Quartile

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 1/4th of the sample or population.

Thus:
 * first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile
 * second quartile (designated Q2) = median = cuts data set in half = 50th percentile
 * third quartile (designated Q3) = 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.

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

Q1 = 25.5

Q2 = 40

Q3 = 42.5

Example 2:

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

Q1 = 7 + 0.75 (15-7) = 13

Q2 = 36 + 0.5 (39-36) = (39+36)/2 = 37.5

Q3 = 40 + 0.25 (41-40) = 40.25

Calculating quartiles
See Quantile for methods. The quartile is calculated as the 4-quantile.