How does one sample a population?
Sampling is the term used when one obtains a sample of a population; the number of
members in the sample is called the sample size. As with most mathematical con-
cepts, there are several types of sampling.
Random samplingis a technique involving a group of subjects (the sample) from
a larger group (population); it is a method that reduces the likelihood of bias. In ran-
dom sampling, each individual is chosen by chance, with each member of the popula-
tion having a known (but often unequal) chance of being included in the sample.
Simple random samplingalso involves a group of subjects (the sample) from a
larger group (population), but in this case, each individual is chosen entirely by
chance, with each member of the population having an equal chance of being includ-
ed in the sample. In fact, each member of the population has an equal chance of being
chosen at any stage of the sampling process.
Independent samplingcomprises samples collected from the same (or different)
populations that have no effect on one another. In other words, there is no correlation
between the samples.
Stratified samplingincludes random samples from various subgroups (also called
subpopulation or stratum of the population) chosen to be representative of the whole
population. It is often thought of as a better technique than simple random sampling.
For example, if a sheep farmer wanted to determine the average weight (amount) of
wool gathered from three types of sheep on his farm, he could divide his flock into the
three subgroups and take samples from those groups.
In cluster samplingthe entire population is divided into clusters (groups); then a ran-
dom sampling is taken of the clusters. This technique is used when a complete list of the
population’s members can’t be studied, but a list of population clusters can be gathered.
What is a statisticand a sample statistic?
A statistic is the measure of the items in a random sample. A sample statistic is meant
to give information about a specific population feature (or parameter). For example, if
a sample mean is gathered for a set of data, that would provide information about the
overall population mean. 257
APPLIED MATHEMATICS
What is the major difference between a population and a sample?
A
population is examined to identify its certain characteristics; a sample is
taken in order to make inferences about the characteristics of the popula-
tion from which the sample was drawn.