Consider a set of N types of job within an organisation, which
has a total of M employees. Let where
be
the number of people who have a job of type j with all people
doing the same type of job getting paid the same salary. Then,
clearly;
If interested in the average salary paid and if M is very large the average may be approximated as follows;
where we sample a total of m people from the organisation and is the salary
paid to the
person we sampled. Ordinary random sampling would involve picking
the m people uniformly from the total population of M people in the organisation.
However, another method would be to ensure that the probability of choosing a person
from job type j is the number of people doing job type j divided by the total
number of people, M. This latter idea is just stratified sampling and is an
important and well known sampling technique.