. Genetics in relation to agriculture. Livestock; Heredity; Variation (Biology); Plant breeding. THE STATISTICAL STUDY OF VARIATION 45 The coefficients that appear are what they are because precisely tliose combinations are possible. There is but one combination in which there are no heads, there are four combinations consisting of 1 head and 3 tails, there are six combinations possible of 2 heads and 2 tails, there are four combinations of 3 heads and 1 tail, and again but 1 with no tails. But this is simpljr the expansion of the l)inomial (1 + 1)'. The prob- ability that when n coins are tos
. Genetics in relation to agriculture. Livestock; Heredity; Variation (Biology); Plant breeding. THE STATISTICAL STUDY OF VARIATION 45 The coefficients that appear are what they are because precisely tliose combinations are possible. There is but one combination in which there are no heads, there are four combinations consisting of 1 head and 3 tails, there are six combinations possible of 2 heads and 2 tails, there are four combinations of 3 heads and 1 tail, and again but 1 with no tails. But this is simpljr the expansion of the l)inomial (1 + 1)'. The prob- ability that when n coins are tossed exactly m of them will be heads and the rest tails, therefore, is given by the ni + 1st term of the binomial expansion (1 + 1)". When n is small a symmetrical frequency polygon is obtained somewhat similar to that given by plotting the yields of individual oat plants. When n is very large more points are obtained. -3ir -2(1 -IT 0, M Qjir 2(r 3(1 Fig. 19.—A normal curve or curve of error showing the relationship between the quar- tile, , the probable error of a single variate, and the standard deviation. Q = .6745(t. In this curve the mode, median and mean are identical. The quartile equals the probable error of a single variate because by definition one-half of the variates lie within its limits; therefore the chances are even that any variate lies within or without it. The proportions of variates within certain areas of the curve are as follow^s: within M + Q, 50 % of the variates, within M + <r, % of the variates, within M + 2Q, % of the variates, within M + 2cr, % of the variates, within M + 3Q, % of the variates, within M ± 3<t, % of the variates. and the polygon becomes a regular curve, the normal probabihty curve or curve of error. It is called the "curve of error" because if a refined set of direct measurements are made and plotted as abscissas, the corre- sponding ordinates represent the frequencies or probabilit
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