Depicting Quantitative Data
Dimensionality: data about running clubs
• Univariate: only one variable describes the data – number of members in each club
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• Bivariate: two variables describe the data
– number of male and female members in each club
• Tri-variate: three variables describe the data – number of men, women, average race finishing
position for the club
• Multivariate: more than three variables
– number of men, women, membership fees, colour, founding year, average race finishing position
Club name: categorical
although note that an alphabetic ordering may be imposed,
making the data ordered ordinal
Number of members: ordered quantitative
Number of women: ordered quantitative
Number of men: ordered quantitative
Membership fees: ordered quantitative
Colour: categorical
Founding year: ordered quantitative
Average race finishing position: ordered quantitative
Univariate (number of members in a club)
Annan & Dist
Argyll & S
Ayr & Seaforth
Bellahouston
Border Harriers
Boundary H
Brit Orienteering Squad
Calderglen Harriers
Camuslang Harriers
Castlemilk
Central Region
…. 100 clubs
Perth Orienteers
Hunters Bog Trotters
Inverness H
Lothian & Borders
Penicuik YMCA
Boundary H
Riyadh HH Harriers
Univeristy of Sunder
Edinburgh Univ
Peeblesshire
N Shields Poly
Deeside Runners
Skelmersdale
Macclesfield H
Spenborough
…. 100 clubs
Univariate (number of members in a club)
Univariate (colour associated with a club)
number of clubs associated with each colour
Pie charts vs bar charts
number of clubs associated with each colour
3D effects
(male and female members)
Annan & Dist
Argyll & S
Ayr & Seaforth
Bellahouston
Border Harriers
Boundary H
Brit Orienteering Squad
Calderglen Harriers
Camuslang Harriers
Castlemilk
Central Region
… 100 clubs
clustered bar chart (alpha)
overview (top) detail (bottom)
clustered bar chart (ordered by female)
stacked bar chart (ordered by total)
100% stacked bar chart (ordered by total)
scatterplot
Bar charts vs Line charts number of new clubs opened each year
number of clubs associated with each colour
average finishing position
Annan & Dist
Argyll & S
Ayr & Seaforth
Bellahouston
Border Harriers
Boundary H
Brit Orienteering Squad
Calderglen Harriers
Camuslang Harriers
… 100 clubs
Tri-variate
bubble plot
scatterplot matrix
Tri-variate: Heat maps
• Typically two (independent) categorical variables,
and a quantitative variable
• The categories are on the two axes
• The quantitative value is represented by change in colour value
– typically: ‘darker’ = ‘more’
• The order of the categories on each axis can be changed (and may be important for identification of patterns)
• Each cell has only one value
Record finishing time for races over the same distance, with different difficulty, at different times of year
Proportion of baby girls given particular names, with respect to different countries
Proportion of baby girls given particular names, with respect to different countries, reordered
Measles cases over time, per US state
Wall Street Journal, Feb 11, 2015
https://onlygrowth.com/blogs/posts/how-to-use-heat-maps-and-eye-tracking-software-to-improve-ux-and-lift-conversion-rates (accessed 25/05/21) https://www.infragistics.com/community/blogs/b/mobileman/posts/geographical-heat-maps-and-how-to-use-them-with-reportplus (accessed 25/05/21)
Tri-variate: Mosaic Plots
Musical themes in the Guardian’s list of “1000 songs to hear before you die”
stubbornmule.net (accessed 25/05/21)
Multivariate
average finishing position
Deeside Runners
Macclesfield H
light green
dark green
Brit Orienteering Squad
light green
Perth Orienteers
light green
light green
Sheffield University
Ayr & Seaforth
East Lothian Orienteers
Glasgow UOC
St Andrews CCC
Edinburgh Triathlete
Forth Valley Orienteers
Scots Vets Harriers
light green
light green
light green
Calderglen Harriers
Multivariate: Parallel coordinates
• Each vertical axis is a dimension, with its values equally spaced along it
• The dimensions are arranged, equally spaced, horizontally
• A single data point is a line that joins its values on each dimension
, “Parallel Coordinates (eagereyes)”, https://eagereyes.org/techniques/parallel-coordinates, 2010 (accessed 18/04/21)
women fees colour
Horsepower
…and many more data items
Car models:
• released from 1970 to 1982
• mileage (MPG)
• number of cylinders
• horsepower
• (plus other features not used here)
, “Parallel Coordinates (eagereyes)”, https://eagereyes.org/techniques/parallel-coordinates, 2010 (accessed 18/04/21)
Each line from left to right represents one car Looking at each pair of axes in turn:
• the cylinder axis has only a few values – all lines pass through a small number of points
• eight-cylinder cars tend to have lower mileage than cars with six and four cylinders (inverse trend)
• more cylinders means more horsepower (almost direct correlation)
• more horsepower means more weight (almost direct correlation)
• older cars are heavier (inverse trend)
, “Parallel Coordinates (eagereyes)”, https://eagereyes.org/techniques/parallel-coordinates, 2010 (accessed 18/04/21)
Parallel coordinate transformations
The iris data set 4 dimensions
– petal width – petal length – sepal width – sepal length
4.8, 3.0, 1.4, 0.3, Iris-setosa 5.1, 3.8, 1.6, 0.2, Iris-setosa 5.3, 3.7, 1.5, 0.2, Iris-setosa 5.0, 3.3, 1.4, 0.2, Iris-setosa 7.0, 3.2, 4.7, 1.4, Iris-versicolor 6.4, 3.2, 4.5, 1.5, Iris-versicolor 6.9, 3.1, 4.9, 1.5, Iris-versicolor 5.1, 2.5, 3.0, 1.1, Iris-versicolor 5.7, 2.8, 4.1, 1.3, Iris-versicolor 6.3, 3.3, 6.0, 2.5, Iris-virginica 5.8, 2.7, 5.1, 1.9, Iris-virginica 7.1, 3.0, 5.9, 2.1, Iris-virginica 6.3, 2.9, 5.6, 1.8, Iris-virginica …….
https://www.data-to-viz.com/graph/parallel.html#code (accessed 18/04/21)
https://www.data-to-viz.com/graph/parallel.html#code (accessed 18/04/21)
Arrange the order of the dimensions on the x-axis to • remove crossings
• highlight relationships (direct or inverse) of interest
See: Siirtola, H. (2000) Direct manipulation of parallel coordinates https://www.data-to-viz.com/graph/parallel.html#code (accessed 18/04/21)
Multivariate: Scatterplot matrix & Parallel coordinates
Munzner (2015), p163, 2015
Multivariate: Bubble Plots
x axis: life expectancy y axis: infant mortality size: population colour: continent
Robertson et al. (2008) Effectiveness of Animation in Trend Visualisation
Multivariate: Star/Radar plots
https://www.data-to-viz.com/caveat/spider.html (accessed 26/05/32)
• Univariate:
– points along a line – bar charts
– histogram
– box plot
– pie chart
• Bivariate
– clustered bar chart
– stacked bar chart
– 100% stacked bar chart – scatter plot
• Tri-variate
– 3D scatter plot
– scatter plot matrix – bubble plot
– heat map
– mosaic plot
• Multivariate
– parallel co-ordinates – bubble plot
– star/radar plot
Depicting Quantitative Data
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