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A surfer recorded the following values for how far the tide rose, in feet, up the beach over a 15-day period.

5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24

Which of the following histograms best represents the data collected?

A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 2, above 6 to 10 that stops at 4, above 11 to 15 that stops at 2, above 16 to 20 that stops at 4, and above 21 to 25 that stops at 3.
A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 1, above 6 to 10 that stops at 4, above 11 to 15 that stops at 5, above 16 to 20 that stops at 1, and above 21 to 25 that stops at 4.
A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 1, above 6 to 10 that stops at 5, above 11 to 15 that stops at 4, above 16 to 20 that stops at 2, and above 21 to 25 that stops at 3.
A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 1, above 6 to 10 that stops at 3, above 11 to 15 that stops at 4, above 16 to 20 that stops at 4, and above 21 to 25 that stops at 3.

1 answer

To determine which histogram accurately represents the data, we first need to calculate the frequency of tide height measurements within the specified ranges.

The given tide measurements are: 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24

Now we will categorize these measurements into the intervals provided:

  1. Interval 1 to 5:

    • Measurements: 5
    • Frequency: 1

  2. Interval 6 to 10:

    • Measurements: 6, 7, 8, 9
    • Frequency: 4

  3. Interval 11 to 15:

    • Measurements: 11, 12, 13, 14, 15
    • Frequency: 5

  4. Interval 16 to 20:

    • Measurements: 16
    • Frequency: 1

  5. Interval 21 to 25:

    • Measurements: 21, 22, 23, 24
    • Frequency: 4

Now combining these:

  • 1 to 5: 1
  • 6 to 10: 4
  • 11 to 15: 5
  • 16 to 20: 1
  • 21 to 25: 4

Comparing these frequencies to the options provided:

  1. Option 1:

    • 1 to 5: 2
    • 6 to 10: 4
    • 11 to 15: 2
    • 16 to 20: 4
    • 21 to 25: 3
    • Incorrect

  2. Option 2:

    • 1 to 5: 1
    • 6 to 10: 4
    • 11 to 15: 5
    • 16 to 20: 1
    • 21 to 25: 4
    • Correct

  3. Option 3:

    • 1 to 5: 1
    • 6 to 10: 5
    • 11 to 15: 4
    • 16 to 20: 2
    • 21 to 25: 3
    • Incorrect

  4. Option 4:

    • 1 to 5: 1
    • 6 to 10: 3
    • 11 to 15: 4
    • 16 to 20: 4
    • 21 to 25: 3
    • Incorrect

The histogram that best represents the data collected is Option 2.