# Page:Popular Science Monthly Volume 71.djvu/179

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PROBABILITY, THE FOUNDATION OF EUGENICS

In the latter ease the sides of the stalls serve as degrees, counting the first of them as 0°, making one more graduation than the number of objects, as should be. The difference between these two methods has to be made clear, and that while the serial position of the median object is always the same in any two arrays whatever be the number of variates, the serial positions of their subdivisions can not be the same, the ignored half interval at either end varying in width according to the number of variates, and becoming considerable when that number is small.

Lines of proportionate length will then be used drawn on a blackboard, and the limits of the array will be also drawn, at a half interval from either end. The base is then to be divided centesimally.

Next join the tops of the lines with a smooth curve, and wipe out everything except the curve, the limit at either side, and the centestimally divided base (Fig. 5). This figure forms a scheme of distribution of variates. Explain clearly that its shape is independent of the number of variates, so long as they are sufficiently numerous to secure statistical constancy.

Show numerous schemes of variates of different kinds, and remark on the prevalent family likeness between the bounding curves. (Words and meanings learnt—schemes of distribution, centesimal graduation of base.)

The third lesson passes from variates, measured upwards from the base, to deviates measured upwards or downwards from the median, and treated as positive or negative values accordingly (Fig. 6).

Draw a scheme of variates on the blackboard, and show that it consists of two parts; the median which represents a constant, and the curve which represents the variations from it. Draw a horizontal line from limit to limit, through the top of the median, to serve as axis to the curve. Divide the axis centesimally, and wipe out everything except curve, axis and limits. This forms a scheme of distribution of deviates. Draw ordinates from the axis to the curve at the twenty-fifth and seventy-fifth divisions. These are the "quartile" deviates.

At this stage the genesis of the theoretical normal curve might be briefly explained and the generality of its application; also some of its beautiful properties of reproduction. Many of the diagrams already shown would be again employed to show the prevalence of approximately normal distributions. Exceptions of strongly marked skew curves would be exhibited and their genesis briefly explained.

It will then be explained that while the ordinate at any specified centesimal division in two normal curves measures their relative variability, the quartile is commonly employed as the unit of variability under the almost grotesque name of "probable error," which is intended to signify that the length of any deviate in the system is as likely as 