1. Accuracy and Precision๏ƒ

Experimental error is the difference between a measured value and the true or accepted value.

Accuracy describes how close a measurement is to the true value. A measurement with high accuracy has only a small difference from the true value.

Precision describes how close repeated measurements are to each other. A set of measurements with high precision shows very little variation between trials.

Accuracy and precision are independent. A result can be accurate but not precise, precise but not accurate, both, or neither. Understanding this distinction helps scientists evaluate the quality of their data and identify sources of error.

accuracy_and_precision
Accuracy โ€” how close a measurement is to the true or accepted value.
Precision โ€” how close repeated measurements are to each other.
High Accuracy + High Precision
Example: A 50.00 g mass measured as 49.99 g, 50.01 g, 50.00 g.
โ†’ Correct and consistent.
High Accuracy + Low Precision
Example: A 25ยฐC water bath measured as 22ยฐC, 27ยฐC, 25ยฐC, 26ยฐC.
โ†’ Correct on average but scattered.
Low Accuracy + High Precision
Example: A scale with a +5 g zero error measuring 50 g as 55.0 g, 55.1 g.
โ†’ Consistent but wrong (systematic error).
Low Accuracy + Low Precision
Example: A worn spring balance measuring 200 g as 150 g, 230 g, 180 g, 260 g.
โ†’ Wrong and inconsistent.

Fill in the Gaps โ€” Accuracy and Precision

Complete the following by filling in the missing words.

Word list (A โ†’ Z): accuracy โ€ข high precision โ€ข low accuracy โ€ข low precision โ€ข precision

  1. __________________ describes how close a measurement is to the true or accepted value.

  2. __________________ refers to how close repeated measurements are to each other.

  3. A set of results that are far from the true value shows __________________.

  4. A set of results that are scattered and inconsistent shows __________________.

  5. A measurement that is both correct and consistent demonstrates both high accuracy and __________________.

Reveal Answer Key

  1. accuracy

  2. precision

  3. low accuracy

  4. low precision

  5. high precision

Multiple-Choice Questions

Choose the best answer for each question.

  1. Which situation shows high accuracy and high precision?

    a. Measurements close to the true value and close to each other
    b. Measurements close to the true value but widely scattered
    c. Measurements far from the true value but tightly grouped
    d. Measurements far from the true value and scattered

  1. Which situation shows high accuracy but low precision?

    a. Readings that average to the true value but vary widely
    b. Readings that are tightly grouped but incorrect
    c. Readings that are both incorrect and inconsistent
    d. Readings that are consistently too high due to zero error

  1. Which situation shows low accuracy but high precision?

    a. A ruler with unclear markings producing scattered measurements
    b. A thermometer giving random values around the true temperature
    c. A balance giving both correct and incorrect readings at random
    d. A faulty scale giving consistent readings that are all too high

  1. Which situation shows low accuracy and low precision?

    a. Results that are correct on average but inconsistent
    b. Results that are consistent but shifted away from the true value
    c. Results that are neither close to the true value nor to each other
    d. Results that are correct and repeatable

  1. What type of error most often causes low accuracy but high precision?

    a. Random error
    b. Systematic error
    c. Recording error only
    d. Environmental noise
Reveal Answer Key

  1. a โ€” Measurements close to the true value and close to each other

  1. a โ€” Readings that average to the true value but vary widely

  1. d โ€” A faulty scale giving consistent readings that are all too high

  1. c โ€” Results that are neither close to the true value nor to each other

  1. b โ€” Systematic error