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Grade 6 · lesson 3 of 4

Use Quartiles and Interquartile Range

Sort the supplied eight-value record, find the medians of its lower and upper four values, then subtract Q1 from Q3.

About 25 minutes, plus any extended practice

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Supplied materials

  • Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
  • Supplied worked-case record: For 1,2,3,4,6,7,8,9, Q1=(2+3)/2=2.5 and Q3=(7+8)/2=7.5.
  • All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Quartiles split ordered data into lower and upper portions. This lesson defines Q1 as the median of the lower half and Q3 as the median of the upper half, excluding a lone overall median for odd counts. Other conventions can differ. IQR=Q3−Q1 describes the middle half’s spread, not the overall range.

Sort the supplied eight-value record, find the medians of its lower and upper four values, then subtract Q1 from Q3. Record minimum, Q1, median, Q3, maximum for a box plot. Use the stated quartile convention consistently.

Write the quartile convention before comparing results. IQR is Q3 minus Q1, not maximum minus minimum. Split the ordered record into lower and upper halves and mark their middle pairs.

  1. Split the ordered record into lower and upper halves and mark their middle pairs.
  2. Work through the supplied example and label what each number or attribute represents.
  3. Sort the supplied eight-value record, find the medians of its lower and upper four values, then subtract Q1 from Q3.
  4. Answer the check, then try the three changed-input practice questions and explain one correction.
Worked example

See the method in action

For 1,2,3,4,6,7,8,9, Q1=(2+3)/2=2.5 and Q3=(7+8)/2=7.5. IQR is five. The median is five and overall range eight. The box stretches from 2.5 to 7.5; whiskers reach one and nine for this simple full-range exercise. Write the quartile convention before comparing results. IQR is Q3 minus Q1, not maximum minus minimum. Split the ordered record into lower and upper halves and mark their middle pairs.

Your turn

Check your reasoning

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Helpful tips
  • Write the quartile convention before comparing results.
  • IQR is Q3 minus Q1, not maximum minus minimum.
Using medians of lower and upper halves, find IQR for [1, 2, 3, 5, 6, 8, 9, 10].

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

6

For eight ordered values, Q1 averages lower-half middle values and Q3 averages upper-half middle values. The result is 6.

Take it further

For 2,3,4,5,9,10,11,12, Q1=3.5,Q3=10.5,IQR=7,median=7.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. Using medians of lower and upper halves, find IQR for [2, 3, 4, 6, 7, 9, 11, 13].
Need a hint?
  • Write the quartile convention before comparing results.
  • IQR is Q3 minus Q1, not maximum minus minimum.
2. Using medians of lower and upper halves, find IQR for [0, 1, 2, 3, 5, 6, 7, 8].
Need a hint?
  • Write the quartile convention before comparing results.
  • IQR is Q3 minus Q1, not maximum minus minimum.
3. Using medians of lower and upper halves, find IQR for [1, 3, 5, 7, 9, 11, 13, 15].
Need a hint?
  • Write the quartile convention before comparing results.
  • IQR is Q3 minus Q1, not maximum minus minimum.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

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