THEORY OF STATISTICS. 
giving the distribution of head-breadths for 1000 men, will serve 
as an example. 
TABLE Y.—Showing the Frequency-distribution of Head-breadths for Students 
at Cambridge. Measurements taken to the mearest tenth of am inch. 
(Cited from W. R. Macdonell, Biometrika, i., 1902, p. 220.) 
Number of Number of 
Ee Men with said Rng Men with said 
: Head-breadth. E Head-breadth. 
55 3 6°3 99 
56 12 6-4 37 
5-7 43 65 15 
58 80 66 12 
59 131 67 3 
60 236 6°8 2 
61 185 RoC 
62 142 Total 1000 
Taking a piece of squared paper ruled, say, in inches and tenths, 
mark off along a horizontal base-line a scale representing class- 
intervals ; a half-inch to the class-interval would be suitable. 
Then choose a vertical scale for the class-frequencies, say 50 
observations per interval to the inch, and mark off, on the 
verticals or ordinates through the points marked 55, 56, 5-7 
. . . . at the centres of the class-intervals on the base-line, heights 
representing on this scale the class-frequencies 3, 12, 43. . . . 
The diagram may then be completed in one of two ways: (1) 
as a frequency-polygon, by joining up the marks on the ver- 
ticals by straight lines, the last points at each end being joined 
down to the base at the centre of the next class-interval (fig. 1); 
or (2) as a column diagram or histogram (to use a term sug- 
gested by Professor Pearson, ref. 1), short horizontals being drawn 
through the marks on the verticals (fig. 2), which now form the 
central axes of a series of rectangles representing the class- 
frequencies. The student should note that in any such diagram, 
of either form, a certain area represents a given number of 
observations. On the scales suggested, 1 inch on the horizontal 
represents 2 intervals, and 1 inch on the vertical represents 50 
observations per interval: 1 square inch therefore represents 
50x 2=100 observations. The diagrams are, however, con- 
ventional : the whole area of the figure is correct in either case, 
but the area over each interval is not correct in the case of the 
frequency-polygon, and the frequency of each fraction of any 
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