How do inferential statistics describe data differently than descriptive statistics?

Answer 1

The term "descriptive statistics" generally refers to such information as the mean (average), median (midpoint), mode (most frequently occurring value), standard deviation, highest value, lowest value, range, and etc. of a given data set. It is a loosely used term, and not always meant to contrast with inferential statistics as the question implies.

But in the context of the question, descriptive statistics would be information that pertains only to the data that has actually been collected. In the case of an instructor calculating an average grade for a class, for example, the collected data would most likely be the only point of interest. Thus, descriptive statistics would be enough.

However, it is more common for a researcher to use a sample of collected data to make inferences and draw conclusions about a larger group (or "population") that the sample represents. For example, if you wanted to know the average age of users of this site, it would be unrealistic to question every singe user. So you might question a small sample and then extend that information to all users.

But if you found the average age in your sample to be 40, you could not immediately assume that 40 is the average for all users. You would need to use inferential statistics to calculate an estimate of how accurately your data represents the larger group. The most common way to do this is to calculate a standard error, which will produce a range within which the population average most likely (but not definitively) lies.

Therefore, in the simplest description (inferential statistics are also a part of much more powerful tests outside of this answer), descriptive statistics refer only to a sample while inferential statistics refer to the larger population from which the sample was drawn.