Quartiles and interquartile range
Find the median, lower quartile and upper quartile of a data set using one explicit convention — order the data, find the median, split the data into a lower and an upper half (leaving out the median itself when there is an odd number of values), and take the median of each half as the lower and upper quartile — while recognising that other textbooks, calculators and software may use slightly different conventions; calculate the interquartile range (IQR = upper quartile − lower quartile) and interpret it as the spread of the middle half of the data; and compare what the range and the IQR reveal, including their different sensitivity to extreme values
Lesson
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“Quartiles and interquartile range means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Two overlapping circles drawn on paper
- Counter tokens or number cards
Extra for the adult
Worked example. 6 is even and a multiple of 3, so it goes in the overlap.
Optional challenge. For Quartiles and interquartile range, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Quartiles and interquartile range, not mastery.
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1 approach
Quartiles and interquartile range means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Two overlapping circles drawn on paper; Counter tokens or number cards. 1. Say the goal of Quartiles and interquartile range in plain words once. 2. Adult sorts numbers into A, B, both, or neither for “even” and “multiple of 3”. 3. Child sorts three sets into a Venn diagram and counts each region. 4. Fresh check: one fresh item placement in the overlap. Record and stop. Done: three correctly sorted Venn diagrams with region counts. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Secondary
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Secondary supports Quartiles and interquartile range. An adult previews and guides; this is a learning page, not a scored quiz.
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Check understanding
- Using the stated convention, find the median (9), lower quartile (6, the median of 3, 5, 6, 7, 8) and upper quartile (14, the median of 11, 12, 14, 15, 21) of the 11 values 3, 5, 6, 7, 8, 9, 11, 12, 14, 15, 21, giving IQR = 8; and for the 10 values 2, 4, 4, 5, 7, 8, 9, 10, 12, 15, find median 7.5, lower quartile 4 and upper quartile 10, giving IQR = 6
- Interpret an IQR in context (e.g. 'the middle half of the puzzle times lie between 6 and 14 minutes, a spread of 8 minutes') and explain that about half of the values lie between the quartiles, with about a quarter below the lower quartile and about a quarter above the upper quartile
- Show that changing the largest value from 21 to 40 increases the range from 18 to 37 but leaves the IQR at 8, and use this to decide — and justify — whether the range or the IQR gives the better summary of spread for a data set with an extreme value or a long tail
“If your child lines up the times their friends took to finish a puzzle, could they find the middle time and the 'quarter-way' times either side of it — and explain why the gap between those quarter-way times is a better guide to how spread out most of the group is than the gap between the very fastest and slowest?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Data & Statistics
- Age range
- Ages 11–14
Standards