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 classintervals
 ; 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 verticals
 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 suggested
 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 classfrequencies.
 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, conventional
 : 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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