Page 41 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology - Chapter 2

Smaller Central value Larger
Figure 2-10. Plot of the normal frequency distribution.

Two terms have been introduced in preceding paragraphs without definition.
These are “population” and “sample,” two important concepts in statistics. A pop-
ulation consists of a well-defined set (either finite or infinite) of elements. Com-
monly, these elements are measurements of a specific nature made on items of a
specified type. A sample is a subset of elements taken from a population. A finite
population might consist of all oil wells drilled in Kansas in 1963. An example of
an infinite geologic population might be all possible thin sections of the Tensleep
Sandstone, or all possible shut-in tests on a well. Note in the latter example that
the population includes not only the limited number of tests that have been run,
but also all possible tests that could be run. Tests that actually were performed
may be regarded as a sample of all potential tests.
Geologists typically attach a different meaning to the noun, “sample,” than do
statisticians. A geological sample, such as a “hand sample” of a rock, a “cuttings
sample” from a well, or a “grab sample” or “channel sample” from a mine face, is
a physical specimen and when represented by a quantitative or qualitative value
would be called an observation or event by a statistician. What a statistician de-
scribes as a sample would likely be called a “collection” or “suite of samples” by a
geologist. In this book, we will always use the noun “sample” in the statistical sense,
meaning a set of observations taken from a population. The verb, “to sample,” has
essentially the same meaning for both geologists and statisticians and means the
act of taking observations.
There are several practical reasons why we might wish to take samples. Many
populations are infinite or so vast that it is only possible to examine a subset.
Sometimes the measurements we make, such as chemical analyses, require the
destruction of the material. By sampling, only a small part of the population is
destroyed. Most geological populations extend deep into the Earth and are not
accessible in their entirety. Finally, even if it were possible to observe an entire
population, it might be more efficient to sample. There is always a point beyond
which the increase in information gained from additional observations is not worth
the increase in the cost of obtaining them.
Although all populations exhibit diversity, there is no real population whose
elements vary without limit. Because any population has characteristic proper-
ties and the variation of its constituent members is limited, it is possible to select
a relatively small, random sample that can adequately portray the traits of the
population.