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Unit 09 · Statistics and Data DisplaysLesson

Day 126Quartiles and Interquartile Range

LearnClassworkAnswer keyPDF packet ↗
Standards 6.SP.A.36.SP.B.5c
LEARNING TARGET

I can calculate quartiles and interquartile range.

01 · LEARN

Build the idea

Sort the data. Find the median, then the median of each half for Q1 and Q3. For an odd count, exclude the overall median from both halves in this course. IQR = Q3 - Q1; range = maximum - minimum.

WORKED EXAMPLE 1

Reading times in minutes are 7, 8, 8, 9, 9, 10. Find Q1, Q3, IQR, and range.

Q1 8, Q3 9; IQR 1 min; range 3 min

Lower half [7, 8, 8] has median 8; upper half [9, 9, 10] has median 9. Subtract Q1 from Q3.

WORKED EXAMPLE 2

Reading times in minutes are 3, 4, 4, 5, 6, 15. Find Q1, Q3, IQR, and range. Explain what IQR describes.

Q1 4, Q3 6; IQR 2 min; range 12 min; IQR is the span of the middle half

Lower half [3, 4, 4] has median 4; upper half [5, 6, 15] has median 6. Subtract Q1 from Q3.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Reading times in minutes are 2, 3, 3, 4, 4, 5. Find Q1, Q3, IQR, and range.

  2. Reading times in minutes are 6, 7, 7, 8, 8, 9. Find Q1, Q3, IQR, and range.

  3. Reading times in minutes are 8, 9, 9, 10, 10, 11. Find Q1, Q3, IQR, and range.

  4. Reading times in minutes are 3, 8, 8, 13, 13, 18. Find Q1, Q3, IQR, and range.

  5. Reading times in minutes are 5, 8, 8, 11, 11, 14. Find Q1, Q3, IQR, and range.

  6. Reading times in minutes are 5, 7, 7, 9, 9, 11. Find Q1, Q3, IQR, and range.

  7. Reading times in minutes are 2, 3, 3, 4, 5, 14. Find Q1, Q3, IQR, and range. Explain what IQR describes.

  8. Reading times in minutes are 5, 6, 6, 7, 8, 17. Find Q1, Q3, IQR, and range. Explain what IQR describes.

  9. Reading times in minutes are 7, 8, 8, 9, 10, 19. Find Q1, Q3, IQR, and range. Explain what IQR describes.

  10. Reading times in minutes are 8, 9, 9, 10, 11, 20. Find Q1, Q3, IQR, and range. Explain what IQR describes.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. Q1 3, Q3 4; IQR 1 min; range 3 min

    Lower half [2, 3, 3] has median 3; upper half [4, 4, 5] has median 4. Subtract Q1 from Q3.

  2. Q1 7, Q3 8; IQR 1 min; range 3 min

    Lower half [6, 7, 7] has median 7; upper half [8, 8, 9] has median 8. Subtract Q1 from Q3.

  3. Q1 9, Q3 10; IQR 1 min; range 3 min

    Lower half [8, 9, 9] has median 9; upper half [10, 10, 11] has median 10. Subtract Q1 from Q3.

  4. Q1 8, Q3 13; IQR 5 min; range 15 min

    Lower half [3, 8, 8] has median 8; upper half [13, 13, 18] has median 13. Subtract Q1 from Q3.

  5. Q1 8, Q3 11; IQR 3 min; range 9 min

    Lower half [5, 8, 8] has median 8; upper half [11, 11, 14] has median 11. Subtract Q1 from Q3.

  6. Q1 7, Q3 9; IQR 2 min; range 6 min

    Lower half [5, 7, 7] has median 7; upper half [9, 9, 11] has median 9. Subtract Q1 from Q3.

  7. Q1 3, Q3 5; IQR 2 min; range 12 min; IQR is the span of the middle half

    Lower half [2, 3, 3] has median 3; upper half [4, 5, 14] has median 5. Subtract Q1 from Q3.

  8. Q1 6, Q3 8; IQR 2 min; range 12 min; IQR is the span of the middle half

    Lower half [5, 6, 6] has median 6; upper half [7, 8, 17] has median 8. Subtract Q1 from Q3.

  9. Q1 8, Q3 10; IQR 2 min; range 12 min; IQR is the span of the middle half

    Lower half [7, 8, 8] has median 8; upper half [9, 10, 19] has median 10. Subtract Q1 from Q3.

  10. Q1 9, Q3 11; IQR 2 min; range 12 min; IQR is the span of the middle half

    Lower half [8, 9, 9] has median 9; upper half [10, 11, 20] has median 11. Subtract Q1 from Q3.

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