Population and Sample are the two fundamental terms of Inferential Statistics. Inferential Statistics uses probability to draw inferences on the characteristics of Populations using Sample Data. As the size of the population is large, it is often impractical or too expensive to collect data from entire population. Hence a small manageable representative portion of population known as sample is used for the study of Population behavior.

A population consists of all subjects that are being studied. A sample is a subset or a group of subjects selected from the population.

For example, if the study is to involve the spending behavior of employed woman in US, the population will consist of all working woman in US. Hence for the study of spending behavior of working woman, a sample may consist of 250 working woman picked 5 each from 50 cities.
In certain cases for some reason all the subjects in the population will be included in the sample. Such a sample of entire population is known as Census. The characteristics of a population like mean or variance are called parameters and their sample counterparts are known as statistics.
The main purpose of the collecting sample data is to use it draw inferences on the population. Hence the sample selected must be representative of population and the survey conducted needs to be unbiased. Probability sampling methods assures the sample is representative and also provides techniques to estimate errors for the sampling done.

The four types of Probability Sampling are as follows:
  1. Random Sampling: In this method each element of the population is equally likely to be included in the sample. For this purpose chance methods like using a lot or generating random numbers are applied. Suppose you have a list of 20,000 University students. You can pick 200 students from the list generating 200 random numbers from 1 to 20,000.
  2. Stratified Sampling: This method consists of two steps. The Population is first divided into smaller groups which are called Strata on the basis of some characteristic. Then each Strata is then sampled using random techniques.
  3. Cluster Sampling: Cluster Sampling is similar to Stratified Sampling, the clusters are identified geographically.
  4. Systematic Sampling: In systematic sampling a rule or pattern is used to select members from population. The rule used also ensures the randomness of selection. For example, suppose you want to select a sample of 100 surgeons from a list of 10,000. You generate a random number between 1 to 100. You include every 100th element from the list into sample starting from the number generated.

Convenience sampling and Volunteer sampling are examples for non probability sampling. Convenience sampling is the technique of using the easily available sample mainly to reduce cost of sampling. Self-selected are volunteer samples are formed when members from population volunteer to be included in the sample.


Solved Example

Question: Classify the sample as random, systematic, convenience or self selected:
  1. 100 employees of a chain of stores with a total employee strength of 2000 is selected, by picking the lots from the employee details pooled together.
  2. An online Grocery company wishes to make a survey on customer satisfaction. The customers are mailed and asked to participate in the survey, by clicking the link provided.
  3. To make a study on student debts, you issue a questionnaire to 50 students in your class.
  4. Every 10th customer in a Departmental Store is surveyed on a newly introduced Laundry product.

Solution:
 
The first situation is an example for random sampling as the chance method of picking a lot is applied here.
For the second survey, the customer needs to be willing and volunteer to participate in the survey by clicking the link. Hence this is an example for Self selected or volunteer sampling. Third situation is a clear example of convenience sampling. In the fourth case the systematic rule of interviewing the 10th customer is used. Hence this is a case of systematic sampling.