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Quartiles

The quartiles split the sorted numbers into four roughly equal parts. The median is the middle value, and for an even count the average of the two middle ones. The lower quartile is the median of the lower half, and the upper quartile is the median of the upper half. The interquartile range is upper minus lower. It is not affected by one single extreme value at the end, the way the mean and the range are. The method here is the median of each half.

Symbols

Example

Sorted: 1, 3, 5, 7, 9, 11, 13, 15. Median $\dfrac{7 + 9}{2} = 8$.

The lower half gives $Q_1 = \dfrac{3 + 5}{2} = 4$, the upper gives $Q_3 = \dfrac{11 + 13}{2} = 12$.

The interquartile range is $12 - 4 = 8$.

← Range and standard deviation · Growth by a fixed percentage →

Part of Mathematics 2P: Statistics.