CHAPTER V.

NORMAL VARIABILITY.

Schemes of Deviations.-Normal Curve of Distribution.-Comparison of the observed with the Normal Curve.-The value of a single Deviation at a known Grade determines a Normal Scheme of Deviations.

Two Measures at two known Grades determine a Normal Scheme of Measures.-The Charms of Statistics.-Mechanical illustration of the Cause of the Curve of Frequency.-Order in apparent Chaos.

Problems in the Law of Error.

Schemes of Deviations.-We have now seen how easy it is to represent the distributionn of any quality among a multitude of men, either by a simple diagram or by a line containing a few figures. In this chapter it will be shown that a considerably briefer description is approximately sufficient.

Every measure in a Scheme is equal to its Middlemost, or Median value, or M, plus or minus a certain Deviation from M. The Deviation, or "Error" as it is technically called, is plus for all grades above 50°, zero for 50°, and minus for all grades below 50°. Thus if (±D) be the deviation from M in any particular case, every measure in a Scheme may be expressed in the

E2