To begin with there are certain fundamental concepts in this section that span the section and are used throughout statistics. Often a sample is taken and the sample is a subgroup of a larger group, the population. From the sample it is desired to learn about the population. For example, a survey is taken on 200 people living in Bangkok and their opinion about the underground train. Results are published and comments are made about it. Is anyone truly concerned about the specific 200 people in the survey? If 200 people do not like the underground train does it really matter? No. In fact there exist well over 200 people in Bangkok that have never taken the underground train. What people really want to learn from the survey is the general opinion within Bangkok about the underground and to do this a sample of 200 people are surveyed and asked questions. If all 200 people surveyed did not like the underground train, this is of concern only because it leads us to believe that the general populace within Bangkok do not like the underground train and perhaps only a small minority like the train. The sample is almost immediately within our minds extrapolated to the population at large. In this case the population at large is people living in Bangkok. Inferential statistics are used to learn about the population from the sample.
Two common techniques to use a sample to learn about a population that go beyond descriptive statistics are hypothesis testing and confidence intervals. Hypothesis testing is used to test a theory. Confidence intervals are used to obtain a range of values for which you might consider the population mean, μ, to be within. Technically, from a frequentist viewpoint, the population mean is either within the interval or not.