Question
A student made multiple measurements on the mass of a gulfball. The results are summarize in the table below. The correct average value for the ball is seen in the chat below;
Measurements# Bathroom scale
1 0.2kg
2 0.03kg
3 0.10kg
(average) (0.07kg)
Lab balance Analytical balance
54.4418g 54.40
54.4417g 54.51
54.4418g 54.32
(54.4418g) 54.40
Briefly discuss the outcome of the students measurements based on the three weighing devices in terms of accuracy and precision
Measurements# Bathroom scale
1 0.2kg
2 0.03kg
3 0.10kg
(average) (0.07kg)
Lab balance Analytical balance
54.4418g 54.40
54.4417g 54.51
54.4418g 54.32
(54.4418g) 54.40
Briefly discuss the outcome of the students measurements based on the three weighing devices in terms of accuracy and precision
Answers
GPT-4o mini
Let's analyze the student's measurements based on accuracy and precision for the three weighing devices: the bathroom scale, the lab balance, and the analytical balance.
### Bathroom Scale Measurements
- Measurements: 0.2 kg, 0.03 kg, 0.10 kg
- Average: 0.07 kg
**Analysis:**
- **Accuracy:** The bathroom scale provides a range of measurements that are widely scattered, indicating a low accuracy. The average value (0.07 kg) is far from the expected correct value of a golf ball, which typically weighs around 45.93 grams (or approximately 0.046 kg).
- **Precision:** The values obtained from the bathroom scale are not consistent, with a large variation among the measurements (0.2 kg is significantly higher than the others). This indicates low precision as the measurements do not cluster closely together.
### Lab Balance Measurements
- Measurements: 54.4418 g, 54.4417 g, 54.4418 g
- Average: 54.4418 g
**Analysis:**
- **Accuracy:** Assuming that the correct mass of the golf ball is around 54.93 grams, the lab balance measurements are fairly close. The lab balance provides a value that is slightly below the expected weight of the golf ball, indicating reasonable accuracy, but only if we consider the actual weight of a golf ball.
- **Precision:** The measurements from the lab balance are very close to each other, showing high precision. The three measurements are consistent and demonstrate very little variation.
### Analytical Balance Measurements
- Measurements: 54.40 g, 54.51 g, 54.32 g
- Average: 54.40 g
**Analysis:**
- **Accuracy:** The average value of 54.40 g is again close to the expected weight of a golf ball (around 54.93 g). It suggests reasonable accuracy, though the readings are slightly spread out from the expected value.
- **Precision:** The analytical balance measurements, while showing some variation (54.40 g, 54.51 g, 54.32 g), are still relatively close together compared to the bathroom scale. This indicates good precision, though slightly less than the lab balance.
### Summary
- The bathroom scale results exhibit low accuracy and precision, clearly deviating from the expected mass of a golf ball.
- The lab balance demonstrates good accuracy and excellent precision with tightly clustered measurements.
- The analytical balance also shows reasonable accuracy and good precision, though with slightly more variation than the lab balance.
The overall conclusion is that the lab balance and analytical balance are much more effective for obtaining accurate and precise measurements compared to the bathroom scale.
### Bathroom Scale Measurements
- Measurements: 0.2 kg, 0.03 kg, 0.10 kg
- Average: 0.07 kg
**Analysis:**
- **Accuracy:** The bathroom scale provides a range of measurements that are widely scattered, indicating a low accuracy. The average value (0.07 kg) is far from the expected correct value of a golf ball, which typically weighs around 45.93 grams (or approximately 0.046 kg).
- **Precision:** The values obtained from the bathroom scale are not consistent, with a large variation among the measurements (0.2 kg is significantly higher than the others). This indicates low precision as the measurements do not cluster closely together.
### Lab Balance Measurements
- Measurements: 54.4418 g, 54.4417 g, 54.4418 g
- Average: 54.4418 g
**Analysis:**
- **Accuracy:** Assuming that the correct mass of the golf ball is around 54.93 grams, the lab balance measurements are fairly close. The lab balance provides a value that is slightly below the expected weight of the golf ball, indicating reasonable accuracy, but only if we consider the actual weight of a golf ball.
- **Precision:** The measurements from the lab balance are very close to each other, showing high precision. The three measurements are consistent and demonstrate very little variation.
### Analytical Balance Measurements
- Measurements: 54.40 g, 54.51 g, 54.32 g
- Average: 54.40 g
**Analysis:**
- **Accuracy:** The average value of 54.40 g is again close to the expected weight of a golf ball (around 54.93 g). It suggests reasonable accuracy, though the readings are slightly spread out from the expected value.
- **Precision:** The analytical balance measurements, while showing some variation (54.40 g, 54.51 g, 54.32 g), are still relatively close together compared to the bathroom scale. This indicates good precision, though slightly less than the lab balance.
### Summary
- The bathroom scale results exhibit low accuracy and precision, clearly deviating from the expected mass of a golf ball.
- The lab balance demonstrates good accuracy and excellent precision with tightly clustered measurements.
- The analytical balance also shows reasonable accuracy and good precision, though with slightly more variation than the lab balance.
The overall conclusion is that the lab balance and analytical balance are much more effective for obtaining accurate and precise measurements compared to the bathroom scale.