By multiplying the 1.50 by 20, 1.55 by 80, etc., and by adding the results, we shall have simplified the process for obtaining the sum total which must then be divided by the number of individuals.
Well, while doing this for the purpose of simplifying the calculation, we have hit upon the method of distributing the individuals in a series, that is, we have regrouped the corresponding figures according to seriation.
Seriation has been discovered as a method of analysing the mean average, and it demonstrates three things: first, the extent of oscillations of anthropologic data, a thing which the mean average completely hides,—indeed, we have seen in the case of the cephalic index the mean averages oscillate between 75 and 85, when calculated for the separate regions, while, in the case of individuals, the oscillations extend from 70 to 90; secondly, it shows the numerical prevalence of individuals for the one or the other measurement; third, and finally, seriation reveals a law, to us, namely, that the distribution of individuals, according to anthropological data, is not a matter of chance; there is a prevalence of individuals corresponding to certain average figures, and the number of individuals diminishes in proportion as the measurements depart from the mean average, equally whether they increase or diminish.
I take from Livi certain numerical examples of serial distribution:
| Stature in inches | Number of observations |
|---|---|
| 60 | 6 |
| 61 | 26 |
| 62 | 32 |
| 63 | 26 |
| 64 | 160 |
| 65 | 154 |
| 66 | 191 |
| 67 | 128 |
| 68 | 160 |
| 69 | 89 |
| 70 | 45 |
| 71 | 7 |
| 72 | 6 |
| 73 | 3 |
| 74 | 1 |
Although these figures are not rigorously exact, there is a certain numerical prevalence of individuals in relation to the stature of 66 inches, and above and below this point the number of individuals diminishes, becoming very few toward the extremes.
The lack of exactness and of agreement in serial distribution is due to the numerical scarcity of individuals. If this number were doubled, if it were centupled, we should see the serial distribution become systematised to the point of producing, for example, such symmetrical series as the following:
| 1 | 1 | 1 |
| 12 | 16 | 15 |
| 66 | 120 | 105 |
| 220 | 560 | 455 |
| 495 | 1,820 | 1,365 |
| 792 | 3,368 | 3,003 |
| 924 | 8,008 | 5,005 |
| —— | 11,440 | 6,435 |
| 792 | 12,870 | ——— |
| 495 | ———— | 6,435 |
| 220 | 11,440 | ——— |
| 66 | 8,008 | 5,005 |
| 12 | 3,368 | 3,003 |
| 1 | 1,820 | 1,365 |
| 560 | 455 | |
| 120 | 105 | |
| 16 | 15 | |
| 1 | 1 |
This law of distribution is one of the most widespread laws; it ordains the way in which the characteristics of animals and plants alike must behave; and the statistical method which is beginning to be introduced into botany sheds much light upon it.