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Step-by-step solution for: Solved Accuracy & Precision Worksheet Accuracy: refers to | Chegg.com
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Step-by-step solution for: Solved Accuracy & Precision Worksheet Accuracy: refers to | Chegg.com
It looks like you've uploaded a worksheet titled "Accuracy & Precision Worksheet" with three problems involving density measurements and analysis of accuracy and precision. I'll solve each problem step by step, explaining the concepts and providing clear answers.
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- Accuracy: How close a measurement is to the true or accepted value.
- Precision: How close repeated measurements are to each other (reproducibility).
We will evaluate:
- Accuracy: Compare each trial to the accepted value.
- Precision: Look at how close the trials are to one another.
---
## ✔ Problem 1
Accepted value: 1.24 g/mL
Measurements:
- Trial #1: 1.20 g/mL
- Trial #2: 1.22 g/mL
- Trial #3: 1.22 g/mL
All values (1.20, 1.22, 1.22) are close to 1.24 g/mL, within ±0.04 g/mL.
So, these results are fairly accurate — they are near the true value.
> ✔ Comment on accuracy: The measurements are accurate, as they are all relatively close to the accepted value of 1.24 g/mL.
The values are very close to each other: 1.20, 1.22, 1.22 → small variation.
The difference between the highest and lowest is only 0.02 g/mL.
> ✔ Comment on precision: The results are precise, since the measurements are reproducible and closely clustered.
These results suggest good technique and minimal random error. Possible reasons include:
- Careful use of measuring tools (e.g., graduated cylinder, balance).
- Consistent procedure across trials.
- Minor systematic error (e.g., slight calibration issue), but not major.
> 🟡 Possible cause: A small systematic error (like a slightly miscalibrated scale), but overall good lab practices led to both accurate and precise data.
---
## ✔ Problem 2
Accepted value: 1.15 g/mL
Measurements:
- Trial #1: 0.95 g/mL
- Trial #2: 1.16 g/mL
- Trial #3: 1.06 g/mL
Compare to 1.15 g/mL:
- 0.95 → off by -0.20 g/mL
- 1.16 → off by +0.01 g/mL
- 1.06 → off by -0.09 g/mL
Only one value (1.16) is close; others are significantly off.
> ✘ Comment on accuracy: The results are not accurate — most values are far from the accepted value.
Values: 0.95, 1.16, 1.06 → spread out over 0.21 g/mL range.
They are not close to each other.
> ✘ Comment on precision: The results are not precise — there's high variability between trials.
This indicates poor technique or large errors:
- Inconsistent measurement methods (e.g., reading meniscus incorrectly).
- Poorly calibrated equipment.
- Human error in mass or volume measurement.
- Contamination or incomplete transfer of sample.
> 🔴 Possible causes: Random errors (e.g., inconsistent pouring, misreading scales) and possibly systematic errors (e.g., dirty equipment, wrong units). This suggests lack of care or faulty instruments.
---
## ✔ Problem 3
Accepted value: 3.75 g/mL
Measurements:
- Trial #1: 4.75 g/mL
- Trial #2: 4.76 g/mL
- Trial #3: 4.74 g/mL
All values are around 4.75 g/mL, while the accepted value is 3.75 g/mL.
Difference: ~1.0 g/mL → very inaccurate.
> ✘ Comment on accuracy: The results are not accurate — all values are significantly higher than the accepted value.
Values: 4.75, 4.76, 4.74 → very close!
Range = 0.02 g/mL → excellent consistency.
> ✔ Comment on precision: The results are very precise — highly reproducible, even if wrong.
High precision but low accuracy suggests:
- Systematic error (same mistake repeated every time).
- Example: Using a calibration error in the balance or volume measurement.
- Or, perhaps using the wrong units (e.g., mistaking mL for cm³ or mislabeling).
- Or, incorrect assumption about mass or volume (e.g., assuming volume was smaller than it actually was).
> 🔵 Possible cause: A systematic error, such as a miscalibrated instrument or misuse of units, leading to consistently high readings.
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## 📝 Summary Table
| Problem | Accuracy | Precision | Likely Cause |
|-------|---------|----------|-------------|
| 1 | Good | Good | Small systematic error, good technique |
| 2 | Poor | Poor | Random errors, poor technique |
| 3 | Poor | Excellent | Systematic error (e.g., miscalibrated tool) |
---
Let me know if you'd like this formatted as a printable answer sheet or need help graphing or calculating percent error!
