Question

Explain the differences between a sample and a population, and offer example (s) to further illustrate your explanation

Answer 1

Population of individuals or objects consists of all those individuals or objects that are relevant in that particular study. For example, the decennial census is a data set containing information about all persons in the country at that time. The number of people per household as listed in the census data constitutes a population of family sizes.

Note that the elements of the populations are really measures rather than individuals.

On the other hand, a sample is any subset of the population of individuals or objects under study.

For example, consider an experiment aimed at investigating the effect of ozone on the weight gain of rats. Suppose there are a billion rats and we want to know an average weight gain if all of them were exposed to ozone. The obvious problem is that it is impractical to measure one billion rats. In the experiment only 22 rats were exposed to ozone. These 22 rats are an example of what is called a sample.

The population consists of all the elements in the entire group but a sample consists of a handful of items.

When information is collected from all the units of the population,it is known as complete enumeration whereas the information gathered from a sample using various sampling methods or techniques such as simple random sampling, systematic sampling etc is known as sample survey.

In inferential statistics our main aim is to identify the unknown parameter which is based on the population.

The unknown parameter is estimated by drawing a sample of a size smaller than the population by various methods of unbiasedness,maximum likelihood etc.