In order to get the information about a population, in many cases, we can not have the information of all the elements of this population because of limit of resources (human, finance, time, ...), or other reasons. Therefore, we take a sample from this population, realize observations, measurements, calculations, analysis and after that generalize the results to the population.

In statistics, this process is known as estimation.

However, because of the variations in population, errors in the collection and processing of data, we have to use scientific methods in order that the estimation is highly confident.

For a population, estimated parameter can be mean, standard deviation, proportion, median, mode, ... For two or more populations, we can estimate difference of means, difference of proportions, ratio of variance, ... We can estimate other properties of population such as normality of data, independence of of variables, ...

But the most popular ones are mean, proportion, and variance (or standard deviation).

There are many samples can be drawn from a population, therefore the value of estimated parameter varies from sample to sample. So we can consider it as a random variable, and this variable has a certain distribution.

Two main types of estimation is point estimate and interval estimate. In the first type we use a specific value to estimate the parameter. In the second type, we use an interval or range of value to estimate the parameter. Depend on the context, we choose one (or both) method to apply.

Considering parameter `alpha` of the population, having to be estimated. We take a sample from this population and determine corresponding statistic `a`. Because of the variation of population and because there are many samples can be drawn from this population, the value of `a` varies.

The estimate is unbiased when:

`bar a=alpha`(1)

If this condition can not satisfied, the estimate is biased.

Standard deviation of estimated parameter is also known as standard error of this parameter.