Question

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.

Answer 1

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**.