142 THEORY OF STATISTICS. 
graphical interpolation (¢f. Chap. VII. §§15, 16). Thus for the 
distribution of pauperism, Example ii., we have 
632+-4=158 
Total frequency under 2:25 per cent. =138 
Difference = 20 
Frequency in interval 2:25 — 2-75 = 89 
Whence @, =2-25 + > x 0-5 = 2-362 per cent. 
Similarly we find @, =4-130 0 
Hence O= hse = (0-884 i 
It is left to the student to’ check the value by graphical 
interpolation. 
23. For distributions approaching the ideal forms of figs. 
5 and 9, the semi-interquartile range is usually about two-thirds 
of the standard deviation. Thus for Example ii. we find 
Q@ 0884 
YT =071. 
The distribution of statures, Example iii., gives the ratio 0°68. 
The short series of wage statistics in Example i. could not be 
expected to give a result in very strict conformity with the 
rule, but the actual ratio, viz. 0°61, does not diverge greatly. 
It follows from this ratio that a range of nine times the semi: 
interquartile range, approximately, is required to cover the same 
proportion of the total frequency (99 per cent. or more) as a range 
of six times the standard deviation. 
24. Of the three measures of dispersion, the semi-interquartile 
range has the most clear and simple meaning. It is calculated, 
like the median, with great ease, and the quartiles may be found, 
if necessary, by measuring two individuals only. If, e.g., the 
dispersion as well as the average stature of a group of men 
is required to be determined with the least possible expenditure 
of time, they may be simply ranked in order of height, and the 
three men picked out for measurement who stand in the centre 
and one-quarter from either end of the rank. This measure of 
dispersion may also be useful as a makeshift if the calculation 
of the standard deviation has been rendered difficult or impossible 
owing to the employment of an irregular classification of the 
frequency or of an indefinite terminal class. Such uses are, 
however, a little exceptional, and, generally speaking, the 
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