Computational Statistics

, Volume 19, Issue 1, pp 9–28 | Cite as

Cumulative curves for exploration of demographic data: a case study of Northwest England

  • Natalia Andrienko
  • Gennady Andrienko


The paper introduces the idea of generalising a cumulative frequency curve to show arbitrary cumulative counts. For example, in demographic studies generalised cumulative curves can represent the distribution of population or area. Generalised cumulative curves can be a valuable instrument for exploratory data analysis. The use of cumulative curves in an investigation of population statistics in Northwest England allowed us to discover interesting facts about relationships between the distribution of national minorities and the degree of deprivation. We detected that, while high concentration of national minorities occurs, in general, in underprivileged districts, there are some differences related to the origin of the minorities. The paper sets the applicability conditions for generalised cumulative curves and compares them with other graphical tools for exploratory data analysis.

Key words

Geographic visualisation Exploratory data analysis Data visualisation Interactive graphics 


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  1. Andrienko, G., and Andrienko, N., 1999. Interactive maps for visual data exploration.International Journal Geographical Information Science,13, 355–374CrossRefGoogle Scholar
  2. Bunting, J., 2000. Measuring deprivation: a review of indices in common use, Scholar
  3. Cleveland, W.S., 1993.Visualizing Data, Hobart Press, Summit, New Jersey.Google Scholar
  4. Lorenz, M.O., 1905. Methods of Measuring the Concentration of Wealth,Journal of the American Statistical Association, New Series,70, 209–219Google Scholar
  5. Slocum, T.A., 1999.Thematic Cartography and Visualization. Prentice-Hall, New JerseyGoogle Scholar
  6. Schmid, C.F., and Schmid, S.E., 1979.Handbook of graphic presentation. Second Edition, John Wiley & Sons, Inc., New YorkGoogle Scholar
  7. Shneiderman, B., 1983. Direct Manipulation: A Step Beyond Programming Languages,Computer, August 1983, 57–69CrossRefGoogle Scholar
  8. Tukey, J.W., 1977.Exploratory Data Analysis. Addison-Wesley, ReadingMATHGoogle Scholar
  9. Tweedie, L., Spence, R., Dawkes, H., and Su, H., 1999. Externalising Abstract Mathematical Models. In: Card, S.K., Mackinlay, J.D., and Shneiderman, B. (Eds.)Readings in Information Visualization: Using Vision to Think, Morgan Kaufmann Publishers, Inc., San Francisco, California, pp. 276–284Google Scholar
  10. Wilk, M.B., and Gnanadesikan, R. (1968. Probability plotting methods for the analysis of data.Biometrica,55(1), 1–17.Google Scholar
  11. Yamahira, T., Kasahara, Y., and Tsurutani, T., 1985. How map designers can represent their ideas in thematic maps.The Visual Computer,1, 174–184.CrossRefGoogle Scholar

Copyright information

© Physica-Verlag 2004

Authors and Affiliations

  • Natalia Andrienko
    • 1
  • Gennady Andrienko
    • 1
  1. 1.SPADE-Spatial Decision Support TeamFraunhofer AIS-Autonomous Intelligent Systems InstituteSankt AugustinGermany

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