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Percentage Error (DP IB Applications & Interpretation (AI)): Revision Note

Amber

Written by: Amber

Reviewed by: Mark Curtis

Updated on

DP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SL

Percentage error

What is percentage error?

  • Percentage error is a measure of how far away an estimated (or rounded) value is from the actual (or exact) value

    • Percentage error, epsilon, can be calculated using the formula epsilon equals open vertical bar fraction numerator v subscript A minus v subscript E over denominator v subscript E end fraction close vertical bar cross times 100 percent sign

      • where v subscript E is the exact value

      • and v subscript A is the approximate value of v subscript E

    • The | | means take the absolute value (the positive value)

      • e.g. vertical line minus 5 vertical line equals 5

      • Percentage errors should always be positive

  • The further away the estimated answer is from the true answer, the greater the percentage error

Examiner Tips and Tricks

The percentage error formula is given in the formula booklet.

Worked Example

Let P equals x cos open parentheses 2 y close parentheses, where  y equals 15 degree and x equals 4.

(a) Calculate the exact value of P.

 

ai-sl-1-1-3-percentage-error-a

(b) Calculate the percentage error when using an estimate of 3.5 for the value of P.

ai-sl-1-1-3-percentage-errorb

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    Amber

    Author: Amber

    Expertise: Maths Content Creator

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

    Mark Curtis

    Reviewer: Mark Curtis

    Expertise: Maths Content Creator

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.