
The digits from each value in the data are split into two – stems and leaves
e.g. the data value 36 would be split into a stem of 3 and a leaf of 6
A stem can have more than one leaf
So the stems become our classes in our data
e.g. the stem of 3 becomes a class interval – covering values from 30 to 39
Any other values in the 30s would join the same stem/class as additional leaves
To draw a stem-and-leaf diagram
STEP 1
Draw a rough version firstAlways draw a rough stem-and-leaf diagram first
Though you can skip this step if the data is given to you in order
Work through the data one value at a time,
Split each value into a stem and a leaf
Lightly cross out each data value as you use it (to ensure none are missed out or used twice)
This gets the data into the correct basic form
grouped into its stems
with the correct number of leaves
STEP 2
Draw a final diagramPut the stems in ascending order
For each stem, rearrange the leaves into ascending order
Ensure your leaves are lined up in neat columns
so the size of each stem/class can be easily seen
STEP 3
Add a key to your diagramThe key should explain how the values have been split into stems and leaves
e.g. does 3|6 mean 36 or 3.6?
The key will let us know!
How do I find the median and quartiles from a stem-and-leaf diagram?
For the median ...
Lightly cross out numbers from the beginning and end
i.e. cross out the lowest number and the highest number
the highest number will be at the end of the last stem
Continue crossing out the next lowest/highest numbers until you meet in the middle
if one number remains in the middle, then it is the median
if two numbers remain find the midpoint between them
(if the midpoint isn't obvious then add them together and divide by 2)
For the lower quartile ...
Find the median first
Repeat the process for the median but on the lower half of the data
(i.e. up to but not including the median)
For the upper quartile ...
Find the median first
Repeat the process for the median but on the upper half of the data
(i.e. from but not including the median)
The interquartile range is the difference between the lower and upper quartiles
IQR = UQ - LQ
Remember to put the number back into its original format
i.e. don't only use the leaf
This is a common mistake when finding the median and quartiles
e.g. writing Median = 6 instead of Median = 36
What else can I do with a stem-and-leaf diagram?
Many things are easy to see in a stem-and-leaf diagram
The data is arranged into classes so it is easy to see the modal class
i.e. the stem with the greatest number of leaves
The data is arranged in order, so the maximum and minimum can be identified easily
This can be used to find the range (maximum value - minimum value)
Outliers can be easily identified (and removed if necessary)
You can compare data sets
Remember to comment on a measure of central tendency ('average')
(use the median)
and a measure of dispersion ('spread')
(use the interquartile range)
A box plot ('box and whisker diagram') can be drawn for the data
For this you need the median, upper and lower quartiles, and maximum and minimum values
What are back-to-back stem-and-leaf diagrams?
These are used when it is helpful for the data to be split into two comparable categories
e.g. boy/girl, child/adult, UK/non-UK, etc.
This makes it easier to compare two data sets
i.e. instead of having two separate stem-and-leaf diagrams
Note that the leaves on the left-hand side of the stems (Boys) increase from the centre outwards
i.e. from the centre to the left
In all other respects back-to-back stem and leaf diagrams are the same as regular stem and leaf diagrams
Examiner Tips and Tricks
Accuracy is important
(Lightly) tick off values as you add them to a stem-and-leaf diagram
Check you have the right number of data values in total on your diagram
Other checks can include ensuring the median has the same number of values above and below it
Worked Example
A hospital is investigating a new drug that claims to reduce blood pressure. They give a set of patients the new drug and three hours later record the amount the blood pressure of every patient has decreased by. The results, measured in mmHG (millimetres of mercury), are given below.
12 31 24 18 21 34 40 19 23 17 16
(a) Draw a stem-and-leaf diagram to show these results.
The data is not in order so the first step is to draw a rough diagram
All values are two digit, so split each so that the first (tens) digit is a stem and the second (units) digit is a leaf
| Blood pressure reduction | ||||
1 | 2 | 8 | 9 | 7 | 6 |
3 | 1 | 4 |
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2 | 4 | 1 | 3 |
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4 | 0 |
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For the final diagram put stems and leaves in order and add a key
| Blood pressure reduction | ||||
1 | 2 | 6 | 7 | 8 | 9 |
2 | 1 | 3 | 4 |
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3 | 1 | 4 |
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4 | 0 |
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Key: 1|2 means a blood pressure reduction of 12 mmHG
(b) Use your stem-and-leaf diagram to find the median blood pressure reduction and the interquartile range.
For the median cross off highest and lowest numbers until we meet in the middle
| Blood pressure reduction | ||||
1 |
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2 | 1 |
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3 |
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4 |
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The median is a leaf of 1 in the stem of 2
Median = 21
Repeat for the lower half and upper half of the data to find the lower and upper quartile
| Blood pressure reduction | ||||
1 |
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| 7 |
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2 | 1 |
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3 | 1 |
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4 |
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The LQ is a leaf of 7 in the stem of 1; LQ = 17
The UQ is a leaf of 1 in the stem of 3; UQ = 31
The question asks for the interquartile range
IQR = UQ - LQ = 31 - 17 = 14
Don't forget units in the final answer!
Median = 21 mmHG
Interquartile range = 14 mmHG
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