The topics covered thus far have all been aimed at descriptive statistics. That is, describing the data we've collected. There's an entire other field of statistics known as inferential statistics that's aimed at drawing conclusions about a population of individuals based only on a sample of individuals from that population.
Imagine I want to understand what proportion of all Udacity students drink coffee. We know you're busy, and in order to get projects in on time, we assume you all must drink a ton of coffee. I send out an email to all Udacity alumni and current student asking the question, "Do you drink coffee?" For purposes of this exercise, let's say the list contained 100,000 emails. Unfortunately, not everyone responds to my email blast. Some of the emails don't even go through. Therefore, I only receive 5,000 responses.
I find that 73% of the individuals that responded to my email blast say they do drink coffee. Descriptive statistics is about describing the data we have. That is, any information we have and share regarding the 5,000 responses is descriptive. Inferential statistics is about drawing conclusions regarding the coffee drinking habits of all Udacity students only using the data from the 5,000 responses. Therefore, inferential statistics in our example is all about drawing conclusions regarding all 100,000 Udacity students using only the 5,000 responses from our sample.
The general language associated with this scenario is as shown here. We have a population which is our entire group of interest. In our case, the 100,000 students. We collect a subset from this population, which we call a sample. In our case, the 5,000 students. Any numeric summary calculated from the sample is called a statistic. In our case, the 73% of the 5,000 that drink coffee. This 73% is the statistic. A numeric summary of the population is known as a parameter. In our case, we don't know this value, as it's a number that requires information from all Udacity students. Drawing conclusions regarding a parameter based on our statistics is known as inference.