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A note on the representation of bimodal distributions

Published online by Cambridge University Press:  04 July 2016

M. C. Campion*
Affiliation:
Lockheed-Georgia Company, Marietta, Georgia, USA

Extract

Reference 1 provides the stimulus for this note, containing, as it does, a trap into which many engineers and statisticians fall. Referring to Fig. 6 of that paper (this was incorrectly labelled — it should have been Fig. 4), a set of observed data is presented on normal probability paper, together with a straight line representing the fitted normal distribution. Since none of the points is far from the line, the conclusion is drawn that the data are well-fitted by a normal distribution.

However, a closer look at the figure shows that the scatter of the ‘observed’ points about the fitted line is not random, but systematic; the first four points all lie above the line, the next six below the line, the next eight above the line, and the last two below the line.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1983 

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References

1. Yeomans, D. G. Choice of Optimal Cabin Capacity, The Aeronautical Journal, March 1983, 863, 87, 95.Google Scholar
2. Taylor, , Manual on Aircraft Loads, AGARD-ograph No. 83, Pergamon Press, 1965.Google Scholar
3. Campion, M. C. The Application of Extreme-Value Techniques to the Evaluation of Structural Strength Criteria and Other Remote Events, ER10075, Lockheed-Georgia Company, December 1968.Google Scholar
4. Gumbel, E. J. Statistical Theory of Extreme Values and Some Practical Applications, Applied Mathematics Series No. 33, National Bureau of Standards, 1954.Google Scholar