Box-and-whisker plots
Box-and-whisker plots are a really effective way to display lots of information.
These plots contain the range, interquartile range, median, lower value, upper value, lower quartile and upper quartile. They can either be drawn on a number line as above or sometimes several of them can be plotted on a graph for the purpose of comparing distributions.
Sometimes you will be required to draw a box-and-whisker plot from a cumulative frequency diagram.
This can be achieved by first finding the median and interquartile range using the normal method and then plotting this onto a number line as shown above. Notice the scale of the number line is the same as in the cumulative frequency.
Question
Draw a box and whisker plot for the following information:
- Range - 75
- Lowest value - 15
- Interquartile range - 43
- Upper quartile - 68
- Median - 44
Note that the highest value has not been given. We need to calculate this from the range (remember the range is how far away the highest value is from the lowest value):
Lowest value + range = highest value
15 + 75 = 90
The lower quartile has not been given. We calculate this from the interquartile range (remember the interquartile range is the difference between the lower quartile and the upper quartile):
Upper quartile – interquartile range = lower quartile
68 - 43 = 25
Once we have all of the values we need we can draw the box and whisker plot.
Question
A utilities company is researching the cost of household gas and electricity bills. They have analysed the data from hundreds of households and found that the median cost is £66 and the interquartile range is £21. The range is £27.50, the cheapest price was £47.50 and the upper quartile was £74. Represent this information with a box-and-whisker plot.
Here are the values that we know:
- Range - £27.50
- Lowest value - £47.50
- Interquartile range - £21
- Upper quartile - £74
- Median - £66
We need to discover the highest value:
Lowest value + range = highest value
47.50 + 27.50 = 75
We need to discover the lower quartile:
Upper quartile – interquartile range = lower quartile
74 - 21 = 53
Once we have all of the values we need we can draw the box and whisker plot.
