Key takeaway: Quartiles are the three checkpoints Q1, Q2 and Q3 that slice a sorted list into four sections holding roughly the same number of entries.
Grade 66.SP.B.5cStatistics and Data
Definition of Quartiles
The quartiles chop sorted data into four groups of roughly equal size, the way two cuts through a pizza make halves and a third and fourth cut make quarters. The second quartile, Q2, is simply the median. The lower checkpoint Q1 sits in the middle of the bottom half, and the upper checkpoint Q3 sits in the middle of the top half.
Start by lining the numbers up from smallest to largest. Locate the median and split the list there. With an odd count, the median belongs to neither half. Next, pick out the center value of each half. Roughly a quarter of the values lie below Q1, a quarter between Q1 and the median, a quarter between the median and Q3, and a quarter above Q3.
Formula and notation
The three cut points are written
\[Q_1 \le Q_2 \le Q_3\]
where \(Q_2\) equals the median. Together with the minimum and maximum they form the five-number summary used to draw a box plot.
Key facts
- About 25% of the data lies below Q1 and about 75% lies below Q3.
- Q2 is the same number as the median of the whole set.
- If the list has an odd length, set the middle entry aside before halving.
- Quartiles hardly react to extremely large or small values.
Quartiles example
A school store recorded the number of items sold in 11 lunch periods, sorted: 6, 9, 11, 14, 15, 18, 21, 22, 27, 30, 41. Find the three quartiles.
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The median is the sixth value: \(Q_2 = 18\).
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Lower half (without 18): 6, 9, 11, 14, 15. Its middle is the third value, so \(Q_1 = 11\).
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Upper half: 21, 22, 27, 30, 41. Its middle is the third value, so \(Q_3 = 27\).
The quartiles are \(Q_1 = 11\), \(Q_2 = 18\) and \(Q_3 = 27\).
Common mistake
Watch out
Mason finds Q1 by adding one quarter of the range to the minimum: \(6 + \frac{41 – 6}{4} = 14.75\).
Why it is wrong
Quartiles are based on counting values, not on distances along the number line. Q1 is the median of the lower half of the sorted list, which is 11. Using the range ignores where the data actually sit.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Statistics and Data