Question

Evelyn surveyed 15 people living in Riverwood and 15 people living in Glenbrook and asked how many people live in their household. She recorded her results in these line plots. Riverwood 1:2 2:2 3:4 4:3 5:1 6:2 7:0 8:1 9:0 10:0 People in household Glenbrook 1:1 2:2 3:2 4:1 5:3 6:2 7:1 8:2 9:0 10:1 People in household Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth. Mean Mean absolute deviation Riverwood 3.7 1.5 Glenbrook

Answer 1

To complete the table, we need to calculate the mean and mean absolute deviation (MAD) for the Glenbrook data.

### Glenbrook Data Summary
The data provided in the line plot for Glenbrook is as follows:

- 1 person: 1 occurrence
- 2 people: 2 occurrences
- 3 people: 2 occurrences
- 4 people: 1 occurrence
- 5 people: 3 occurrences
- 6 people: 2 occurrences
- 7 people: 1 occurrence
- 8 people: 2 occurrences
- 9 people: 0 occurrences
- 10 people: 1 occurrence

### Step 1: Calculate the Mean for Glenbrook

1. **Count the total number of people**:
\[
1(1) + 2(2) + 3(2) + 4(1) + 5(3) + 6(2) + 7(1) + 8(2) + 9(0) + 10(1) = 1 + 4 + 6 + 4 + 15 + 12 + 7 + 16 + 0 + 10 = 65
\]
Total households: \(1 + 2 + 2 + 1 + 3 + 2 + 1 + 2 + 0 + 1 = 15\)

2. **Mean calculation**:
\[
\text{Mean} = \frac{\text{Total number of people}}{\text{Total households}} = \frac{65}{15} \approx 4.33
\]

### Step 2: Calculate the Mean Absolute Deviation (MAD)

1. **Calculate the deviations from the mean**:
- Deviation for 1: \(1 - 4.33 = -3.33\)
- Deviation for 2: \(2 - 4.33 = -2.33\)
- Deviation for 3: \(3 - 4.33 = -1.33\)
- Deviation for 4: \(4 - 4.33 = -0.33\)
- Deviation for 5: \(5 - 4.33 = 0.67\)
- Deviation for 6: \(6 - 4.33 = 1.67\)
- Deviation for 7: \(7 - 4.33 = 2.67\)
- Deviation for 8: \(8 - 4.33 = 3.67\)
- Deviation for 10: \(10 - 4.33 = 5.67\)

2. **Calculate the absolute deviations**:
- Absolute deviation for 1: \(3.33\)
- Absolute deviation for 2: \(2.33\)
- Absolute deviation for 3: \(1.33\)
- Absolute deviation for 4: \(0.33\)
- Absolute deviation for 5: \(0.67\)
- Absolute deviation for 6: \(1.67\)
- Absolute deviation for 7: \(2.67\)
- Absolute deviation for 8: \(3.67\)
- Absolute deviation for 10: \(5.67\)

3. **Calculate the total of absolute deviations**:
\[
\text{Total absolute deviations} = (1 \times 3.33) + (2 \times 2.33) + (2 \times 1.33) + (1 \times 0.33) + (3 \times 0.67) + (2 \times 1.67) + (1 \times 2.67) + (2 \times 3.67) + (0 \times 0) + (1 \times 5.67)
\]
Calculating:
\[
= 3.33 + 4.66 + 2.66 + 0.33 + 2.01 + 3.34 + 2.67 + 7.34 + 0 + 5.67 = 32.25
\]

4. **Calculate the Mean Absolute Deviation (MAD)**:
\[
\text{MAD} = \frac{\text{Total absolute deviations}}{\text{Total households}} = \frac{32.25}{15} \approx 2.15
\]

### Final Results for Glenbrook
- Mean: \(4.3\) (rounded to the nearest tenth)
- Mean Absolute Deviation: \(2.2\) (rounded to the nearest tenth)

### Completed Table
| | Mean | Mean Absolute Deviation |
|---------------|------|-------------------------|
| Riverwood | 3.7 | 1.5 |
| Glenbrook | 4.3 | 2.2 |