Track 3 · Visualising and Exploring Data · Lesson 4 of 11
Box plots and dot plots
Build a box plot from the five-number summary and the 1.5 × IQR rule, compare groups with side-by-side box plots, and recognise what a box plot hides.
An airport operations team must decide which airline's departures need attention. Four airlines, 2 500 flights, delays from 17 minutes early to more than eight hours late: side-by-side box plots compress all of that into four pictures that can be compared at a glance — as long as you know what they leave out.
A box plot (box-and-whisker plot) draws the five-number summary of a numeric variable:
- the box runs from the first quartile to the third quartile , so it holds the middle half of the data;
- the line inside the box is the median;
- the whiskers reach out to the most extreme observations that are not flagged as outliers;
- observations beyond the fences are drawn individually as outliers.
Quartiles here use the standard method of most statistical software (Hyndman–Fan type 7): the -quantile sits at position in the sorted data, interpolating between neighbours when that position is not a whole number.
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute the quartiles, IQR, fences and whisker ends for a box plot
- Compare groups using medians, box widths and outliers on a shared axis
- Explain why skewed data produce many “outliers” that are not errors
- Recognise what box plots hide and show the individual points when it matters