Statistics can be broken into two basic types.
The first is known as descriptive statistics. This is a
set of methods to describe data that we have collected.
Ex. Of 350 randomly selected people in the town of Luserna, Italy, 280 people had the last name Nicolussi. An example of descriptive statistics is the following statement :
Ex. On the last 3 Sundays, Henry D. Carsalesman sold 2, 1, and 0 new cars respectively. An example of descriptive statistics is the following statement :
These are both descriptive statements because they can actually
be verified from the information provided.
The second type of statistics in inferential statistics.
This is a set of methods used to make a generalization, estimate,
prediction or decision.
Ex. Of 350 randomly selected people in the town of Luserna, Italy, 280 people had the last name Nicolussi. An example of inferential statistics is the following statement :
We have no information about all people living in Italy,
just about the 350 living in Luserna. We have taken that information
and generalized it to talk about all people living in Italy.
The easiest way to tell that this statement is not descriptive
is by trying to verify it based upon the information provided.
Ex. On the last 3 Sundays, Henry D. Carsalesman sold 2, 1, and 0 new cars respectively. An example of inferential statistics are the following statements :
Although this statement is true for the last 3 Sundays, we do
not know that this is true for all Sundays.
There is nothing in the information given that tells us that this
statement is true.
Again, this statement is not verifiable based upon the information
provided.
The major use of inferential statistics is to use information
from a sample to infer something about a population.