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v.]   NORMAL VARIABILITY.   65

accidents befall each shot in its career. In rare cases, a long run of luck continues to favour the course of a particular shot towards either outside place, but in the large majority of instances the number of accidents that cause Deviation to the right, balance in a greater or less degree those that cause Deviation to the left. Therefore most of the shot finds its way into the compartments that are situated near to a perpendicular line drawn from the outlet of the funnel, and the Frequency with which shots stray to different distances to the right or left of that line diminishes in a much faster ratio than those distances increase. This illustrates and explains the reason why mediocrity is so common.

If a larger quantity of shot is put inside the apparatus, the resulting curve will be more humped, but one half of the shot will still fall within the same distance as before, reckoning to the right and left of the perpendicular line that passes through the mouth of the funnel. This distance, which does not vary with the quantity of the shot, is the "Prob : Error," or "Prob Deviation," of -any single shot, and has the same value as our Q. But a Scheme of Frequency is unsuitable for finding the values of either M or Q. To do so, we must divide its strangely shaped area into four equal parts by vertical lines, which is hardly to be effected except by a tedious process of " Trial and Error." On the other hand M and Q can be derived from Schemes of Distribution with.no more trouble than is needed to divide a line into four equal parts.

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