3. Characterizing and Displaying Multivariate Data

  1. Alvin C. Rencher

Published Online: 27 MAR 2003

DOI: 10.1002/0471271357.ch3

Methods of Multivariate Analysis, Second Edition

Methods of Multivariate Analysis, Second Edition

How to Cite

Rencher, A. C. (2002) Characterizing and Displaying Multivariate Data, in Methods of Multivariate Analysis, Second Edition, John Wiley & Sons, Inc., New York, NY, USA. doi: 10.1002/0471271357.ch3

Author Information

  1. Brigham Young University, USA

Publication History

  1. Published Online: 27 MAR 2003
  2. Published Print: 22 FEB 2002

ISBN Information

Print ISBN: 9780471418894

Online ISBN: 9780471271352



  • random variable;
  • mean;
  • variance;
  • standard deviation;
  • covariance;
  • independence;
  • orthogonal variables;
  • correlation;
  • scatter plot;
  • mean vector;
  • data matrix;
  • covariance matrix;
  • correlation matrix;
  • subset of variables;
  • linear combination;
  • generalized sample variance;
  • total sample variance;
  • missing values;
  • distance between vectors


Several techniques are given in this chapter for summarizing and plotting a multivariate data set. Univariate and bivariate procedures are reviewed in the first three sections, followed by nine sections covering techniques suitable for a higher number of variables.

The mean, variation, and covariation of several variables can be summarized in the mean vector and covariance matrix. The latter can be easily converted to a correlation matrix. The mean vector, covariance matrix, and correlation matrix can be extended to subsets of variables and to linear combinations of variables. The chapter concludes with measures of overall variability and methods of estimating missing values.

Most techniques are illustrated graphically or numerically, and additional examples are provided by the problems at the end of the chapter.