On inheritance of hair and eye colour / by John Brownlee.

  • Brownlee, John, 1868-1927.
Date:
[1913]
Catalogue details

Licence: In copyright

Credit: On inheritance of hair and eye colour / by John Brownlee. Source: Wellcome Collection.

Provider: This material has been provided by The University of Glasgow Library. The original may be consulted at The University of Glasgow Library.

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    that not only are the errors independent, but positive and negative errors of like size occur with equal frequency. But there is no necessity iu nature for the odds to be equal on both sides. If we take a six-sided die, for instance, six can only be thrown once on the average for five times the other numbers are thrown. If we take n dice, then the proportion in which the sixes will turn up are given by the terms of the expression n sixes turning up only once in 6 times. 7. Cei'tain quantities are specially important. The mean of the obser- vations is one of these, this being regularly used in all statistical work for purposes of comparison. The next most important is the standard devia- tion, which is the square root of the second moment taken round a vertical line through the mean, and which is equivalent in dynamics to the radius of gyration. The mean may be defined as the average value of the quantities con- sidered. It is obtained by multiplying the size of each unit by the number of times it occurs, taking the sum of all such values and dividin this sum by the total number of units considered. Thus, if the size occurs VI times, and the size b, n times, the mean is given by ma -)- nb Hi —|— It If more sizes exist, and the sum be denoted by 2 as usual, then the mean . . , 2 ma IS given by 2 rn 8. In the case of the mean can readily be found. Suppose the expression expanded as before, and suppose that the frequency value ]i^ corresponds to the value of the size h, andp“iry to the value (h-\-a), et(^, where a is the increase of value in passing from one term to the next, then we have at once, as corresponding to the expression 2'«a, p’^ h -j- q(h -|- «) + p —^ q'^ (A -f- 2a) -j- . . . . X which equals A + np^~^q A -f- p’'”^ q^ h . -j- nap By -|- n(n - l)ap“2^2 ^ ap°-~^ q^ . — Hp + y) + ’*“7 (p + iT ’ Mean = P + V) + + <]T~^ (B + q) — li -\- H aq since {p -f- <]) = 1. fcD e