Quartiles are conceptually similar to the median, except that their are three of them: Q1​,Q2​ and Q3​, dividing the sorted dataset into 4 equal-size parts.

Q2​ is the median, dividing the datapoints in two.

Q1​ is halfway between the first value and the median, at position

Q3​ is halfway between the median and the last value, at position

Note: you will not need to find quartiles by hand on IB exams. These examples are for conceptual understanding only.

Example

Find the quartiles of the dataset [4,2,2,6,3,7,8,9].

First we sort the data: [2,2,3,4,6,7,8,9].

There are n=8 items, so

• Q1​ is at 48+1​=2.25 (average of second and third).

• Q2​ (the median) is at 28+1​=4.5

• Q3​ is at 43(8+1)​=6.75 (average of sixth and seventh)

So the quartiles are:

ie Q1​=2.5, Q2​=5 and Q3​=7.5.

More examples: