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Class 12 · Science and environment

Limitations and error

Your results look neat. But what could have made them wrong, and what can they not tell anyone?

What you will learn: Name sources of error and limitations and their effect on conclusions.

Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓

Jump to: Check yourself · For grown-ups · For teachers

Safety first

Spirit thermometer and ice water only. Wipe spills.

Keep it safe:

  • Use a spirit (red or blue) thermometer, not a mercury one. Use ice water only; no hot water is needed.
  • Wipe up spills at once so no one slips.

You will need

  • A thermometerOr the made-up readings on this page.
  • A cup of ice and waterFor calibration.
  • Paper for a limitations table

Time: About 40 minutes.

The story

Tara's results look perfect: the shaded classroom was cooler on every day she measured. Then Dhruv puts her thermometer in a cup of ice water. It reads 1 °C, not 0 °C. Tara groans. What else could have gone wrong, and what can her results not tell anyone?

The idea

Random error makes repeated readings scatter above and below the true value. Repeating and taking a mean reduces its effect.

Systematic error shifts every reading the same way, for example a thermometer that always reads 1 °C high. Repeating does not remove it; calibrating against a known value does.

A limitation is something the study cannot show because of how it was done, such as measuring only in one month or only in one school.

Stating errors and limitations honestly makes a conclusion more trustworthy, because readers know how far it reaches.

A table of errors and limits in a classroom temperature study. A thermometer reading 1 °C high is a systematic error: every reading is 1 °C high; next time check it in ice water. Readings that scatter by about 0.3 °C show random error: values spread; repeat and use the mean. Measuring on only 5 October days is a limitation: it cannot show May heat; measure in May too.Errors and limits in a classroom temperature studyProblemTypeEffectBetter next timeReads 1 °C highSystematicAll 1 °C highIce-water checkScatter ±0.3 °CRandomValues spreadRepeat, use meanOnly 5 Oct daysLimitationNot May heatMeasure in May
A table of errors and limits in a classroom temperature study. A thermometer reading 1 °C high is a systematic error: every reading is 1 °C high; next time check it in ice water. Readings that scatter by about 0.3 °C show random error: values spread; repeat and use the mean. Measuring on only 5 October days is a limitation: it cannot show May heat; measure in May too.

Worked example

Finding a systematic error (made-up readings)

  1. In ice water, which should read 0 °C, the thermometer read 1 °C.
  2. So every reading was 1 °C too high.
  3. A noon classroom reading of 31 °C becomes 31 − 1 = 30 °C.
  4. Limitation: only 5 October days were measured, so the study says nothing about May.

The correction fixes the systematic error. The limitation stays and is stated in the report.

Try it

  1. List what could go wrong.

    Instruments, timing, people, place.

  2. Sort each one.

    Random error, systematic error or limitation?

  3. Test for a systematic error.

    Put the thermometer in ice water. Does it read 0 °C?

  4. Correct what you can.

    Apply any calibration correction to every reading.

  5. State the rest.

    Write what the study cannot show, and how a next study could do better.

What you make (paper or offline)

Your limitations table

A table of errors and limitations with their type, effect and an improvement.Errors and limits in a classroom temperature studyProblemTypeEffectBetter next timeReads 1 °C highSystematicAll 1 °C highIce-water checkScatter ±0.3 °CRandomValues spreadRepeat, use meanOnly 5 Oct daysLimitationNot May heatMeasure in May
A table of errors and limitations with their type, effect and an improvement.

Each problem, its type and its effect.

Any correction you made, with the working.

What the study cannot show.

Make it on paper. Keep it with you. Nothing to upload.

Check yourself

Five questions about what this page teaches. Choose an answer and press Check answer, or open "See the answer and why". Nothing is saved or sent: your choices stay on this screen and disappear when you leave or reload the page.

  1. Question 1 of 5A thermometer reads 1 °C too high every time. What kind of error is this?

    See the answer and why
    • A. A limitation of the sample Not this one. It is a fault in the instrument, not in who or when was measured.
    • B. Random error Not this one. Random error scatters readings both ways, not always the same way.
    • C. Systematic error Correct. It shifts every reading the same way.
    • D. No error, since it is the same each time Not this one. Being consistent does not make it right.
  2. Question 2 of 5That thermometer read 31 °C in a classroom. What is the corrected temperature?

    See the answer and why
    • A. 32 °C Not this one. That adds the error instead of taking it away.
    • B. 29 °C Not this one. That takes the error away twice.
    • C. 31 °C Not this one. That ignores the known 1 °C error.
    • D. 30 °C Correct. 31 − 1 = 30 °C.
  3. Question 3 of 5Readings of one cup of water: 24.8, 25.3, 24.9 and 25.2 °C. What do they show?

    See the answer and why
    • A. Random error: repeats and a mean help Correct. They scatter above and below a middle value.
    • B. Proof that the water kept heating up Not this one. The values go up and down, not steadily up.
    • C. A broken thermometer to throw away Not this one. Small scatter is normal for any instrument.
    • D. Systematic error: all are shifted one way Not this one. They are not all shifted the same way.
  4. Question 4 of 5A study measured classrooms on only 5 October days. Which is a limitation?

    See the answer and why
    • A. It proves shade cools rooms in every season Not this one. Five October days cannot show every season.
    • B. The mean of 5 days is always wrong Not this one. A mean can be right for the days measured.
    • C. It cannot show what happens in May heat Correct. October results may not hold in the hottest month.
    • D. October has no weather worth measuring Not this one. October is fine; the limit is measuring only then.
  5. Question 5 of 5How could you find a systematic error in a thermometer?

    See the answer and why
    • A. Take more readings and average them Not this one. Averaging reduces random error, not a fixed shift.
    • B. Ignore it, since all of the readings move together Not this one. The shift still makes every value wrong.
    • C. Use the same thermometer once more Not this one. It would repeat the same shift.
    • D. Check it in ice water, which should read 0 °C Correct. Comparing with a known value shows any shift.

Think back

Which error in your own work could you correct, and which could you only state?

Does stating a limitation make a study weaker or more trustworthy?

Investigate further

  • Find a news report on a study. Does it state any limitations?
  • Calibrate a kitchen scale with a 1 L bottle of water (about 1 kg).

For grown-upsTap a heading to open it. The safety notes are at the top of the page.

Before you start
  • A spirit thermometer and a cup of ice water, or use the readings on the page.
Questions that help
  • "Would repeating fix that error?"
  • "What can your results not tell us?"
What's really going on

Real studies always have errors and limits; good ones say so and explain their effect.

Other ways to do it
  • Use a kitchen scale and a known mass instead of a thermometer.

For teachersLearning aims, classroom ideas and what to look for.

Learning aims
  • Distinguish random error, systematic error and limitations.
  • Correct a calibration error and state what a study cannot show.
Subject links
  • Physics and chemistry: measurement uncertainty.
  • All subjects: evaluating a study.

These links are general. They have not been checked against a specific board syllabus.

In the classroom
  • Groups calibrate several thermometers in the same ice water and compare offsets.
What to look for
  • Errors sorted correctly.
  • Limitations linked to the conclusion.
ProLearners Assist