Measurement Math Example 2

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Example 2

medium
A scale consistently reads 0.5 kg too high (systematic error). A second scale gives variable readings due to vibration (random error). Explain the difference and how each affects measurements.

Solution

  1. 1
    Systematic error (bias): the scale always reads 0.5 kg too high — every measurement is off by the same amount in the same direction; mean is biased
  2. 2
    Random error (noise): vibration causes each reading to vary unpredictably around the true value — individual readings are noisy but average to the truth
  3. 3
    Effect of systematic error: cannot be reduced by taking more measurements; requires calibration
  4. 4
    Effect of random error: reduced by averaging multiple measurements — more readings → closer to true value

Answer

Systematic error creates constant bias (unaffected by sample size); random error creates noise (reduced by averaging).
Distinguishing bias from noise is critical. Systematic errors mislead even with perfect precision; random errors scatter around the truth. More data helps only with random error; systematic errors require fixing the measurement process.

About Measurement

Measurement is the process of assigning numerical values to attributes of objects or events according to a defined rule or scale.

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Example 4 hard

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