Calculating Absolute Percentage Error

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📚 Part 1: Understanding Error Calculations

WALT: We are learning to calculate absolute error and percentage error from measurement data.

Key Formulas:

• Absolute Error = |Measured Value – Actual Value|

• Percentage Error = (Absolute Error ÷ Actual Value) × 100%

1. A student measures a desk as 120 cm long. The actual length is 125 cm. What is the absolute error?

5 cm

-5 cm

245 cm

0.96 cm

2. Using the same example above (absolute error = 5 cm, actual value = 125 cm), what is the percentage error?

25%

0.04%

3. A recipe calls for 500g of flour. Sarah measures 485g. Calculate both errors:

Absolute Error: _____________ g

Percentage Error: _____________ %

4. Which statements about error calculations are correct? (Select all that apply)

Absolute error is always positive

Percentage error helps compare errors across different measurements

A smaller percentage error means more accurate measurement

Absolute error has the same units as the original measurement

✏️ Part 2: Real-World Applications

5. A carpenter measures a board as 2.45 metres. The actual length is 2.50 metres.

Show your working to find the percentage error:

6. In a budget, Maya estimated her weekly groceries would cost $80. She actually spent $92.

a) Absolute Error: $ _____________

b) Percentage Error: _____________ %

c) Is this an overestimate or underestimate? _________________________

7. A thermometer reads 23°C when the actual temperature is 25°C. Another thermometer reads 47°C when the actual temperature is 50°C. Which thermometer is more accurate? Explain your reasoning:

8. Complete this statement: "Understanding measurement error is important because..."

🎯 Extension Challenge

9. Advanced Problem: A GPS device shows three different distance measurements for the same journey. The actual distance is 15.2 km. Calculate which measurement is most accurate:

Measurement A: 14.8 km → Percentage Error: _____________ %

Measurement B: 15.7 km → Percentage Error: _____________ %

Measurement C: 14.9 km → Percentage Error: _____________ %

Most accurate measurement: _____________

10. Reflection: Describe a situation where a 5% error would be acceptable and another where it would be problematic: