How can random errors be reduced?

Take repeat readings and calculate a mean, use a larger sample, or use equipment with finer resolution.

What is a systematic error?

An error that shifts all readings in the same direction by a consistent amount, such as a zero error.

Give two ways to reduce a systematic error.

Check and correct the zero, calibrate the instrument against a known standard, or use a different method.

How close together repeated readings are; it is not the same as accuracy.

How close a measurement is to the true value.

What is the difference between repeatability and reproducibility?

Repeatability: same person, method and equipment. Reproducibility: different people, equipment or methods.

The smallest change in a quantity that an instrument can detect.

How do you find a percentage uncertainty?

(absolute uncertainty ÷ measured value) × 100%.

How do you combine uncertainties when adding or subtracting?

Add the absolute uncertainties.

How do you combine uncertainties when multiplying or dividing?

Add the percentage uncertainties.

How do you treat the uncertainty when a quantity is raised to a power?

Multiply the percentage uncertainty by the power, e.g. 2% in r gives 4% in r².

How is the uncertainty in a gradient found from a graph?

Draw best-fit and worst acceptable lines, calculate both gradients, and take the difference.

Errors, uncertainties and error barsAQA A-Level Physics: Flashcards

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What is a random error?

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What is a random error?: An unpredictable error that scatters readings above and below the true value.
How can random errors be reduced?: Take repeat readings and calculate a mean, use a larger sample, or use equipment with finer resolution.
What is a systematic error?: An error that shifts all readings in the same direction by a consistent amount, such as a zero error.
Give two ways to reduce a systematic error.: Check and correct the zero, calibrate the instrument against a known standard, or use a different method.
Define precision.: How close together repeated readings are; it is not the same as accuracy.
Define accuracy.: How close a measurement is to the true value.
What is the difference between repeatability and reproducibility?: Repeatability: same person, method and equipment. Reproducibility: different people, equipment or methods.
Define resolution.: The smallest change in a quantity that an instrument can detect.
How do you find a percentage uncertainty?: (absolute uncertainty ÷ measured value) × 100%.
How do you combine uncertainties when adding or subtracting?: Add the absolute uncertainties.
How do you combine uncertainties when multiplying or dividing?: Add the percentage uncertainties.
How do you treat the uncertainty when a quantity is raised to a power?: Multiply the percentage uncertainty by the power, e.g. 2% in r gives 4% in r².
How is the uncertainty in a gradient found from a graph?: Draw best-fit and worst acceptable lines, calculate both gradients, and take the difference.

Exam questions on Errors, uncertainties and error bars

A student measures the diameter of a wire with a micrometer screw gauge that reads to the nearest 0.01 mm. With the jaws closed and nothing between them, the gauge reads 0.02 mm. The student then measures the diameter at five different places along the wire and the readings vary slightly, between 0.41 mm and 0.45 mm.
Explain why calculating the mean of the readings taken at the five places reduces the effect of random error but does not remove the zero error.2 marks
A student determines the density of a metal cube. The mass of the cube is 85.0 ± 0.5 g and the length of each side is 2.00 ± 0.02 cm.
Calculate the percentage uncertainty in the density of the metal.2 marks
A student times 20 complete oscillations of a simple pendulum of length 0.800 ± 0.002 m. The time for 20 oscillations is 35.9 ± 0.4 s. The acceleration of free fall can be found from g = 4π²L/T², where T is the period of the pendulum.
Calculate the period T of the pendulum and its absolute uncertainty.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).