The upper quartile of a set of data is the median of the higher half of the data.

The lower quartile of a set of data is the median of the lower half of the data.

**Example 1
**

Find the lower quartile of the following set of data:

3 4 5 5 7 7 7 8 9 10

**Answer**

Divide the data into two halves.

3 4 5 5 7 7 7 8 9 10

The lower quartile is the median of the blue lower half.

3 4 5 5 7

The lower quartile is **5**.

**Example 2
**

Find the upper quartile of the following set of data:

3 4 5 5 7 7 7 8 9

**Answer**

There are an odd number of numbers so divide the data into two halves, ignoring the middle number, 7.

3 4 5 5 7 7 7 8 9

The upper quartile is the median of the red higher half.

7 7 8 9

The median here is the mean of 7 and 8.

The upper quartile is** 7½**.