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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 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.
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
Q_{1} = 25.5
Q_{2} = 40
Q_{3} = 42.5
Example 2:
Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42
Q_{1} = 7 + 0.75 (15-7) = 13
Q_{2} = 36 + 0.5 (39-36) = (39+36)/2 = 37.5
Q_{3} = 40 + 0.25 (41-40) = 40.25
Calculating quartilesEdit
See Quantile for methods. The quartile is calculated as the 4-quantile.
See alsoEdit
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
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