In case census data cannot be collected,
statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that
inferences and conclusions can safely extend from the sample to the population
as a whole. An experimental study involves taking measurements of the
system under study, manipulating the system, and then taking additional
measurements using the same procedure to determine if the manipulation has
modified the values of the measurements. In contrast, an observational study does not involve experimental
manipulation.
Two main
statistical methodologies are used in data analysis : Descriptive statistics, which summarizes (Frequency Distribution) data
from a sample using indexes such
as the mean or standard deviation, and inferential statistics, which draws conclusions
from data that are subject to random variation (e.g., observational errors,
sampling variation). Descriptive statistics are most often
concerned with two sets of properties of a distribution (sample or population) : central tendency (or location)
seeks to characterize the distribution's central or typical value, while dispersion (or variability)
characterizes the extent to which members of the distribution depart from its
center and each other. Inferences on mathematical statistics are made under the
framework of probability theory, which deals with the
analysis of random phenomena. To make an inference upon unknown quantities, one
or more estimators are evaluated using the sample.
