The aim of this paper is to give a general idea of the difference between the difference forms of statistical analysis. The two main basic areas in the statistical science are Descriptive and Inferential statistics. These branches are tighly associated, but we can clearly differentiate between their roles and objectives.

Descriptive statistics corresponds to essentially the act of defining characteristics of a statistical measurement from a population. Roughly speaking, descriptive statistics includes the use of a observational study of a population, achieved by summarizing and organizing data obtained from a random sample. In order to put the data collected in categories, most statisticians use graphs, charts, tables and standard statistical measurements such as averages, percentiles, and measures of variation.

One of the most common uses of descriptive statistics is in sports (all kind of sports). In fact, baseball statisticians spend a great deal of time and effort examining the data they get from the games and summarizing, categorizing to come up with statements of fact regarding the season. There are many examples that would make this clear. For example in 1948 there were over 600 games played in the American League. To determine who had the best batting average in that season, you would need to take the official score sheets for each game, make a list each batter, determine the results of each time the player is at bat, add the total number of hits and the total number of times the player is at bat in order to calculate with a batting average. The statistics showed that the best player in 1948 was Ted Williams. On the other hand knowing who were the 25 best players at a given season demands a quite more complex, no doubt about it.

The use of modern computers with incredibly powerful applications, and the capability to use many statistical functions on spreadsheet programs such as Excel means that the sophistication of the data we can collect becomes more detailed, and it can be formatted and presented with only a few clicks of the mouse. The imaginary games and sports events developed through the use of a computer software program is fundamentally the collection of big amounts of data and finding correlations in such a way as to be able to compare like activities.

Inferential statistics is the process of choosing and measuring the validity of conclusions about a group based upon data obtained from a sample of the group. Political polling is a great example of inferential statistics. In order to be able to try to predict who the winner of a presidential election is likely to be, typically a sample of a few thousand carefully chosen Americans are asked for their vote intention. From the answers given to this question, statisticians are able to predict, or infer who the general population will vote for with a reasonable confidence level. Clearly, the fundamental elements in inferential statistics are choosing the righ sample of members of the general population will be polled and which questions are asked. Imagine a situation with two candidates, and the polled population, or sample population is asked: Will you give your vote to Candidate X in the next election? the answer will be either yes, no, or undecided. Based on the results you can determine that 51% of the sample group will Give their vote to Candidate X.

Turning to inferential statistics, you can {predict with a certain degree of confidence that Candidate X will win the election. However, we have to be careful because the the sampling techniques may have given rise to incorrect inferences. A classic example is the 1948 Presidential election. Based on a poll taken by the Gallup Organization, President Harry Truman believed he would get approximately 45% of the votes which would imply losing to Thomas Dewey. In fact, as history has proven many times, inferential mistakes happen and Truman won more than 49% of the votes and of course, won the election. This caused a change in some of the sampling techniques and the Gallup Organization has accurately anticipated the Presidential election winner since.