There are two types of statistics.  The first is called descriptive statistics.  Descriptive statistics is defined as using statistical methods to describe or summarize a collection of data.  It quantitatively describes a collection of data in a broad sense. Descriptive statistics are not developed on the basis of the probability theory, much like how inferential statistics is.  An example of a descriptive statistic could be seen with a population of people. If you are given every piece of information about this group of people, the descriptive statistics would basically be the information that couldn’t be answered with a number.  Therefore that wouldn’t include sample size, age or height. Descriptive statistics would be questions like demographics, sex, etc.  They are answered not with a number but with a word.  Descriptive statistics would also be any number that describes or summarizes a number.  For example a grade point average would be considered a descriptive statistic.  It summarizes the student’s entire college/high school career into one number. Another example of a descriptive statistic would be passing completion of a quarterback in football.  It is the percentage of completed passes compared to passes attempted.  Say I gave you a quarterback passing completion percentage of 60%.  We don’t know whether or not the quarterback threw only ten passes or ten thousand!  We don’t know if they were for tons of yards or only 1 yard a throw!  Were the 40% of throws incomplete or intercepted?  Since it is an overall look at his passing, it would be a descriptive statistic.

The next type of statistic is referred to as inferential statistics.  Inferential statistics is when we draw conclusions from data points that are in a random variation.  Random variation can be accomplished with observational errors or just simply sampling variation.  Inferential statistics is a type of statistic with many names, such as statistical inference, inferential statistics, and statistical induction.  The most common use of statistic inference is with populations of information and we take a random sample of this population. Common uses of statistic inference are with the use of a confidence level, an alpha level, and a confidence interval.   This is mainly the type of statistic you deal with when taking a class in college.  Typically the statistic inference questions use a statistical model with some random variation and concludes with a proposition normally accepting or rejecting a null hypothesis.  They use an estimate, confidence interval, credible interval, and clustering to provide some proof of the conclusion of the null hypothesis.  A common statistical inference question ends with a T score, Z score, or Chi-test either in or out the rejection region.  Then a sentence is given at the end to overall describe what the statistical inference work was done for.  For example- “Since our Z score is within the rejection region, we can conclude that the pill does make a significant difference in test scores therefore we may reject the null hypothesis.”



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