---
🔍 Definitions Recap:
- Accuracy: How close a measurement is to the true or accepted value.
- Precision: How close repeated measurements are to each other (reproducibility).
We will evaluate:
- Accuracy: Compare each trial to the accepted value.
- Precision: Look at how close the trials are to one another.
---
## ✔ Problem 1
Accepted value: 1.24 g/mL
Measurements:
- Trial #1: 1.20 g/mL
- Trial #2: 1.22 g/mL
- Trial #3: 1.22 g/mL
a) Accuracy
All values (1.20, 1.22, 1.22) are close to 1.24 g/mL, within ±0.04 g/mL.
So, these results are fairly accurate — they are near the true value.
> ✔ Comment on accuracy: The measurements are accurate, as they are all relatively close to the accepted value of 1.24 g/mL.
b) Precision
The values are very close to each other: 1.20, 1.22, 1.22 → small variation.
The difference between the highest and lowest is only 0.02 g/mL.
> ✔ Comment on precision: The results are precise, since the measurements are reproducible and closely clustered.
c) What may have caused these results?
These results suggest good technique and minimal random error. Possible reasons include:
- Careful use of measuring tools (e.g., graduated cylinder, balance).
- Consistent procedure across trials.
- Minor systematic error (e.g., slight calibration issue), but not major.
> 🟡 Possible cause: A small systematic error (like a slightly miscalibrated scale), but overall good lab practices led to both accurate and precise data.
---
## ✔ Problem 2
Accepted value: 1.15 g/mL
Measurements:
- Trial #1: 0.95 g/mL
- Trial #2: 1.16 g/mL
- Trial #3: 1.06 g/mL
a) Accuracy
Compare to 1.15 g/mL:
- 0.95 → off by -0.20 g/mL
- 1.16 → off by +0.01 g/mL
- 1.06 → off by -0.09 g/mL
Only one value (1.16) is close; others are significantly off.
> ✘ Comment on accuracy: The results are not accurate — most values are far from the accepted value.
b) Precision
Values: 0.95, 1.16, 1.06 → spread out over 0.21 g/mL range.
They are not close to each other.
> ✘ Comment on precision: The results are not precise — there's high variability between trials.
c) What may have caused these results?
This indicates poor technique or large errors:
- Inconsistent measurement methods (e.g., reading meniscus incorrectly).
- Poorly calibrated equipment.
- Human error in mass or volume measurement.
- Contamination or incomplete transfer of sample.
> 🔴 Possible causes: Random errors (e.g., inconsistent pouring, misreading scales) and possibly systematic errors (e.g., dirty equipment, wrong units). This suggests lack of care or faulty instruments.
---
## ✔ Problem 3
Accepted value: 3.75 g/mL
Measurements:
- Trial #1: 4.75 g/mL
- Trial #2: 4.76 g/mL
- Trial #3: 4.74 g/mL
a) Accuracy
All values are around 4.75 g/mL, while the accepted value is 3.75 g/mL.
Difference: ~1.0 g/mL → very inaccurate.
> ✘ Comment on accuracy: The results are not accurate — all values are significantly higher than the accepted value.
b) Precision
Values: 4.75, 4.76, 4.74 → very close!
Range = 0.02 g/mL → excellent consistency.
> ✔ Comment on precision: The results are very precise — highly reproducible, even if wrong.
c) What may have caused these results?
High precision but low accuracy suggests:
- Systematic error (same mistake repeated every time).
- Example: Using a calibration error in the balance or volume measurement.
- Or, perhaps using the wrong units (e.g., mistaking mL for cm³ or mislabeling).
- Or, incorrect assumption about mass or volume (e.g., assuming volume was smaller than it actually was).
> 🔵 Possible cause: A systematic error, such as a miscalibrated instrument or misuse of units, leading to consistently high readings.
---
## 📝 Summary Table
| Problem | Accuracy | Precision | Likely Cause |
|-------|---------|----------|-------------|
| 1 | Good | Good | Small systematic error, good technique |
| 2 | Poor | Poor | Random errors, poor technique |
| 3 | Poor | Excellent | Systematic error (e.g., miscalibrated tool) |
---
Let me know if you'd like this formatted as a printable answer sheet or need help graphing or calculating percent error!
Parent Tip: Review the logic above to help your child master the concept of precision and accuracy worksheet.
