Quartiles

Updated 15 Sep 2026

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What it is
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  the three values that divide a sorted data set into 4 equal-sized sections (Q1 = 25th percentile, Q2 = median/50th percentile, Q3 = 75th percentile)
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Position formula (ungrouped data)
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  $\text{Position of } Q_i = \dfrac{i(n+1)}{4}$ for $i = 1, 2, 3$ , applied to sorted data
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  if the position isn't a whole number, the quartile value is interpolated between the two bracketing sorted values
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Example
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  for $n=40$ sorted scores: $Q_1$ falls at position $10.25$ (between the 10th and 11th values), $Q_2$ at position $21.5$ (between the 21st and 22nd), $Q_3$ at position $31.75$ (between the 31st and 32nd)
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Related

Linked references 5