Question
Emma rides the bus to and from school each day. For 10 days, she timed her morning commute. She did the same for her afternoon commute. She recorded her results in these line plots.
Morning
20:0
21:0
22:1
23:3
24:4
25:0
26:1
27:1
28:0
29:0
30:0
Commute time (minutes)
Afternoon
20:0
21:0
22:0
23:0
24:1
25:1
26:2
27:2
28:2
29:1
30:1
Commute time (minutes)
Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth.
Mean Mean absolute deviation
Morning 24 1
Afternoon
Answers
GPT-4o mini
To complete the table for the afternoon commute, we need to calculate the mean and mean absolute deviation (MAD) for Emma's afternoon bus commute times using the data provided.
1. **Data from the Afternoon Commute:**
- 20 minutes: 0 times
- 21 minutes: 0 times
- 22 minutes: 0 times
- 23 minutes: 0 times
- 24 minutes: 1 time
- 25 minutes: 1 time
- 26 minutes: 2 times
- 27 minutes: 2 times
- 28 minutes: 2 times
- 29 minutes: 1 time
- 30 minutes: 1 time
2. **List the Times:**
- We can write down the commute times based on your counts:
- 24: 1 time
- 25: 1 time
- 26: 2 times → 26, 26
- 27: 2 times → 27, 27
- 28: 2 times → 28, 28
- 29: 1 time
- 30: 1 time
So, the commute times are:
- 24, 25, 26, 26, 27, 27, 28, 28, 29, 30
3. **Mean Calculation:**
- Sum of the times:
\[
24 + 25 + 26 + 26 + 27 + 27 + 28 + 28 + 29 + 30 = 24 + 25 + 26 + 26 + 27 + 27 + 28 + 28 + 29 + 30 = 26.5 \text{ (10 data points)}
\]
- Mean:
\[
\text{Mean} = \frac{\text{Sum of the times}}{\text{Total number of times}} = \frac{ 26.5}{10} = 27.6
\]
- Therefore, the mean is **27.6 minutes**.
4. **Mean Absolute Deviation (MAD):**
- First, we calculate the absolute deviations from the mean of 27.6:
- |24 - 27.6| = 3.6
- |25 - 27.6| = 2.6
- |26 - 27.6| = 1.6 (counted twice)
- |27 - 27.6| = 0.6 (counted twice)
- |28 - 27.6| = 0.4 (counted twice)
- |29 - 27.6| = 1.4
- |30 - 27.6| = 2.4
- Now, we can calculate the absolute deviations:
\[
3.6 + 2.6 + 1.6 + 1.6 + 0.4 + 0.4 + 1.4 + 2.4 = 14.8
\]
- Then, average it:
\[
\text{MAD} = \frac{14.8}{10} = 1.48 \text{ (there are 10 data points)}
\]
- Rounding to the nearest tenth gives us MAD of **1.5**.
**Final Table:**
| | Mean | Mean Absolute Deviation |
|----------------|-------|-------------------------|
| Morning | 24 | 1 |
| Afternoon | 27.6 | 1.5 |
1. **Data from the Afternoon Commute:**
- 20 minutes: 0 times
- 21 minutes: 0 times
- 22 minutes: 0 times
- 23 minutes: 0 times
- 24 minutes: 1 time
- 25 minutes: 1 time
- 26 minutes: 2 times
- 27 minutes: 2 times
- 28 minutes: 2 times
- 29 minutes: 1 time
- 30 minutes: 1 time
2. **List the Times:**
- We can write down the commute times based on your counts:
- 24: 1 time
- 25: 1 time
- 26: 2 times → 26, 26
- 27: 2 times → 27, 27
- 28: 2 times → 28, 28
- 29: 1 time
- 30: 1 time
So, the commute times are:
- 24, 25, 26, 26, 27, 27, 28, 28, 29, 30
3. **Mean Calculation:**
- Sum of the times:
\[
24 + 25 + 26 + 26 + 27 + 27 + 28 + 28 + 29 + 30 = 24 + 25 + 26 + 26 + 27 + 27 + 28 + 28 + 29 + 30 = 26.5 \text{ (10 data points)}
\]
- Mean:
\[
\text{Mean} = \frac{\text{Sum of the times}}{\text{Total number of times}} = \frac{ 26.5}{10} = 27.6
\]
- Therefore, the mean is **27.6 minutes**.
4. **Mean Absolute Deviation (MAD):**
- First, we calculate the absolute deviations from the mean of 27.6:
- |24 - 27.6| = 3.6
- |25 - 27.6| = 2.6
- |26 - 27.6| = 1.6 (counted twice)
- |27 - 27.6| = 0.6 (counted twice)
- |28 - 27.6| = 0.4 (counted twice)
- |29 - 27.6| = 1.4
- |30 - 27.6| = 2.4
- Now, we can calculate the absolute deviations:
\[
3.6 + 2.6 + 1.6 + 1.6 + 0.4 + 0.4 + 1.4 + 2.4 = 14.8
\]
- Then, average it:
\[
\text{MAD} = \frac{14.8}{10} = 1.48 \text{ (there are 10 data points)}
\]
- Rounding to the nearest tenth gives us MAD of **1.5**.
**Final Table:**
| | Mean | Mean Absolute Deviation |
|----------------|-------|-------------------------|
| Morning | 24 | 1 |
| Afternoon | 27.6 | 1.5 |