Errors in measurements: human, systematic and random

No measurement is perfect

Every measurement differs a little from the true value. The best we can do is keep the error as small as reasonably possible, and say how big it might be. Your book sorts errors into three kinds.

Human errors come from the person: misjudging a pointer, an eye not in front of the mark, or reaction time when starting and stopping a clock. Training helps; automated or digital instruments help most.

Systematic errors shift every reading by the same amount. Causes are zero error, poor calibration or incorrect marking. Compare with a more accurate instrument and apply a correction factor.

Random errors make repeated readings differ under the same conditions. Unpredictable changes in temperature, pressure, humidity or voltage cause them. Take many readings and use their mean.

Ask two questions. Does it shift every reading the same way? Systematic. Does it scatter the readings unpredictably? Random. If it comes from you, it is human.

Key terms

Human error

Errors of perception, procedure or reaction time.

Systematic error

A consistent difference from a definite cause.

Random error

Repeated readings differ under the same conditions.

Correction factor

The amount added or subtracted after comparing with a more accurate instrument.

Short questions with model answers

1. Q1. Why does your book time 30 oscillations of a pendulum instead of one?

   • Starting and stopping the watch adds reaction time once.
   • Divide the total time by 30.

   To shrink the effect of reaction time and random errors on one oscillation.

2. Q2. Three timings of the same event are 2.3 s, 2.5 s and 2.4 s. What value do you record?

   • 2.3 s + 2.5 s + 2.4 s = 7.2 s
   • 7.2 s ÷ 3 = 2.4 s

   2.4 s, the mean.

Common mistakes

• ✗ Averaging many readings to remove a zero error.

  ✓ A zero error shifts every reading equally, so the mean keeps it. Apply a correction instead.

• ✗ Calling a badly calibrated balance a random error.

  ✓ Poor calibration has a definite cause and a steady effect: systematic.

• ✗ Calling reaction time a systematic error of the stopwatch.

  ✓ It comes from the person, not the watch: your book lists it as human error.

MCQs

1. 1. The reaction time in starting a stopwatch causes:

   1. (a) Systematic error
   2. (b) Human error
   3. (c) Random error
   4. (d) Zero error
   Show answer

   (b) It depends on the person (p. 19).

2. 2. Zero error, poor calibration and incorrect marking cause:

   1. (a) Human errors
   2. (b) Random errors
   3. (c) Systematic errors
   4. (d) No error
   Show answer

   (c) All three shift every reading by the same amount.

3. 3. Random errors are reduced by:

   1. (a) Taking many readings and their mean
   2. (b) Applying one correction factor
   3. (c) Using a longer metre rule
   4. (d) Ignoring odd readings
   Show answer

   (a) Their causes are unpredictable, so averaging cancels the scatter (p. 19).

4. 4. Your book says the best way to reduce human errors is to:

   1. (a) Take one careful reading
   2. (b) Apply a correction factor
   3. (c) Measure in a cold room
   4. (d) Use automated or digital instruments
   Show answer

   (d) Machines remove the person's perception and reaction time (p. 19).

5. 5. Quick Quiz: an air current makes the balance fluctuate. This is:

   1. (a) Human error
   2. (b) Random error
   3. (c) Systematic error
   4. (d) Zero error
   Show answer

   (b) An unpredictable change in the surroundings scatters the readings.

Quick revision

• Human errors come from the person; digital instruments reduce them most.
• Systematic errors shift every reading equally; fix with a correction factor.
• Random errors scatter readings; take many and use the mean.