Sampling
A Population is a collection of all the data points being studied. For example, if we are studying the annual incomes of all the people in India, then the population under study would consist of data points representing the incomes of each and every person in India.
A Sample is a part of a population.
In the above example the following would be some possible samples:
The annual incomes of all the people in Mumbai.
The annual incomes of all the people in India over forty years of age.
Your own annual income (assuming you are in India).
The annual incomes of the first hundred people mentioned in your telephone directory.
Samples, being smaller in size than their population, are easier to study. Hence, if we want to draw some conclusions about a population, we can do so by studying a suitable sample of the population.
Example
In which of the following cases do the samples appear to be suitable for arriving at conclusions about the corresponding populations?
1.
Population
:
Annual income of every person in India.
Sample
Annual income of randomly selected persons in Mumbai.
Answer
Not a representative sample because it is Mumbai.
2.
Likely customers for an exclusive credit card scheme.
Regular commuters on public transport buses.
May not be a representative sample because regular commuters on public transport buses may not be in the income range high enough to support an exclusive credit card holding.
The following notations are used to denote population parameters and sample statistics.
Characteristic
Parameter
Statistic
Size
Mean
Standard Deviation
Proportion
N
μ
σ
p
n
S