Answer :
Sure! Let's break down the problem and figure out which team's measurement was the most accurate and which was the most precise. We will compare the given measurements to the later, more reliable measurement of 98.0 meters. Here are the details for each team:
1. Team A:
- Measurement: [tex]\( 96.0 \, \text{m} \pm 2.0\% \)[/tex]
- Error Range: [tex]\( 96.0 \times 0.02 = 1.92 \, \text{m} \)[/tex]
2. Team B:
- Measurement: [tex]\( 100.0 \, \text{m} \pm 0.4 \, \text{m} \)[/tex]
3. Team C:
- Measurement Range: Between [tex]\( 98.2 \, \text{m} \)[/tex] and [tex]\( 98.6 \, \text{m} \)[/tex]
- Average Measurement: [tex]\( \frac{98.2 + 98.6}{2} = 98.4 \, \text{m} \)[/tex]
- Error Range: [tex]\( \frac{98.6 - 98.2}{2} = 0.2 \, \text{m} \)[/tex]
4. Team D:
- Measurement: [tex]\( 102.0 \, \text{m} \)[/tex]
- No error range provided
### Determining Accuracy
Accuracy measures how close each team's measurement is to the actual length of 98.0 meters. We will calculate the absolute error for each team.
- Team A: [tex]\( |98.0 - 96.0| = 2.0 \, \text{m} \)[/tex]
- Team B: [tex]\( |98.0 - 100.0| = 2.0 \, \text{m} \)[/tex]
- Team C: [tex]\( |98.0 - 98.4| = 0.4 \, \text{m} \)[/tex]
- Team D: [tex]\( |98.0 - 102.0| = 4.0 \, \text{m} \)[/tex]
Since Team C’s measurement (0.4 m) is the smallest error, Team C has the most accurate measurement.
### Determining Precision
Precision measures the consistency of the measurements, which is indicated by a smaller error range.
- Team A: [tex]\( 1.92 \, \text{m} \)[/tex]
- Team B: [tex]\( 0.4 \, \text{m} \)[/tex]
- Team C: [tex]\( 0.2 \, \text{m} \)[/tex]
- Team D: Error range is not provided, so it is assumed to be very precise.
From these values, Team D is assumed to be the most precise because no error range was given, suggesting high confidence in their measurement.
### Conclusion:
- Most Accurate Measurement: Team C
- Most Precise Measurement: Team D
I hope this step-by-step explanation helps you understand how to determine which measurements were the most accurate and precise. If you need further clarification, feel free to ask!
1. Team A:
- Measurement: [tex]\( 96.0 \, \text{m} \pm 2.0\% \)[/tex]
- Error Range: [tex]\( 96.0 \times 0.02 = 1.92 \, \text{m} \)[/tex]
2. Team B:
- Measurement: [tex]\( 100.0 \, \text{m} \pm 0.4 \, \text{m} \)[/tex]
3. Team C:
- Measurement Range: Between [tex]\( 98.2 \, \text{m} \)[/tex] and [tex]\( 98.6 \, \text{m} \)[/tex]
- Average Measurement: [tex]\( \frac{98.2 + 98.6}{2} = 98.4 \, \text{m} \)[/tex]
- Error Range: [tex]\( \frac{98.6 - 98.2}{2} = 0.2 \, \text{m} \)[/tex]
4. Team D:
- Measurement: [tex]\( 102.0 \, \text{m} \)[/tex]
- No error range provided
### Determining Accuracy
Accuracy measures how close each team's measurement is to the actual length of 98.0 meters. We will calculate the absolute error for each team.
- Team A: [tex]\( |98.0 - 96.0| = 2.0 \, \text{m} \)[/tex]
- Team B: [tex]\( |98.0 - 100.0| = 2.0 \, \text{m} \)[/tex]
- Team C: [tex]\( |98.0 - 98.4| = 0.4 \, \text{m} \)[/tex]
- Team D: [tex]\( |98.0 - 102.0| = 4.0 \, \text{m} \)[/tex]
Since Team C’s measurement (0.4 m) is the smallest error, Team C has the most accurate measurement.
### Determining Precision
Precision measures the consistency of the measurements, which is indicated by a smaller error range.
- Team A: [tex]\( 1.92 \, \text{m} \)[/tex]
- Team B: [tex]\( 0.4 \, \text{m} \)[/tex]
- Team C: [tex]\( 0.2 \, \text{m} \)[/tex]
- Team D: Error range is not provided, so it is assumed to be very precise.
From these values, Team D is assumed to be the most precise because no error range was given, suggesting high confidence in their measurement.
### Conclusion:
- Most Accurate Measurement: Team C
- Most Precise Measurement: Team D
I hope this step-by-step explanation helps you understand how to determine which measurements were the most accurate and precise. If you need further clarification, feel free to ask!
