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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 quartilesEdit

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

See alsoEdit

• Interquartile range
• Quantile
• Percentile
• Summary statistics

External linksEdit

• Quartiles - an example how to calculate it
• Free Online Software (Calculator) computes Quartiles for any data set according to 8 different definitions.da:Kvartil

fa:چارک (آمار) fr:Quartilenl:Kwartiel