that if certain qualities vary normally, such and such will be the results; that these qualities are of a class that are found, whenever they have been tested, to vary normally to a fair degree of approximation, and consequently we may infer that our results are trustworthy indications of real facts.
A talent is a sum whose exact value few of us care to know, although we all appreciate the inner sense of the beautiful parable. I will, therefore, venture to adapt the phraseology of the allegory to my present purpose by substituting for “talent” the words “normal-talent.” The value of this normal talent in respect to each and any specified quality or faculty is such that one-quarter of the people receive for their respective shares more than one normal-talent over and above the average of all the shares. Our normal-talent is therefore identical with what is technically known as the “probable error.” Therefrom the whole of the following table starts into life, evolved from that of the “probability integral.”
| v and below | u | t | s | r | R | S | T | U | V and above. | Total | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| –4° | –3° | –2° | –1° | M | +1° | +2° | +3° | +4° | |||
| 35 | 180 | 672 | 1613 | 2500 | 2500 | 1613 | 672 | 180 | 35 | 10,000 | |
| 2 | 7 | 16 | 25 | 25 | 16 | 7 | 2 | 100 |