A pie chart is a circular chart divided into
sectors, illustrating numerical proportion.
In a pie chart, the arc length of each sector,
is proportional to the quantity it represents.
While it is named for its resemblance to a
pie which has been sliced, there are variations
on the way it can be presented. The earliest
known pie chart is generally credited to William
Playfair's Statistical Breviary of 1801.
Pie charts are very widely used in the business
world and the mass media. However, they have
been criticized, and many experts recommend
avoiding them, pointing out that research
has shown it is difficult to compare different
sections of a given pie chart, or to compare
data across different pie charts. Pie charts
can be replaced in most cases by other plots
such as the bar chart.
Example
The following example chart is based on preliminary
results of the election for the European Parliament
in 2004. The table lists the number of seats
allocated to each party group, along with
the derived percentage of the total that they
each make up. The values in the last column,
the derived central angle of each sector,
is found by multiplying the percentage by
360°.
*Because of rounding, these totals do not
add up to 100 and 360.
The size of each central angle is proportional
to the size of the corresponding quantity,
here the number of seats. Since the sum of
the central angles has to be 360°, the central
angle for a quantity that is a fraction Q
of the total is 360Q degrees. In the example,
the central angle for the largest group) is
135.7° because 0.377 times 360, rounded to
one decimal place, equals 135.7.
Use, effectiveness and visual perception
An obvious flaw exhibited by pie charts is
that they cannot show more than a few values
without separating the visual encoding from
the data they represent. When slices become
too small, pie charts have to rely on colors,
textures or arrows so the reader can understand
them. This makes them unsuitable for use with
larger amounts of data. Pie charts also take
up a larger amount of space on the page compared
to the more flexible bar charts, which do
not need to have separate legends, and can
display other values such as averages or targets
at the same time.
Statisticians generally regard pie charts
as a poor method of displaying information,
and they are uncommon in scientific literature.
One reason is that it is more difficult for
comparisons to be made between the size of
items in a chart when area is used instead
of length and when different items are shown
as different shapes.
Further, in research performed at AT&T Bell
Laboratories, it was shown that comparison
by angle was less accurate than comparison
by length. This can be illustrated with the
diagram to the right, showing three pie charts,
and, below each of them, the corresponding
bar chart representing the same data. Most
subjects have difficulty ordering the slices
in the pie chart by size; when the bar chart
is used the comparison is much easier. Similarly,
comparisons between data sets are easier using
the bar chart. However, if the goal is to
compare a given category with the total in
a single chart and the multiple is close to
25 or 50 percent, then a pie chart can often
be more effective than a bar graph.
Variants and similar charts
Exploded pie chart
A chart with one or more sectors separated
from the rest of the disk is known as an exploded
pie chart. This effect is used to either highlight
a sector, or to highlight smaller segments
of the chart with small proportions.
Polar area diagram
The polar area diagram is similar to a usual
pie chart, except sectors are equal angles
and differ rather in how far each sector extends
from the center of the circle. The polar area
diagram is used to plot cyclic phenomena.
For example, if the count of deaths in each
month for a year are to be plotted then there
will be 12 sectors all with the same angle
of 30 degrees each. The radius of each sector
would be proportional to the square root of
the death count for the month, so the area
of a sector represents the number of deaths
in a month. If the death count in each month
is subdivided by cause of death, it is possible
to make multiple comparisons on one diagram,
as is seen in the polar area diagram famously
developed by Florence Nightingale.
The first known use of polar area diagrams
was by André-Michel Guerry, which he called
courbes circulaires, in an 1829 paper showing
seasonal and daily variation in wind direction
over the year and births and deaths by hour
of the day. Léon Lalanne later used a polar
diagram to show the frequency of wind directions
around compass points in 1843. The wind rose
is still used by meteorologists. Nightingale
published her rose diagram in 1858. The name
"coxcomb" is sometimes used erroneously: this
was the name Nightingale used to refer to
a book containing the diagrams rather than
the diagrams themselves. It has been suggested
that most of Nightingale's early reputation
was built on her ability to give clear and
concise presentations of data.
Spie chart
A useful variant of the polar area chart is
the spie chart designed by Feitelson. This
superimposes a normal pie chart with a modified
polar area chart to permit the comparison
of a set of data at two different states.
The base pie chart represents the first state
in the usual way, with different slice sizes.
The second state is represented by the superimposed
polar area chart, using the same angles as
the base, and adjusting the radii to fit the
data. This is useful, among other things,
for visualizing hazards to different population
groups. For example, the base pie chart can
show the distribution of age and gender groups
in the general population, and the overlay
their representation among road casualties;
age and gender groups that are especially
susceptible to being involved in accidents
then stand out as slices that extend far beyond
the original pie chart. The R Graph Gallery
provides an example.
Ring chart / Sunburst chart / Multilevel pie
chart
A ring chart, also known as a sunburst chart
or a multilevel pie chart, is used to visualize
hierarchical data, depicted by concentric
circles. The circle in the centre represents
the root node, with the hierarchy moving outward
from the center. A segment of the inner circle
bears a hierarchical relationship to those
segments of the outer circle which lie within
the angular sweep of the parent segment.
===3x pie cake / Perspective pie cake A 3x
pie cake, or perspective pie cake, is used
to give the chart a 3D look. Often used for
aesthetic reasons, the third dimension does
not improve the reading of the data; on the
contrary, these plots are difficult to interpret
because of the distorted effect of perspective
associated with the third dimension. The use
of superfluous dimensions not used to display
the data of interest is discouraged for charts
in general, not only for pie charts.
Doughnut chart
A doughnut chart is functionally identical
to a pie chart, with the exception of a blank
center and the ability to support multiple
statistics at once. Doughnut charts provide
a better data intensity ratio to standard
pie charts since the blank center can be used
to display additional, related data as shown
in the example.
History
The earliest known pie chart is generally
credited to William Playfair's Statistical
Breviary of 1801, in which two such graphs
are used. This invention was not widely used
at first; the French engineer Charles Joseph
Minard was one of the first to use it in 1858,
in particular in maps where he needed to add
information in a third dimension. It has been
said that Florence Nightingale invented it,
though in fact she just popularised it and
she was later assumed to have created it due
to the obscurity of Playfair's creation.
See also
Pie menu
Notes
References
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