Stem and leaf diagrams
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Below is a quick summary of what is covered in this article.
Summary
- A stem and leaf diagram is used to order and present data
- A stem and leaf diagram reveals the shape of the data and enables quartiles to be found.
- Two sets of data can be compared using back-to-back stem and leaf diagrams.
- While a steam and leaf diagram preserves the detail of data they can be time consuming to draw.
- Stem and leaf diagrams reveal the shape of distribution of the data. Which enables the quartiles to be found easily from the diagrams.
Drawing steam and leaf diagrams
This sections shows how to construct steam and leaf diagrams.
The blood glucose of 30 males is recorded. The results, in mmol/litre, are shown below;
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- Draw a steam and leaf diagram to represent the data.
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The data on a steam leaf diagram is presented in ascending order but it is a lot harder to draw the diagram in ascending order. Therefore it is easier to draw a steam and leaf diagram entering the data as it appears and put it in ascending order afterwards.
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We can now proceed in putting the data in ascending order. Notice on the diagram below we have added a key.
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Using the previous steam and leaf diagram find;
- the mode
- the lower quartile
- the upper quartile
- the median
At the end of each leaf we can add another number to show the number of observations in that leaf as shown below;
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Mode
To find the mode we simply look at the steam and check which number occurs most often in a stem. From the diagram you can see that the mode is 4.8
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Lower quartile
Here we have to use the nth lower quartile formula. There are 30 observations;
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So we must pick the 8th term as the lower quartile;
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Upper quartile
We do the same here; There are 30 observations;
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So we must pick the 23rd term;
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Median
We use the median formula; again we have 30 observations;
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We therefore pick the 15.5th term which is 4.15;
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Andrew records the resting pulse rate for 16 boys and girls. The results are shown below;
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- Construct a back-to-back steam and leaf diagram to represent the data
- Comment on the results.
We must draw the steam leaf diagram entering the data as it appears and order it later. Remember to add the key.
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Unordered
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Ordered
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- The back-to-back steam and leaf diagram shows that boys’ pulse rate tends to be lower than the girls.
