Error Bars and Uncertainty

Name:

Date:

📊 Part 1: Understanding Uncertainty

1. Which statement best describes measurement uncertainty?

The difference between measured and actual values

The range within which the true value is likely to lie

A mistake made during the experiment

The precision of the measuring instrument only

2. A student measures the length of a wire as 25.4 cm using a ruler with 1 mm divisions. What is the absolute uncertainty?

± 0.1 cm

± 0.05 cm

± 0.5 cm

± 1.0 cm

3. Which factors contribute to measurement uncertainty? (Select all that apply)

Instrument precision limitations

Human reaction time

Environmental conditions

Random fluctuations

4. Error bars on a graph represent:

The range of uncertainty in measurements

The maximum possible error

The average of all measurements

The systematic error only

🔢 Part 2: Calculating Uncertainties

5. A digital balance reads 45.23 g with an uncertainty of ± 0.01 g. Calculate the percentage uncertainty.

Percentage uncertainty = ___________

6. The following measurements were taken for the time period of a pendulum: 2.1 s, 2.0 s, 2.2 s, 1.9 s, 2.1 s

a) Calculate the mean time: ___________

b) Calculate the range: ___________

c) Estimate the uncertainty (range ÷ 2): ___________

7. A student measures voltage as 12.5 V ± 0.2 V and current as 2.0 A ± 0.1 A. When calculating power (P = VI), explain why the uncertainty in power will be larger than the individual uncertainties.

📈 Part 3: Interpreting Error Bars

8. Two data points on a graph have values of 15.2 ± 0.8 and 16.1 ± 0.6. Do these measurements agree within their uncertainties? Show your working.

Conclusion: ________________________________

9. A student plots a graph showing the relationship between temperature and resistance. The error bars are very large compared to the data points. What does this suggest about:

a) The precision of the measurements: ________________________________

b) The reliability of any conclusions: ________________________________

c) Possible improvements to the experiment: ________________________________

10. Sketch error bars on the data point below to show an uncertainty of ± 0.5 units in both x and y directions.

• (Data point at coordinates 5, 8)

11. Explain why error bars are essential when presenting experimental physics data to the scientific community.