Accuracy and Precision Lesson Plans & Worksheets Reviewed by Teachers - Free Printable

Let's solve the problem step by step based on the image you provided. This is a chemistry worksheet focusing on accuracy and precision in measurements.

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Part 1: Definitions

Fill in the blanks:

- Accuracy – how close a measurement is to the true or accepted value.
- Precision – how close a measurement is to each other (or how reproducible they are).

> ✔ These are standard definitions:
> - Accuracy = closeness to the true value
> - Precision = closeness of repeated measurements to each other

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Part 2: Accuracy vs. Precision (Target Diagrams)

We have three targets. Let’s analyze each one:

#### Target 1
- All shots are clustered near the center (bullseye).
- Accurate? Yes (close to the true value)
- Precise? Yes (clustered together)

✔ Answer:
- Accurate? Yes
- Precise? Yes

#### Target 2
- Shots are spread out but centered around the bullseye.
- Accurate? Yes (average is near the center)
- Precise? No (not tightly grouped)

✔ Answer:
- Accurate? Yes
- Precise? No

#### Target 3
- Shots are tightly clustered but far from the bullseye.
- Accurate? No (far from true value)
- Precise? Yes (very consistent, just off-target)

✔ Answer:
- Accurate? No
- Precise? Yes

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Part 3: Density Measurement Data

#### First Set of Data (7 Teams):
| Team | Density (g/cm³) |
|------|------------------|
| 1 | 2.65 |
| 2 | 2.75 |
| 3 | 2.80 |
| 4 | 2.77 |
| 5 | 2.60 |
| 6 | 2.65 |
| 7 | 2.68 |

#### Step 1: Calculate Average Density

Add all values:
```
2.65 + 2.75 + 2.80 + 2.77 + 2.60 + 2.65 + 2.68 = 19.30
```

Divide by 7:
```
19.30 ÷ 7 = 2.757... ≈ 2.76 g/cm³
```

✔ Average density: 2.76 g/cm³

#### Step 2: Find Highest Value
- Highest value = 2.80 g/cm³

#### Step 3: Divide by 2
```
2.80 ÷ 2 = 1.40
```

So, the precision can be shown as:
> 2.76 ± 1.40 g/cm³

But wait — this range (±1.40) is too large because it suggests the values could be from 1.36 to 4.16, which is unrealistic.

Let’s re-evaluate: The question says:
> "Divide this number by 2" → probably referring to range, not absolute value.

Wait — perhaps the intention is to find the range (max – min), then divide by 2 for half-range.

Let’s check:
- Max = 2.80
- Min = 2.60
- Range = 2.80 – 2.60 = 0.20
- Half-range = 0.20 ÷ 2 = 0.10

Then the precision would be expressed as:
> 2.76 ± 0.10 g/cm³

That makes more sense.

But the prompt says:
> "Subtract the highest value from the lowest value: ________ Divide this number by 2: ________"

So:
- Subtract highest from lowest: 2.80 – 2.60 = 0.20
- Divide by 2: 0.20 ÷ 2 = 0.10

✔ So:
- Difference: 0.20
- Divided by 2: 0.10
- Precision: 2.76 ± 0.10 g/cm³

This shows that the measurements vary within ±0.10 around the average.

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Part 4: Second Set of Data (More Precise?)

Now we have new data:

| Team | Density (g/cm³) |
|------|------------------|
| 1 | 2.60 |
| 2 | 2.70 |
| 3 | 2.80 |
| 4 | 2.75 |
| 5 | 2.65 |
| 6 | 2.62 |
| 7 | 2.78 |

Compare with first set.

Let’s compute the range again:
- Max = 2.80
- Min = 2.60
- Range = 0.20 → same as before

So the precision (spread of data) is similar.

But let’s look at values: both sets have values ranging from 2.60 to 2.80.

Now check if the precision is the same?

→ Yes, because the range is the same (0.20 g/cm³), so the spread is similar.

But let’s see if the data points are more precise (i.e., closer together).

In the second set:
- Values: 2.60, 2.70, 2.80, 2.75, 2.65, 2.62, 2.78
- Spread: still from 2.60 to 2.80 → same range

So precision is about the same.

However, note that the first set had:
- 2.65, 2.75, 2.80, 2.77, 2.60, 2.65, 2.68

The second set has slightly different values, but same range, so similar precision.

But let’s calculate the standard deviation roughly:

Both sets have similar variation.

So the answer to:
> "Is this more precise, less precise, or the same precision?"

✔ Answer: Same precision

Because the range and spread are comparable.

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✔ Final Answers Summary:

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

#### Targets:
1. Accurate: Yes, Precise: Yes
2. Accurate: Yes, Precise: No
3. Accurate: No, Precise: Yes

#### Density Calculations:
- Average density: 2.76 g/cm³
- Highest value: 2.80 g/cm³
- Subtract highest from lowest: 0.20
- Divide by 2: 0.10
- Precision: 2.76 ± 0.10 g/cm³

#### Second Data Set:
- Is it more precise, less precise, or same? → Same precision

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🔍 Final Note:

- Accuracy depends on how close to the true value (accepted density of aluminum is ~2.70 g/cm³). So both sets are fairly accurate.
- Precision depends on how close the values are to each other. Both sets have similar ranges, so precision is the same.

Let me know if you'd like help calculating standard deviation for deeper analysis!