Box plots
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Agroup of students did a test. The summary data us shown in the table below.
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- Given that there were no outliers draw a box plot to illustrate the data.
- We’re not concerned with the outlier marks. Drawing the box plot should be easy.
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The blood glucose of 30 males is recorded. The results in mmol/litre are shown in the stem and leaf diagram below.
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- Draw a box plot to represent the data
The highest value which is not an outlier is 5.1 and is the only outlier.
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It is important to lebal the box plot diagram as we have done in this example.
Comparing data with box plots
Box plots can be used to compare data. In the following example we shall compare two sets of data using box plots.
In this example you’ll need the data from the previous example.
The blood glucose level of 30 males is recorded. The results, in mmol/litre, are summarised below;
An outlier is an observation that falls either 1.5 × interquartile range above the upper quartile or 1.5 × interquartile range below the lower quartile.
- Given that there is only one outlier for males draw a box plot on the same diagram representing the data in the previous example and this example
- Compare the blood glucose level for males and females
- We already know there is only one outlier but we will need to find out which and here it lies.
Outliers are values less than 3.6 – 1.5 × 1.1 = 1.95 and values greater than 4.7 + 1.5 × 1.1 = 6.35
The outlier is therefore: 1.4Notice that in this example we don’t know the lowest value which is not an outlier. So we shall draw the end at the outlier boundary. We don’t need to worry about the highest value which is not an outlier since there are no outliers in that direction.
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The males have a higher median blood glucose than girls. Notice that the width of the box plots represents the interquartile range. Therefore the interquartile range and the range for the blood glucose are smaller for the females.
