Unit 09 · Statistics and Data DisplaysLesson

Day 131Histograms and Intervals

LearnClassworkAnswer keyPDF packet ↗
Standards 6.SP.B.4
LEARNING TARGET

I can construct and interpret a histogram with equal-width bins.

Build the idea

Group numerical values into adjacent, nonoverlapping intervals. Count each observation in exactly one interval, draw touching bars, and label the numerical axis and the frequency axis.

WORKED EXAMPLE 1

Daily reading times in minutes: 3, 16, 11, 3, 1, 19. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes.

Frequencies 3, 0, 1, 2

Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

WORKED EXAMPLE 2

Daily reading times in minutes: 2, 5, 6, 19, 18, 14, 17, 3, 3, 14. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes. Which interval has the greatest frequency? Include ties.

Frequencies 3, 2, 2, 3; greatest: 0–4, 15–19

Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

Your turn

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

  1. Daily reading times in minutes: 11, 7, 14, 11, 7, 8. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes.

  2. Daily reading times in minutes: 14, 13, 7, 11, 9, 3. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes.

  3. Daily reading times in minutes: 10, 9, 2, 15, 15, 6. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes.

  4. Daily reading times in minutes: 13, 4, 3, 10, 1, 15, 15, 16, 18, 5. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes.

  5. Daily reading times in minutes: 10, 10, 10, 0, 4, 19, 0, 0, 4, 17. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes.

  6. Daily reading times in minutes: 3, 6, 7, 3, 18, 2, 2, 13, 12, 3. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes.

  7. Daily reading times in minutes: 16, 12, 7, 19, 5, 14, 2, 18, 11, 16. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes. Which interval has the greatest frequency? Include ties.

  8. Daily reading times in minutes: 8, 7, 8, 17, 7, 6, 17, 8, 7, 2. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes. Which interval has the greatest frequency? Include ties.

  9. Daily reading times in minutes: 10, 11, 12, 4, 5, 14, 12, 16, 0, 14. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes. Which interval has the greatest frequency? Include ties.

  10. Daily reading times in minutes: 17, 15, 18, 8, 8, 9, 14, 1, 4, 11. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes. Which interval has the greatest frequency? Include ties.

Answers and reasoning

Reveal the teacher answer key
  1. Frequencies 0, 3, 3, 0

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  2. Frequencies 1, 2, 3, 0

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  3. Frequencies 1, 2, 1, 2

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  4. Frequencies 3, 1, 2, 4

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  5. Frequencies 5, 0, 3, 2

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  6. Frequencies 5, 2, 2, 1

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  7. Frequencies 1, 2, 3, 4; greatest: 15–19

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  8. Frequencies 1, 7, 0, 2; greatest: 5–9

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  9. Frequencies 2, 1, 6, 1; greatest: 10–14

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  10. Frequencies 2, 3, 2, 3; greatest: 5–9, 15–19

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

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