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13
Thus the average stature of girls in the schools of Group B at the age of 8 last birthday was 121*2 cm.,
the number measured N = 580, and the standard deviation σ = 6"2626, the value of 3 σ/N is therefore
therefore .8. The range of stature within which subsequent averages might be expected to fall is
1212 + .8, that is from 1204 to 122 cm. Similarly the range of weight will be 22.8 to 23.6 kilos.
Taking the averages 1212 and 23-2 as the centre and the limits as the angles a rectangle has been
plotted out which shows the area within which it is 1,000 to 1 all subsequent averages should
fall. Similar rectangles are drawn for other ages and groups. When the edges of such a rectangle
Diagram II.
do not overlap those of another rectangle belonging to the same age group it may be definitely
concluded that some cause other than chance has been responsible for the differences observed.
When they do overlap chance is not definitely excluded, though this does not prove that no other
explanation is possible.
In the diagrams the dimensions of the children in the schools of group A are represented by rectangles
with dotted outlines, group B with continuous lines and group C with dot and dash. When,
as sometimes occurs, the rectangle of one age group overlaps that of another age group, the differences
must not necessarily be taken as due to chance, since the material, that is children at different ages,