# Stem and Leaf Diagrams(Edexcel International A Level Maths: Statistics 1)

Author

Paul

Expertise

Maths

## Stem and Leaf Diagrams

#### What is a stem and leaf diagram?

• A stem and leaf diagram shows ALL RAW data and groups it into class intervals
• Stem and leaf diagrams lend themselves to two-digit data but can be used with three-digit data, rarely more

• The numbers in brackets indicate how many values are in that class interval
• These are not always included but can be useful when there is a large amount of data to display

#### How do I draw a stem and leaf diagram?

• Identify the stems and the leaves
• Leaves would always be single digits
• the number 2 would be represented by 12 | 2
• If starting from unordered data draw two diagrams
• The first diagram should get the data into the right format
• i.e.     a list of stems with their corresponding leaves
• The second diagram should have stems and leaves in order, with a key
• This helps accuracy as values are less likely to be missed out

#### What are stem and leaf diagrams used for?

• The data is arranged into classes so at a glance it is possible to see the modal class interval
• As the data is in order the median, quartiles, maximum and minimum can be identified easily
• Check you can do this – find the minimum, maximum, median and upper and lower quartiles from the stem and leaf diagram at the start of this revision note
• Note that these five values are those needed in order to construct a boxand-whisker diagram (box plot)
• Outliers, once defined, can be easily identified and removed

#### What about back-to-back stem and leaf diagrams?

• These are used when it is helpful for the data to be split into two comparable categories such as boy/girl, child/adult, UK/non-UK. Etc

• Note that the leaves on the left-hand side of the stems (Boys) increase from the centre outwards

#### Are there any variations on stem and leaf diagrams?

• There are a few minor variations on stem and leaf diagrams that you may see online or in different textbooks

• Some or all the different/extra features in the diagram above may appear
• These differences can be applied to back-to-back stem and leaf diagrams
• With large amounts of data, the stems may be split into two rows
• Every stem will be listed twice
• The first row for a stem will contain leaves 0 - 4
• The second row will contain leaves 5 - 9

#### What might I be asked to do with a stem and leaf diagram?

• You may be asked to draw or complete a stem and leaf diagram
• Find statistical measuresmedian, quartiles and interquartile range in particular
• From which you may be required to draw a box-and-whisker diagram
• Identify and remove outliers
• Compare data shown by stem and leaf diagrams (either separate or back-to-back); comment on two things and each should be in both terms of the maths and the context of the question
• a comment about average (use median)

e.g. the girls’ median of 88% was higher than the boys’ median of 65% so on average the girls performed better on the test

e.g. the girls’ interquartile range of 30% was greater than the boys’ 15% so the boys had more consistent scores on the test

• Analyse what would happen to statistical measures such as the median and quartiles if a value changed or a new value were to be added to the data

#### Worked example

The following stem and leaf diagrams show the times taken by some children and adults to complete a level on a computer game.

2 | 3 represents a time of 23 seconds

(a)
Compare the times taken to complete the level between the children and the adults.
(b)
It is later discovered two of the adults’ times had been omitted from the diagram –times of 23 and 42 seconds.
Briefly explain whether adding these times would change the adults’ median time.
(a)
Compare the times taken to complete the level between the children and the adults.

(b)
It is later discovered two of the adults’ times had been omitted from the diagram –times of 23 and 42 seconds.
Briefly explain whether adding these times would change the adults’ median time.

#### Exam Tip

• 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 either side of it

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