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At a casual examination, or for demonstrative purposes, the extremes may be prominent, but for all further considerations the quartiles are the real values upon which to rest calculations.
Here we must remember that the mutual distance of the ordinates has been a wholly arbitrary one in all our previous considerations. And so it is, as long as only one curve is considered at a time. But as soon as two are to be compared, it is obvious that free choice is no longer allowed. The comparison must be made on a common basis, and to this effect the quartiles must be brought together.
Moreover if the agreement with the law of probability is once conceded, the whole curve is defined by the average and the quartiles, and the result of hundreds of measurements or countings may be summed up in three, or, in the case of symmetrical curves, perhaps in two figures. Also in comparing different curves with one another, the quartiles are of great importance.
The lowest of the curve is about 1890, in the Median, the average and in each of the quartiles. Second, the incoming of the Irish immigrants, who began to be land-holders about 1850, multiplied the number of small holdings of land.
This point corresponds to the important value called the probable error, and was designated by Galton as the quartile. For it is evident that the average and the two quartiles divide the whole of the observations into four equal parts. Choosing the quartiles as the basis for calculations we are independent of all the secondary causes of error, which necessarily are inherent in the extremes.
In the discussion of the methods of comparing two curves, we have pointed to the quartiles as the decisive points, and to the necessity of drawing the curves so that these points are made to overlie one another, on each side of the average.
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