Accuracy, precision, and percent error worksheet - Free Printable

Let's solve each question step by step from the Accuracy, Precision, and % Error Practice Worksheet.

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Question 1:

You are given a block of metal with a *known* mass of 110.2 grams. You measure its mass three times and get:

- 100.2 g
- 100.1 g
- 100.3 g

#### a. What was your average mass?

To find the average:

$$
\text{Average} = \frac{100.2 + 100.1 + 100.3}{3} = \frac{300.6}{3} = 100.2 \text{ g}
$$

✔ Answer: 100.2 g

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#### b. What was the range of your data?

Range = Highest value – Lowest value
= 100.3 g – 100.1 g = 0.2 g

✔ Answer: 0.2 g

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#### c. Which is better, the accuracy or the precision of your measurements?

- Precision: How close the measurements are to each other.
→ The three values (100.1, 100.2, 100.3) are very close → High precision

- Accuracy: How close the measurements are to the true value.
→ True value = 110.2 g; measured average = 100.2 g → Big difference → Low accuracy

So, precision is better than accuracy.

✔ Answer: Precision is better

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#### d. What is your percent error?

Percent error formula:

$$
\% \text{Error} = \left| \frac{\text{Experimental} - \text{Accepted}}{\text{Accepted}} \right| \times 100\%
$$

$$
= \left| \frac{100.2 - 110.2}{110.2} \right| \times 100\% = \left| \frac{-10.0}{110.2} \right| \times 100\% \approx 9.07\%
$$

✔ Answer: ≈ 9.07%

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Question 2:

Length of object is known to be 14.54 cm.

| Student | Trial 1 | Trial 2 | Trial 3 | Trial 4 | Trial 5 |
|--------|--------|--------|--------|--------|--------|
| A | 14.8 | 14.1 | 14.5 | 14.6 | 14.2 |
| B | 14.8 | 14.2 | 14.6 | 14.5 | 14.8 |
| C | 14.6 | 14.5 | 14.5 | 14.4 | 14.6 |

We need to determine accuracy (how close to 14.54 cm) and precision (how consistent the readings are).

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#### Student A:
- Values: 14.8, 14.1, 14.5, 14.6, 14.2
- Range: 14.8 – 14.1 = 0.7 cm → Low precision
- Average: (14.8+14.1+14.5+14.6+14.2)/5 = 72.2 / 5 = 14.44 cm
- Difference from true: |14.44 – 14.54| = 0.10 cm → Moderate accuracy

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#### Student B:
- Values: 14.8, 14.2, 14.6, 14.5, 14.8
- Range: 14.8 – 14.2 = 0.6 cm → Low precision
- Average: (14.8+14.2+14.6+14.5+14.8)/5 = 72.9 / 5 = 14.58 cm
- Difference: |14.58 – 14.54| = 0.04 cm → Good accuracy

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#### Student C:
- Values: 14.6, 14.5, 14.5, 14.4, 14.6
- Range: 14.6 – 14.4 = 0.2 cm → High precision
- Average: (14.6+14.5+14.5+14.4+14.6)/5 = 72.6 / 5 = 14.52 cm
- Difference: |14.52 – 14.54| = 0.02 cm → Very good accuracy

✔ So:
- Most precise: Student C (smallest spread)
- Most accurate: Student C (closest average to 14.54)

But let’s check options:

> a. Student C has done the most precise and accurate work. ✔

This matches our analysis.

✔ Answer: a

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Question 3:

A student finds density of aluminum = 2.85 g/cm³
Accepted value = 2.6999 g/cm³

$$
\% \text{Error} = \left| \frac{2.85 - 2.6999}{2.6999} \right| \times 100\%
= \left| \frac{0.1501}{2.6999} \right| \times 100\% \approx 5.56\%
$$

✔ Answer: ≈ 5.56%

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Question 4:

Student finds specific heat of water = 4.29 J/g°C
Accepted value = 4.18 J/g°C

$$
\% \text{Error} = \left| \frac{4.29 - 4.18}{4.18} \right| \times 100\%
= \left| \frac{0.11}{4.18} \right| \times 100\% \approx 2.63\%
$$

✔ Answer: ≈ 2.63%

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✔ Final Answers Summary:

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1)
a. Average mass = 100.2 g
b. Range = 0.2 g
c. Better: Precision
d. Percent error = 9.07%

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2)
Correct answer: a. Student C has done the most precise and accurate work.

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3)
Percent error = 5.56%

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4)
Percent error = 2.63%

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