In descriptive statistics, a

**quartile** is any of the three values which divide the sorted data set into four equal parts, so that each part represents one fourth of the sampled population.

**first quartile** (designated Q_{1}) = **lower quartile** = cuts off lowest 25% of data = *25th percentile* **second quartile** (designated Q_{2}) = *median* = cuts data set in half = *50th percentile* **third quartile** (designated Q_{3}) = **upper quartile** = cuts off highest 25% of data, or lowest 75% = *75th percentile*

The difference between the upper and lower quartiles is called the

*interquartile range*.

One possible rule (employed by the TI-83 calculator boxplot and 1-Var Stats functions) is as follows:

- Use the median to divide the ordered data set into two halves. Do not include the median into the halves.
- The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

The examples below assume this rule. Another possible rule would be to include the median in the halves when calculating the quartiles. This would give significantly different answers to the examples.

**Example 1**
Data Set: 6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36

Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49

**Example 2**
Ordered Data Set: 7, 15, 36, 39, 40, 41

**Example 3**
Ordered Data Set: 1 2 3 4