Accuracy and Precision interactive worksheet - Free Printable

Let's solve each part of the Accuracy & Precision Worksheet step by step, based on the definitions:

- Accuracy: How close a measurement is to the true or accepted value.
- Precision: How close repeated measurements are to each other (reproducibility).

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Problem 1

Accepted density = 1.24 g/mL

| Trial | Measurement |
|-------|-------------|
| #1 | 1.20 g/mL |
| #2 | 1.22 g/mL |
| #3 | 1.22 g/mL |

#### a) Accuracy
The measurements (1.20, 1.22, 1.22) are all close to the accepted value of 1.24 g/mL, with differences of only 0.04 and 0.02 g/mL.
✔ Comment: The results are fairly accurate, as they are near the true value.

#### b) Precision
The values are very close to each other: two trials are identical (1.22), and one is only 0.02 away.
✔ Comment: The results are highly precise, since the measurements are reproducible.

#### c) Possible causes
- The slight underestimation could be due to systematic error, such as:
- Using an improperly calibrated balance.
- Not accounting for air buoyancy.
- Using a container that adds extra volume (e.g., not taring properly).
- However, the precision is good, suggesting random errors are minimal.

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Problem 2

Accepted density = 1.15 g/mL

| Trial | Measurement |
|-------|-------------|
| #1 | 0.95 g/mL |
| #2 | 1.16 g/mL |
| #3 | 1.26 g/mL |

#### a) Accuracy
The values range from 0.95 to 1.26 g/mL. Only Trial #2 (1.16) is close to 1.15; others are significantly off.
- Trial #1: 0.20 below → low accuracy
- Trial #3: 0.11 above → moderate accuracy

✘ Comment: The results are not accurate, as most measurements are far from the accepted value.

#### b) Precision
The measurements vary widely: 0.95 → 1.16 → 1.26 — a spread of 0.31 g/mL.
✘ Comment: The results are not precise, because the measurements are inconsistent and not reproducible.

#### c) Possible causes
- Random errors such as:
- Poor technique in measuring volume or mass.
- Spilling or loss of sample between trials.
- Inconsistent reading of the graduated cylinder.
- Systematic error might also be present (e.g., incorrect calibration), but the lack of precision suggests more likely random errors.

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Problem 3

Accepted density = 3.75 g/mL

| Trial | Measurement |
|-------|-------------|
| #1 | 4.75 g/mL |
| #2 | 4.76 g/mL |
| #3 | 4.74 g/mL |

#### a) Accuracy
All measurements are around 4.75 g/mL, while the true value is 3.75 g/mL.
This means all values are overestimated by about 1.0 g/mL.

✘ Comment: The results are not accurate — they are consistently high.

#### b) Precision
The three values are extremely close: 4.75, 4.76, 4.74 → variation of just 0.02 g/mL.

✔ Comment: The results are very precise, as the measurements are highly reproducible.

#### c) Possible causes
- Systematic error (bias) is likely responsible:
- For example, if the mass was measured incorrectly (e.g., scale not zeroed, tared incorrectly).
- Or if volume was underestimated (e.g., meniscus read too low).
- Alternatively, contamination (e.g., impurities increasing mass).
- But since the values are consistent, random errors are small, so the issue is likely a consistent mistake in procedure or equipment.

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✔ Summary Table

| Problem | Accuracy | Precision | Likely Cause |
|--------|----------|-----------|--------------|
| 1 | Fairly accurate | High precision | Minor systematic error (e.g., slightly under-measured mass or over-measured volume) |
| 2 | Low accuracy | Low precision | Random errors (poor technique, spillage, inconsistent readings) |
| 3 | Low accuracy | High precision | Systematic error (e.g., scale miscalibrated, contaminated sample, improper taring) |

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Final Notes:

- High accuracy + high precision = Good results.
- Low accuracy + high precision = Systematic error.
- High accuracy + low precision = Random errors.
- Low accuracy + low precision = Both types of errors present.

This worksheet illustrates how accuracy and precision are independent concepts!