Uncertainty in a Measurement and Where It Comes From · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Every measurement comes with a range

Science · Chemistry · ages 18-19
Name ______________________   Date ____________

  1. You measure a table five times: 120.1, 120.3, 120.2, 120.3 and 120.1 cm. What is the range of the readings, in cm?

    Answer: ______________

  2. You step on a scale five times and it shows nearly the same weight each time, yet every reading is 2 kg too heavy. Which is true of this scale?

    • It is accurate but not precise
    • It is precise but not accurate
    • It is neither precise nor accurate

  3. Your five table readings span 120.1 cm to 120.3 cm. Which report is honest?

    • 120.2 cm, plus or minus 0.1 cm, from 5 readings
    • 120.20 cm, plus or minus 0.02 cm, from 5 readings
    • 120.2 cm, plus or minus 0.2 cm, from 1 reading

  4. A balance reads 2 kg heavy on every single weighing. What kind of error is this, and what reveals it?

    • Scatter in the readings, revealed by weighing five times
    • A steady bias, revealed by weighing a known standard
    • A mistake in subtraction, revealed by checking the math

  5. You may fill a special flask only once, so repeating is impossible. Where does its uncertainty come from?

    • Half the range of repeats you cannot take
    • The mean of readings taken by other students
    • The tolerance the maker printed on the glassware

  6. Weighing yourself five times on the same scale will reveal that the scale always reads 2 kg heavy.

    Circle one:   True   False

  7. Five scale readings are 11, 13, 12, 14 and 12. You estimate the uncertainty as half the range. What uncertainty do you report?

    Answer: ______________

  8. A student quotes a table length as 120.234 cm with an uncertainty of 0.1 cm. What is the mistake?

    • The value claims digits far past where the uncertainty stops
    • The uncertainty must always be bigger than the value itself
    • Five readings are too few to support any quoted result
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Every measurement comes with a range W1-mt_JXw4D9DReI-s1

  1. 0.2 · Highest minus lowest: 120.3 minus 120.1 is 0.2.
  2. It is precise but not accurate · Close repeats mean precise. Sitting 2 kg off means not accurate.
  3. 120.2 cm, plus or minus 0.1 cm, from 5 readings · Half the 0.2 cm range is 0.1 cm, and the reader must know 5 readings stand behind it.
  4. A steady bias, revealed by weighing a known standard · A push that is always the same way is systematic, and only a known truth shows it.
  5. The tolerance the maker printed on the glassware · With no repeats possible, the printed tolerance is the only honest source.
  6. False · Repeats reveal scatter, not a steady bias. Agreement can still be wrong.
  7. 1.5 · The range is 14 minus 11, which is 3, and half of 3 is 1.5.
  8. The value claims digits far past where the uncertainty stops · An uncertainty of 0.1 cm means the tenths place is the last one you know.
Worksheet · LightMySky