Page 50 - Petrology of Sedimentary Rocks

This formula simply averages the skewness obtained using the $16 and $84 points with
the skewness obtained by using the $5 and $95 points, both determined by exactly the
same principle. This is the best skewness measure to use because it determines the
skewness of the “tails” of the curve, not just the central portion, and the “tails” are just
where the most critical differences between samples lie. Furthermore it is geometri-
cally independent of the sorting of the sample. Because in the skewness formula a
measure of phi spread occurs both in numerator and denominator, the Sk1 value is a pure
number and should not be written with 41 attached. Skewness values should always be
recorded with a + or-sign to avoid possible confusion.
Symmetrical curves have Sk1 = .OO; those with excess fine material (a tail to the

right) have positive skewness and those with excess coarse material (a tail to the left)
have negative skewness. The more the skewness value departs from .OO, the greater the
degree of asymmetry. The following verbal limits on skewness are suggested: Sk, from
+I.00 to +.30, strongly fine-skewed; +.30 to +.lO, fine-skewed; +.I0 to -.lO, near-
symmetrical, -.I0 to -.30, coarse-skewed; and -.30 to -I .OO, strongly coarse-skewed.
The absolute mathematical limits of the measure are + 1.00 to -1.00, and few curves
have Sk1 values beyond +.80 and -.80.

Measures of Kurtosis or Peakedness

In the normal probability curve, defined by the Gaussian formula, the phi diameter
interval between the $5 and $95 points should be exactly 2.44 times the phi diameter
interval between the $25 and ~$75 points. If the sample curve plots as a straight line on
probabi Ii ty paper (i.e., if it follows the normal curve), this ratio will be obeyed and we
say it has normal kurtosis (1.00). Departure from a straight line will alter this ratio,
and kurtosis is the quantitative measure used to describe this departure from normality.
It measures the ratio between the sorting in the “tails” of the curve and the sorting in
the central portion. If the central portion is better sorted than the tails, the curve is
said to be excessively peaked or leptokurtic; if the tails are better sorted than the
central portion, the curve is deficiently or flat-peaked and platykurtic. Strongly
platykurtic curves are often bimodal with subequal amounts of the two modes; these
plot out as a two-peaked frequency curve, with the sag in the middle of the two peaks
accounting for its platykurtic character. The kurtosis measure used here is the Graphic
Kurtosis, KG, (Folk) given by the formula

This value answers the question, “for a given spread between the $25 and $75 points,
how much is the $5 to $95 spread deficient (or in excess)?” For normal curves, KG =
1.00; leptokurtic curves have KG over 1.00 (for example a curve with KG = 2.00 has
exactly twice as large a spread in the tails as it should have for its $25~$75 spread,
hence is much poorer sorted in the tails than in the central portion); and platykurtic
curves have KG under 1.00 (in a curve with KG = 0.70, the tails have only 0.7 the spread

they should have with a given $25~$75 spread). Kurtosis, like skewness, involves a ratio
of spreads hence is a pure number and should not be written with (I attached.

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