Wednesday, 22 March 2017

Statistics

What is Statistics?

In an effort to present a lot of mathematical formulas, we sometimes lose track of the central idea of the discipline. It is important to remember the big picture when we get too close to the subject.                                                                                                 Let us consider a vast wall that separates our lives from the place where the information resides.It is impossible to see over or around this wall, but every now and then we have the good fortune of having some pieces of data thrown over to us. On the basis of this fragmentary sampled data, we are supposed to infer the composition of the remainder on the other side. This is the aim of statistical inference.                                                                                                                                                                                           The population is usually vast and infinite, whereas the sample is just a handful of numbers.                                                                                                                                                                       There is an enormous possibility for error, of course. If all of the left- handed people. I know also have artistic ability, am I allowed to generalize this to a statement that all left-handed people.In this case I do not have much  data to make my claim ,and my statement should reflect a large possibility of error .Maybe most of my friends are also artists .In this case we say that the sample data is biased because it contains more artists then would be found in a representative sample of  the population. The separate concepts of sample and population for numerically valued data. The sample average is a number that we use to infer the value of the population mean. The average of several numbers is itself a number that we obtain. The population mean, however is on the other side of the imaginary wall and is not observable. In fact, the population mean is almost an unknowable quantity that could not be observed even after a lifetime of study.                                                                                                                                                                                    Statistical inference is the process of generalizing from a sample of data to the larger population. The sample average is a simple statistic that immediately comes to mind. The student t-test is the principal method used to make inferences about the population mean on the basis of the sample average.