Question

Ross surveyed a sample of first-time surfers and a sample of experienced surfers at the Island Wave surf shop. He recorded their surfboard lengths in these line plots.
First-time
6:0

7:0

8:0

9:2

10:0
10.1:2
11:1
Surfboard length (feet)
Experienced
6:1
6.1:1
7:1
7.1:2
8:1
8.1:1
9:1

10:0

11:0
Surfboard length (feet)
Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth.
Mean Mean absolute deviation
First-time 10
Experienced
0.8

Answer 1

To calculate the mean and mean absolute deviation (MAD) for both the first-time surfers and the experienced surfers based on the surfboard lengths, we will follow these steps:

1. **First-time surfers:**
- Data points based on the line plot:
- 6 feet: 0
- 7 feet: 0
- 8 feet: 0
- 9 feet: 2
- 10 feet: 0
- 10.1 feet: 2
- 11 feet: 1

- Actual data for first-time surfers:
- 9, 9, 10.1, 10.1, 11 (from the counts)

- Calculating the mean:
\[
\text{Mean} = \frac{\sum \text{data points}}{\text{number of data points}} = \frac{9 + 9 + 10.1 + 10.1 + 11}{5}
\]
\[
= \frac{49.2}{5} = 9.84 \approx 9.8 \text{ (rounded to the nearest tenth)}
\]

- Calculating the absolute deviations from the mean:
- \(|9 - 9.84| = 0.84\)
- \(|9 - 9.84| = 0.84\)
- \(|10.1 - 9.84| = 0.26\)
- \(|10.1 - 9.84| = 0.26\)
- \(|11 - 9.84| = 1.16\)

- Mean absolute deviation:
\[
\text{MAD} = \frac{0.84 + 0.84 + 0.26 + 0.26 + 1.16}{5} = \frac{3.36}{5} = 0.672 \approx 0.7 \text{ (rounded to the nearest tenth)}
\]

2. **Experienced surfers:**
- Data points based on the line plot:
- 6 feet: 1
- 6.1 feet: 1
- 7 feet: 1
- 7.1 feet: 2
- 8 feet: 1
- 8.1 feet: 1
- 9 feet: 1

- Actual data for experienced surfers:
- 6, 6.1, 7, 7.1, 8, 8.1, 9 (from the counts)

- Calculating the mean:
\[
\text{Mean} = \frac{6 + 6.1 + 7 + 7.1 + 8 + 8.1 + 9}{7} = \frac{43.3}{7} \approx 6.186 \approx 6.2 \text{ (rounded to the nearest tenth)}
\]

- Calculating the absolute deviations from the mean:
- \(|6 - 6.186| = 0.186\)
- \(|6.1 - 6.186| = 0.086\)
- \(|7 - 6.186| = 0.814\)
- \(|7.1 - 6.186| = 0.914\)
- \(|8 - 6.186| = 1.814\)
- \(|8.1 - 6.186| = 1.914\)
- \(|9 - 6.186| = 2.814\)

- Mean absolute deviation:
\[
\text{MAD} = \frac{0.186 + 0.086 + 0.814 + 0.914 + 1.814 + 1.914 + 2.814}{7} = \frac{7.6}{7} \approx 1.086 \approx 1.1 \text{ (rounded to the nearest tenth)}
\]

### Final Table:
| | Mean | Mean Absolute Deviation |
|---------------|------|------------------------|
| First-time | 9.8 | 0.7 |
| Experienced | 6.2 | 1.1 |

So the completed table is:
- **First-time:** Mean = 9.8, Mean Absolute Deviation = 0.7
- **Experienced:** Mean = 6.2, Mean Absolute Deviation = 1.1