Uncertainties, errors and precision

Measurement, maths and practical skills · Lesson 2 of 5

Lesson 2 of 5

Lesson 2 of 5 · Measurement, maths and practical skills

Uncertainties, errors and precision

8 min read · about 1 h 45 min with practice3 quick checks≈3% of the testCore

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Uncertainty questions are some of the most reliable marks in the whole qualification. They use the same few rules every year, they appear in every paper (not just the practical one), and the top grades separate from the rest on the precise vocabulary. Expect to identify an error, calculate and combine percentage uncertainties, quote a result with a sensible uncertainty, and judge whether it agrees with an accepted value.

By the end you’ll be able to

Distinguish random from systematic errors (including zero errors and parallax) and state how each is reduced
Define and apply precision, repeatability, reproducibility, resolution and accuracy correctly in context
Estimate uncertainty from instrument resolution or half the range of repeat readings, and express it as absolute, fractional and percentage uncertainty
Combine uncertainties for sums/differences (add absolute), products/quotients (add percentage) and powers (multiply percentage by the power)
Judge whether a result agrees with an accepted value using percentage difference against combined percentage uncertainty

What the exam asks

Vocabulary in context. For example: “Explain why the readings are precise but not accurate.” Or: “State what is meant by the resolution of the micrometer.”
Error type and remedy. For example: “The ammeter has a zero error of +0.02 A. Explain the effect on the value of R and how to correct it.”
Calculate uncertainties, from an instrument’s resolution or from repeat readings, as absolute or percentage values.
Combine uncertainties through a formula such as $g = 4\pi^2 l/T^2$ , or , then quote the final answer as value ± uncertainty.

Check your understanding

3 questions on uncertainties, errors and precision. Every option is explained once you answer.

Answers are checked on our side, every option is explained, and your result feeds your mastery for this topic. It’s free.

Flashcards

The first 3 of 11 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.

PromptCard 1 of 3

Accuracy versus precision?

0% read · 8 min left

Courselo

Uncertainties, errors and precision

Measurement, maths and practical skills · Lesson 2 of 5

Lesson 2 of 5

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Lesson 2 of 5 · Measurement, maths and practical skills

Uncertainties, errors and precision

8 min read · about 1 h 45 min with practice3 quick checks≈3% of the testCore

Reading is free. Sign in to tick off lessons, keep your place and track your mastery.

By the end you’ll be able to

Distinguish random from systematic errors (including zero errors and parallax) and state how each is reduced
Define and apply precision, repeatability, reproducibility, resolution and accuracy correctly in context
Estimate uncertainty from instrument resolution or half the range of repeat readings, and express it as absolute, fractional and percentage uncertainty
Combine uncertainties for sums/differences (add absolute), products/quotients (add percentage) and powers (multiply percentage by the power)
Judge whether a result agrees with an accepted value using percentage difference against combined percentage uncertainty

What the exam asks

Vocabulary in context. For example: “Explain why the readings are precise but not accurate.” Or: “State what is meant by the resolution of the micrometer.”
Error type and remedy. For example: “The ammeter has a zero error of +0.02 A. Explain the effect on the value of R and how to correct it.”
Calculate uncertainties, from an instrument’s resolution or from repeat readings, as absolute or percentage values.
Combine uncertainties through a formula such as $g = 4\pi^2 l/T^2$ , or , then quote the final answer as value ± uncertainty.

Check your understanding

3 questions on uncertainties, errors and precision. Every option is explained once you answer.

Answers are checked on our side, every option is explained, and your result feeds your mastery for this topic. It’s free.

Flashcards

The first 3 of 11 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.

PromptCard 1 of 3

Accuracy versus precision?

0% read · 8 min left

ρ

=

R

A

/

L

\rho = RA/L

Term	Meaning	How it shows up
Accuracy	how close a measurement is to the true value	a mean far from the accepted value is inaccurate
Precision	how closely repeated readings agree (a small spread)	9.62, 9.60, 9.63 are precise, but inaccurate if $g$ = 9.81
Repeatable	the same person, method and equipment give the same results	a student repeats the experiment three times
Reproducible	a different person, method or equipment gives the same results	another group gets the same value with a light gate
Resolution	the smallest change an instrument can detect	a micrometer reads to 0.01 mm
Uncertainty	the interval within which the true value is expected to lie	$d = 0.372 \pm 0.010$ mm
Zero error	the instrument reads a non-zero value when it should read zero	a micrometer reads 0.03 mm with the jaws closed
Valid	the measurement really measures what the investigation needs, with other variables controlled	timing a swing that is not small-angle can invalidate a test of $T = 2\pi\sqrt{l/g}$

	Random error	Systematic error
Effect	readings scatter unpredictably on both sides of the true value	every reading is shifted the same way, by the same amount or the same fraction
Typical causes	reaction time varying, judging a meniscus, fluctuating readings, draughts	zero error, a miscalibrated scale, a consistent parallax angle, a delay that happens every time
Reduced by	repeating and averaging; plotting many points and using a best-fit line; measuring larger quantities (e.g. timing 20 oscillations)	calibrating, correcting the zero error, improving technique; not by repeating
On a graph	points scatter about the line	the line shifts (wrong intercept) or its gradient changes

Result	Rule	Example
$y = a + b$ or $a - b$	add absolute uncertainties: $\Delta y = \Delta a + \Delta b$	ΔT from two thermometer readings
$y = ab$ or $a/b$	add percentage uncertainties	$R = V/I$
$y = a^n$	multiply the percentage by $\lvert n\rvert$	$A = \pi d^2/4$ doubles the percentage in ; halves it
$y = ka$ with $k$ exact	percentage unchanged	$\pi$ , $\tfrac{1}{2}$ , 20 oscillations

g

=

0.0149

\times

9.857

=

0.15

{m s}^{- 2}

\Delta g = 0.0149\times9.857 = 0.15\ \text{m s}^{-2}

Uncertainties, errors and precision

By the end you’ll be able to

What the exam asks

Check your understanding

Flashcards

Uncertainties, errors and precision

By the end you’ll be able to

What the exam asks

Check your understanding

Flashcards

Core ideas

The language of measurement

Random and systematic errors

Uncertainty in a single measurement

Combining uncertainties

Quoting a result

Does the result agree?

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

vii.Check your understanding

viii.Flashcards

By the end you’ll be able to

What the exam asks

vii.Check your understanding

viii.Flashcards

Core ideas

The language of measurement

Random and systematic errors

Uncertainty in a single measurement

Combining uncertainties

Quoting a result

Does the result agree?

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards

Check your understanding

Flashcards