 |
 |
 |
 |
|
 |
 |
382
Hereditary Genius
converse way, of working from the outside inwards, because the
exact mean is not supposed to have been ascertained, and also
because this method of working would be somewhat the more
convenient, even if we had ascertained the mean. Now, wherever the
mean may lie, it is certain that the chance is 500 to 1, 000 against an
observation being on one specified side of it—say the minus side.
Therefore Column IV. by showing that no observation lies outside the
class — 3.5 sec. tacitly states that it is 500 to 1, 000 (or .500 to 1.00)
against any observation lying between — 3.5 sec. and the mean;
1.500 is therefore written in Column V. opposite — 3.5 sec. Again,
as according to IV. there are only 2 cases in the class — 3.5 sec. it is
(500 — 2 =) 498 to 1, 000 that any observation will lie between class
— 3.0 sec. and the average, and .498 is written in Column V.
opposite to — 3.0. sec. Similarly (498 — 13 =) .486 is written
opposite to — 2.5 sec. and we proceed in this way until we fall within
the observations that form part of the group of the mean, 168 in
number. Our remainder is 68; it ought, strictly speaking, to be equal to
one half of 168, or 84; we therefore may conclude that the mean has
been taken a trifle too high.
A calculation made in exactly the same way, from + 3.5 sec.
inwards to the mean, will take in the other portion of the mean group,
namely, 100. Now we compare our results with Quetelet's Column N,
and see to which of his grades the numbers in our Column V. are
severally equal; the grades in question are written in Column VI. In
proportion as these observations are strictly accordant with the law of
deviation from a mean, so the intervals between the grades in Column
VI. will approach to equality. What they actually are, is shown in
Column VII. We cannot expect the two extreme terms to give results
of much value, because the numbers of observations are too few; but
taking only the remainder into consideration, we find that the average
 |
|
 |
|