Descriptive Statistics vs. Inferential Statistics

Statistics as a subject is broken into two branches: Descriptive Statistics and Inferential Statistics.  It’s really pretty simple.  Descriptive statistics includes collecting, organizing, summarizing, and presenting data.  Inferential statistics is when we “make inferences”, do hypothesis testing, determine relationships, and make predictions. 

For example, let’s say we have data on the incomes of 100 students at a school.  This data can be summarized by finding the average income of those 100 students and we could describe the difference each income is above or below the average.  We could also go into Excel and construct a table with this data in it, or make a pie chart or bar chart, maybe a frequency distribution of the number or proportion of students in each class or range (< 20K, 20K – 30K, etc.).  This is descriptive statistics!

Now if this group is representative of the whole school, we could then estimate and test various hypotheses about these 100 students’ average income to the school as a whole.  These conclusions will be subject to some error, and we could even quantify this probability of error.  We are “inferring”, so this would be inferential statistics.