9.4.2 Box Plots

What are box plots and when should they be used?

• Box Plots are also known as BoxandWhisker Diagrams (you’ll see why below)
• They are used when we are particularly interested in splitting data up into quartiles
• Often, data will contain extreme values – consider the cost of a car: there are far more family cars around than there are expensive sports cars
So if you had 50 data values about the prices of cars and 49 of them were family cars but 1 was a sports car then the sports car’s value does not fit in with the rest of the data
• Using quartiles and drawing a box plot allows us to split the data and so we can see what is happening at the low, middle and high points in the data

What do I need to know?

1. Drawing Box Plots

• You need to know five values to draw a box plot:

Lowest data value

Lower quartile

Median

Upper quartile

Highest data value

• Conversely, if you are given a box plot you can work out these five values plus other useful statistics like range and interquartile range (IQR)
• Box plots are normally drawn on square or graph paper so you will need to be accurate
• For example, given the following information draw a box plot on the graph paper provided

• Plot each point first with a small line – it doesn’t matter that they are not listed in order
• The middle three values (lower quartile, median and upper quartile) make the box
• The lowest and highest value make the ‘whiskers’

2. Comparing Box Plots

• If you are asked to compare box plots (for example between two classes) you should mention at least two things – one about averages, ie. median, and one about spread, ie. IQR or range

(a)

(b)

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