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Beginners statistics:

Pie charts

On this page: Example, with R,  Definition and Use,  Test yourself,  References  Download R  R is Free, very powerful, and does the boring calculations & graphs for scientists.

Example, with R

Pie charts (or pie diagrams, or pie graphs) are the most popular way that elementary school teachers and journalists present frequency distributions.

Data courtesy Carpaneto & Fusari (2000)

Provided the pie chart is circular, the area of each slice is dictated by the proportion of values in that class.

  • Note the values in f do not have to be arranged in ascending order, but can be arranged in any convenient order.
  • The values in f are converted to proportions (as p=f/sum(f)) so the angle of each slice is p*360 degrees.
  • Given the pie is circular, each segment's area is f/sum(f) of the total.
    So, if f comprised 4 equal values, you would get 4 identically-shaped 90 degree slices.
  • When no other information is available (e.g. pie(f)) R labels each pie slice with the order each frequency appears in f.

Definition and Use

The pie chart is a circular chart divided into sectors. The central angle of the each sector (and hence its arc length and area) is proportional to the value it represents.

Tips and Notes

  • Most statisticians consider that the pie chart is one of the worst ways to display information.
    The human eye is bad at comparing relative areas, but good at judging linear measures.
    Most people are not too good at comparing differently-oriented angles either.
  • Others have challenged this position (see Spence, 2005), but one point is generally agreed - elliptical, exploded, 3-dimensional or otherwise non-circular pie graphs are most certainly misleading, and should never be used.
  • When someone presents a non-circular pie chart it either means that they know nothing about stats, or they assume you know nothing about stats, or they are trying to mislead you, or all three of those things.

Test yourself

Comment on the pie charts below:

  1. Distribution of Dark Matter

    Public Domain - NASA 

  2. US Population

    Public Domain - NASA 

    Useful references

    Cleveland, W.S. & McGill, R. (1984). Graphical perception : Theory, experimentation, and application to the development of graphical methods. Journal of the American Statistical Association 79, 531-540.Full text 
    Tests experimentally how accurately people extract quantitative information from graphs - and rejects the pie diagram.

    Kabacoff, R.I. (2012) Quick-R: Pie Charts. Full text 
    Covers simple pie chart, pie chart with annotated percentages and 3D pie charts

    Spence, I.(2005). No humble pie: The origins and usage of a statistical chart. Journal of Educational and Behavioral Statistics. 30 (4), 353-368. Full text 
    A lively but questionable defense of pie charts.

    Wikipedia: Pie chart. Full text 
    Informative text on pie charts. Warns about the drawbacks of 3D charts, but should make it clear that this applies to all non-circular charts.

    See Also