Unknown population & Known sample

 The population is always unknown. Population parameters like population mean µ, population variance σ² and population correlation ρ are also unknown.  Population is a collection of all objects under study. These objects may or may not be human beings. In many situations it is impossible to study the whole population. In other situations we are bound by limited time and money. A sample is a representative part of this population. If this sample is drawn in a proper manner so that it can reflect the variability in the population with respect to the object of study, we can make correct inferences about the population from the sample itself. With data collected from this sample, we compute sample mean, sample variance and sample correlation. These are called sample statistics. We want the sample mean to be as close as possible to population mean, sample variance to be as close as possible to the population variance and sample correlation to be as close as possible to population correlation.

Unknown population & Known sample – Example

The following example can illustrate the concept of unknown population and known sample.

A company wants to know the efficacy of medicine B that is being sold currently in the market.

Population: It is the collection of all individuals in the world who are prescribed medicine B. The details of all individuals taking medicine B are unknown. It will require lot of time and money to know about all these individuals. So it is impossible to know the population. Proportion of people cured from a disease after the use of medicine B in the whole population is unknown. This is denoted by π. This is a population parameter.

But we want to estimate π!

Sample: With a prior knowledge of all the age groups using this medicine we can select a sample of 20 individual who have been taking this medicine. We have to do some research in sampling. These 20 people are thoroughly examined and the proportion of people cured from the disease is calculated. This sample proportion p is a sample statistics. With this p (known) we are estimating (unknown) π.

We are estimating π with p!