In a number list, quartiles are the numbers that divide the list into quarters (4 equal parts).

In order to get the quartiles, you first put the list of numbers in order, then you cut the list into four equal parts, and the quartiles are at the "cuts".

For example: in the number list: 5, 8, 4, 4, 6, 3, 8, or arranged in order as: 3, 4, 4, 5, 6, 8, 8, the quartiles are the cuts at 4, 5, and 8, to cut the list into 4 quarters: Q1=4, Q2=5, and Q3=8.

It is also possible that a "cut" is between 2 numbers,a nd in this case, the quartile is the average of the two numbers. For example:

1, 3, 3, 4, 5, 6, 6, 7, 8, 8, Q1=3, Q2=(5+6)/2=5.5, and Q3=7.

Quartiles are useful in showing all the statistically important values of a number list in a "Box and Whisker Plot", like this: