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Measurements and Their Errors

Limitation of physical measurements

  • 9 things to know
  • Papers 1 and 3

Overview

Random and systematic error, precision and accuracy, and combining absolute and percentage uncertainties.

What you need to know

Answer each one before you reveal it.

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Evaluation

What are absolute and fractional uncertainty, and what does accuracy mean?

Evaluation

How is percentage uncertainty found, and how do uncertainties combine when adding?

Evaluation

How do uncertainties combine when quantities are multiplied, divided or raised to a power?

Evaluation

How are the extreme lines of best fit used to find uncertainty in a gradient?

Evaluation

How is gradient uncertainty calculated, what is a zero error, and how can it be corrected?

Evaluation

Why are absolute uncertainties added when two measurements are subtracted?

Evaluation

How do you combine uncertainty for a square root, and how many figures should you quote?

Numbers

When two measurements are multiplied together, how do you combine their uncertainties?

Process

When two measurements are added together, how do you combine their absolute uncertainties?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How do random errors affect readings relative to the true value?

    Model answer

    Random errors cause readings to scatter unpredictably above and below the true value.

  2. 2

    How can taking repeat measurements help reduce the effect of random errors?

    Model answer

    Taking repeat measurements allows random errors to partially cancel out, as some readings will be above and some below the true value.

  3. 3

    Why does calculating a mean from repeated measurements reduce random error?

    Model answer

    Calculating a mean averages out the random scatter, giving a value closer to the true value than any single measurement.

  4. 4

    In what direction do systematic errors shift readings from the true value?

    Model answer

    Systematic errors shift all readings in the same direction (all too high or all too low) by a consistent amount.

  5. 5

    Can systematic errors be reduced by taking repeat measurements? Explain why.

    Model answer

    No, because systematic errors affect every reading by the same amount in the same direction, so repeating measurements does not reduce them.

  6. 6

    How can recalibrating an instrument help reduce systematic error?

    Model answer

    Recalibration adjusts the instrument to give correct readings, removing any consistent offset from the true value.

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AP = 4πr²σT⁴.
BThe surface area of a spherical star is 4πr².
CP₁/P₂ = (r₁²/r₂²) × (T₁⁴/T₂⁴).

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