Accuracy and Precision worksheet - Free Printable

Let's solve the worksheet step by step and fill in all the blanks.

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Part 1: Definitions

Accuracy – how close a measurement is to the true or accepted value.
Precision – how close a measurement is to other measurements (or how consistent the measurements are).

> ✔ So, fill in:
> - Accuracy: the true or accepted value
> - Precision: other measurements (or repeated measurements)

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Part 2: Precision vs Accuracy (Target Diagrams)

We have three targets with "hits" (dots). Let’s analyze each:

#### Target 1: Dots are clustered together but far from the center (bullseye).
- Precise? Yes — they're close to each other.
- Accurate? No — not near the bullseye.
- ✔ Answer: Precise, not accurate

#### Target 2: Dots are clustered tightly around the bullseye.
- Precise? Yes — tight cluster.
- Accurate? Yes — near the center.
- ✔ Answer: Both accurate and precise

#### Target 3: Dots are scattered and far from the bullseye.
- Precise? No — spread out.
- Accurate? No — not near center.
- ✔ Answer: Neither accurate nor precise

> Fill in the boxes under the targets:
> 1. Precise, not accurate
> 2. Both accurate and precise
> 3. Neither accurate nor precise

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Part 3: Precision Problems

Given data:
| Team | Measurement |
|------|-------------|
| 1 | 2.65 cm |
| 2 | 2.75 cm |
| 3 | 2.80 cm |
| 4 | 2.77 cm |
| 5 | 2.60 cm |
| 6 | 2.65 cm |
| 7 | 2.68 cm |

#### Step 1: Average length (mean)
Add all values and divide by 7:

$$
\text{Sum} = 2.65 + 2.75 + 2.80 + 2.77 + 2.60 + 2.65 + 2.68
$$

Break it down:
- 2.65 + 2.75 = 5.40
- 5.40 + 2.80 = 8.20
- 8.20 + 2.77 = 10.97
- 10.97 + 2.60 = 13.57
- 13.57 + 2.65 = 16.22
- 16.22 + 2.68 = 18.90

$$
\text{Average} = \frac{18.90}{7} = 2.70 \text{ cm}
$$

✔ Average length is 2.70 cm

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#### Step 2: Subtract highest from lowest value (Range)

- Highest = 2.80 cm
- Lowest = 2.60 cm
- Range = 2.80 − 2.60 = 0.20 cm

✔ 0.20 cm

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#### Step 3: Divide range by 2

$$
\frac{0.20}{2} = 0.10 \text{ cm}
$$

This gives the approximate ± range from the average.

✔ 0.10 cm

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#### Step 4: Precision of the measurement

Expressed as:
Average ± (half the range)

So:
$$
2.70 \pm 0.10 \text{ cm}
$$

✔ The precision was 2.70 ± 0.10 cm

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✔ Final Answers:

#### Definitions:
- Accuracy – how close a measurement is to the true or accepted value
- Precision – how close a measurement is to other measurements (or repeated measurements)

#### Target Analysis:
1. Precise, not accurate
2. Both accurate and precise
3. Neither accurate nor precise

#### Precision Problems:
- The average length is 2.70 cm.
- Subtract the highest from the lowest: 0.20 cm.
- Divide by 2: 0.10 cm.
- The precision of the measurement was 2.70 ± 0.10 cm.

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