With this model we may illustrate many other essential facts about variability which must be borne in mind when approaching the problems of Eugenics. Before we allow the peas to fall we know quite definitely what the general distribution of them all will be, but we do not know at all the future position of any single pea. Of this we can speak only in terms of probability; the chances are very high that it will fall in one of the three middle compartments, very low that it will be in one of the extreme compartments. But the chances are equal, whatever they are, that it will fall above or below the average or middle position. We see then that in any group there are many more individuals near the average, i. e., mediocre, than there are in the classes removed from the average and the farther the remove of a class from the average the smaller the number of individuals in that class. Yet all the individuals belong to the same whole group. This leads to the very important fact that _an individual may belong to a group without representing it fairly_. The average individuals are the most representative. But in order to get a correct idea of the whole group we must know, first, to what _extent_ deviations occur in each direction, above and below the group average, and, second, the average _amount_ by which each individual of the group deviates from this group average. That is, we must know the amount of variability as well as the extent of the greatest divergence from the average. The best measure of the amount of variability exhibited by any group of objects or organisms is not the simple average or mean of all the individual deviations from the average of the group; it is the square root of the mean squared deviations from the group average. This is called the _index_ of variability or "standard deviation." In order to make possible the comparison of the variabilities of characteristics measured in unlike units, such as weight and stature, this index must be converted into an equivalent abstract quantity. This is done by reducing the index of variability to per cents of the group average, giving what is called the _coefficient_ of variability. Thus, for example, in stature the index of variability (standard deviation) of certain classes of men is approximately 2.7 inches; that is, in a large group of men the amount of individual variation from the average height of 69 inches amounts to 2.7 inches. This gives an abstract _coefficient_ of about 4.0 per cent, for 2.7 equals 3.9 per cent of 69. Similarly the index of variability of the weight of a group of university students has been found to be about 16.5 pounds; the average weight is about 153 pounds, and the coefficient of variability is therefore about 10.8 per cent (16.5 equals 10.78 per cent of 153). Although pounds and inches may not be compared, these two abstract coefficients may be, and we may say that men are more than twice as variable in weight as in stature.