Accuracy and Precision Worksheet: Complete with ease | airSlate ... - Free Printable

Problem Analysis:

The task involves solving several problems related to accuracy, precision, error, and percent error. Let's break down each part of the problem step by step.

---

Part 1: Define the following terms

1. Accuracy:
- Accuracy refers to how close a measured value is to the true (accepted) value. It measures the correctness of a measurement.

2. Precision:
- Precision refers to how close repeated measurements are to each other. It measures the reproducibility or consistency of measurements.

---

Part 2: Complete the diagram below

The diagram likely involves filling in blanks related to accuracy and precision. Based on the context, the completed diagram might look like this:

```
accuracy | precision
-------------- | ---------------
accurate | precise
inaccurate | imprecise
```

- Accurate means the measurements are close to the true value.
- Precise means the measurements are close to each other.
- Inaccurate means the measurements are far from the true value.
- Imprecise means the measurements are not close to each other.

---

Part 3: Group measurements and calculations

A group of students measured the mass of an object, and their results are given in the table below:

| Mass (g) | 2.66 | 2.75 | 2.80 | 2.60 | 2.65 | 2.60 | 2.77 |
|----------|------|------|------|------|------|------|------|

#### (a) Calculate the average mass
The average mass is calculated as the sum of all measurements divided by the number of measurements.

\[
\text{Average mass} = \frac{\sum \text{Mass}}{\text{Number of measurements}}
\]

\[
\text{Sum of masses} = 2.66 + 2.75 + 2.80 + 2.60 + 2.65 + 2.60 + 2.77 = 18.83
\]

\[
\text{Number of measurements} = 7
\]

\[
\text{Average mass} = \frac{18.83}{7} = 2.69 \, \text{g}
\]

#### (b) Calculate the data range (highest value – lowest value)
The highest value is \(2.80 \, \text{g}\), and the lowest value is \(2.60 \, \text{g}\).

\[
\text{Data range} = \text{Highest value} - \text{Lowest value} = 2.80 - 2.60 = 0.20 \, \text{g}
\]

#### (c) Calculate the approximate standard deviation from the average (range ÷ 4)
The approximate standard deviation can be estimated using the formula:

\[
\text{Standard deviation} \approx \frac{\text{Data range}}{4}
\]

\[
\text{Standard deviation} \approx \frac{0.20}{4} = 0.05 \, \text{g}
\]

#### (d) State the precision of the experiment (average ± standard deviation)
The precision is expressed as the average value plus or minus the standard deviation.

\[
\text{Precision} = \text{Average mass} \pm \text{Standard deviation} = 2.69 \pm 0.05 \, \text{g}
\]

---

Part 4: Calculate the percent error for a sample of aluminum

The accepted density of aluminum is \(2.70 \, \text{g/cm}^3\). The measured density is \(2.85 \, \text{g/cm}^3\).

The formula for percent error is:

\[
\text{Percent error} = \left| \frac{\text{Experimental value} - \text{Accepted value}}{\text{Accepted value}} \right| \times 100\%
\]

Substitute the values:

\[
\text{Percent error} = \left| \frac{2.85 - 2.70}{2.70} \right| \times 100\%
\]

\[
\text{Percent error} = \left| \frac{0.15}{2.70} \right| \times 100\% = 0.0556 \times 100\% = 5.56\%
\]

---

Part 5: Calculate the percent error for a sample of water

The accepted density of water is \(1.00 \, \text{g/mL}\). The measured density is \(0.98 \, \text{g/mL}\).

Using the same formula for percent error:

\[
\text{Percent error} = \left| \frac{\text{Experimental value} - \text{Accepted value}}{\text{Accepted value}} \right| \times 100\%
\]

Substitute the values:

\[
\text{Percent error} = \left| \frac{0.98 - 1.00}{1.00} \right| \times 100\%
\]

\[
\text{Percent error} = \left| \frac{-0.02}{1.00} \right| \times 100\% = 0.02 \times 100\% = 2.00\%
\]

---

Final Answers:

1. Definitions:
- Accuracy: Closeness to the true value.
- Precision: Consistency of repeated measurements.

2. Completed Diagram:
```
accuracy | precision
-------------- | ---------------
accurate | precise
inaccurate | imprecise
```

3. Calculations for mass measurements:
- (a) Average mass: \(2.69 \, \text{g}\)
- (b) Data range: \(0.20 \, \text{g}\)
- (c) Standard deviation: \(0.05 \, \text{g}\)
- (d) Precision: \(2.69 \pm 0.05 \, \text{g}\)

4. Percent error for aluminum:
\[
\boxed{5.56\%}
\]

5. Percent error for water:
\[
\boxed{2.00\%}
\]