Exploring Multivariate Data

This Demonstration explores two five-dimensional datasets. Basic multivariate numerical statistical summaries are provided, but the emphasis is on interactive graphical exploration using three common displays. The "simulation" dataset has 1000 (five-dimensional) observations and is produced in real-time using built-in Mathematica functions. The variables in the simulation data are uniform(0, 10), triangular(0, 10), Poisson(3), standard normal, and beta(5, 3). The "pollen" data has 3848 (six-dimensional) observations. The "pollen" data is a famous dataset used in a statistical analysis competition at the 1986 Joint Meetings of the American Statistical Association. In the pollen dataset, the first five variables are "ridge", "nub", "crack", "weight", and "density". The sixth variable is just an index number and is not used. A careful exploration of the pollen data will reveal some surprising results.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The viewpoint sliders will adjust dynamically when you use the mouse to zoom or rotate!
Theoretically, the five simulation variables are (mutually) independent and this independence is reflected by a correlation matrix that is approximately a 5×5 identity matrix. The coordinate axes are color coded (: red, : green, : blue) and the axis is thicker than the others to assist in tracking the orientation of the 3D data cloud. For a thorough discussion of the pollen data, see the following reference.
R. A. Becker, L. Denby, R. McGill, and A. R. Wilks, "Datacryptanalysis: A Case Study," AT&T Bell Laboratories, Statistical Research Reports No. 36, 1986.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+