appropriate illustration. Suppose a man firing at a mark from some sheltered spot, but such that the range crossed a broad exposed valley up or down which a strong wind was generally blowing. If the shot-marks were observed we should find them clustering about two centres to the right and left of the bullseye. And if the results were plotted out in a curve they would yield such a double-peaked curve as we have described. But if the winds were equally strong and prevalent in opposite directions, we should find that the averaging process redressed the consequent disturbance.
If however the curve represented, as it is decidedly more likely to do, some outcome of natural phenomena in which there was, so to say, a real double aim on the part of nature, it would be otherwise. Take, for instance, the results of measuring a large number of people who belonged to two very heterogeneous races. The curve of facility would here be of the kind indicated on p. 45, and if the numbers of the
two commingled races were equal it would display a pair of twin peaks. Again the question arises, ‘ought’ we to involve the whole range within the scope of a single average? The answer is that the obligation depends upon the purpose we have in view. If we want to compare that heterogeneous race, as a whole, with some other, or with itself at some other time, we shall do well to average without analysis. All statistics of population, as we have already seen (v.[** TN: space] p. 47), are forced to neglect a multitude of discriminating characteristics of the kind in question. But if our object were to interpret the causes of this abnormal error-curve we should do well to break up the statistics into corresponding parts, and subject these to analysis separately.
Similarly with the measurements of the ancient buildings. In this case if all our various ‘errors’ were thrown together into one group of statistics we should find that the resultant curve of facility displayed, not two peaks only, but a succession of them; and these of various magnitudes, corresponding to the frequency of occurrence of each particular measurement. We might take an average of the whole, but hardly any rational purpose could be subserved in so doing; whereas each separate point of maximum frequency of occurrence has something significant to teach us.
§ 37. One other peculiar case may be noticed in conclusion. Suppose a distinctly asymmetrical, or lop-sided curve of facility, such as this:—
Laws of error, of which this is a graphical representation, are, I apprehend, far from uncommon. The curve in question, is, in fact, but a slight exaggeration of that of barometrical heights as referred to in the last