Page 53 - Petrology of Sedimentary Rocks

better than any other method if the sediment is bimodal. Or, one may plot as a contour
map the diameter of the largest particle in the sample. Try new methods all the time.

Measures of Average Size and Standard Deviation

Mode, Median and Mean. In the left-hand figure, both curves have a mode at about 2@,
but B has a much finer median. The Graphic Mean (which is the average of the three
heavy dots at the 16, 50, and 84 percentiles) is about 2.24 for A and about 4.2~ for B. In
the right-hand figure, B has a much coarser median and mode, but actually is finer if
you consider the entire sediment; the Graphic Mean for A would be about (0.7 + 2.4 +
2.6)/3, or I .Y$, and for curve B would be about (1.4 + I .7 + 4. I )/3, or 2.4+. The Mean
gives the best overall indication of average size; the mode is of real value, but the
median is not a good measure.

Primary Mode This histogram illustrates the difference between
c Secondary Mode the several modes, at of average size. 8.30. there
Note
measures
2.54
and
The
are
two
about
r-l Median I median has half the sample finer and half the
sample coarser than itself; the left four columns
total 50% of the sample so the median is 4.0$.
The $I Mean, computed by the method of mo-
ments, is based on the entire curve (5 x 0.50
0 1234 5 6 7 8 9 10 + IO x l.5$ + 25 x 2.5~). . . . . I3 x 8.54 + 6 x
0 9.5@)/100; the 4 Mean is thus 4.7+. The Graphic
Mean, which is a rapid and close approximation to
the $ Mean, is also 4.74 but this must be found on
the cumulative curve. Changing the 6-74, grade to
16% and the 8-Y@ grade to 2%, will affect the
means but will not at all affect the primary mode
or median (prove this for yourself).

Cumulative and Frequency (dashed) curves for
well-sorted sediment (A) and poorly sorted sedi-
ment (B). In the well-sorted sediment, the cumu-
16 lative curve is much steeper, the frequency curve
is much higher and much less spread out, and the
range between I6 and 84 percentiles (which equals
2a) is much smaller, hence the standard deviation
is much smaller.

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