A note on the representation of bimodal distributions

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.