MATERIALS ENGINEERING CONCEPTS - Materials for Civil and Construction Engineers - page 28

Bias

(a) (b) (c)

FIGURE 1.18 Exactness of measurements: (a) precise but not
accurate, (b) accurate but not precise, and (c) precise and accurate.

contain precision and bias statements. These statements provide the limits
of acceptable test results variability. Laboratories are usually required to
demonstrate testing competence and can be certified by the American Ma-
terial Reference Laboratory (AMRL).

1.6.1 Sampling
Typically, samples are taken from a lot or population , since it is not practi-
cal or possible to test the entire lot. By testing sufficient samples, it is pos-
sible to estimate the properties of the entire lot. In order for the samples to
be valid they must be randomly selected. Random sampling requires that all
elements of the population have an equal chance for selection. Another im-
portant concept in sampling is that the sample must be representative of the
entire lot. For example, when sampling a stockpile of aggregate, it is impor-
tant to collect samples from the top, middle, and bottom of the pile and to
combine them, since different locations within the pile are likely to have
different aggregate sizes. The sample size needed to quantify the character-
istics of a population depends on the variability of the material properties
and the confidence level required in the evaluation.
Statistical parameters describe the material properties. The mean and
the standard deviation are two commonly used statistics. The arithmetic
mean is simply the average of test results of all specimens tested. It is a mea-
sure of the central tendency of the population. The standard deviation is a
measu r e of the dispersion or spread of the results. The equations for the
mean and standard deviation s of a sample are x

n

x i

a

i = 1

x = (1.15)

n

n

2

1 x i - x 2

1/2

a

i = 1

s = £ ≥ (1.16)

n - 1