Page:Popular Science Monthly Volume 59.djvu/461

Rh 'ribs' (Fig. 3). In any hundred individuals from one locality the number of ribs may vary from 15 to 21. If we put in one pile the shells having the same number of ribs and arrange the piles in order, from 15 to 20, upon a level base we shall get a figure which is the frequency polygon for the ribs of Pecten shells from the given locality (Fig. 4).

Frequency polygons may be obtained in the same way from measurements or countings made on almost any organ of any plant or animal. The shapes of the polygons are probably never exactly alike in different organs; consequently, there is a field for the comparing of polygons and for drawing interpretations from differences in their form.

In comparing frequency polygons attention should be directed, first of all, to two characters; namely, the position and relative proportion of individuals included in the modal class and the spread of the polygon at the base. This spread is known technically as the range. While

some frequency polygons have a high mode and narrow range others have a low mode and a broad range. The importance of this fact is that a narrow range implies relatively small variability, since relatively few individuals depart far from the modal condition. On the other hand, wide range implies great variability. Range, however, is not an accurate measure of variability because it is too easily affected by the accidental occurrence of even one aberrant individual. We need a measure of variability that shall take into account the departures of all the individuals from the mode. One such measure is the arithmetical average of all the departures from the mean in both directions; and this measure has been widely employed. At present another method is preferred; namely, the square root of the average of the squared departures. This measure is called the standard deviation. The standard deviation is of great importance, because it is the index of variability. This index in the case of measured organs is, like the range, a concrete number; consequently indices are not always comparable, being expressed, e. g., in feet, millimeters, degrees or pounds. So it has been proposed to reduce all indices (except those based on countings) to