Types of measurement errors and minimization

Error is the difference between the measured value and the true value of a quantity. Errors are divided into three types.

1. Gross errors

These are human mistakes: wrong reading, wrong recording, wrong choice of instrument, or careless use of the instrument (e.g. ignoring the loading effect).

Minimizing: take great care in reading and recording; take several readings (at least three) and compare them; use the correct instrument and range; have another person check.

2. Systematic errors

These errors repeat in the same direction (always high or always low) under the same conditions. There are three kinds:

• Instrumental errors: friction in bearings, worn parts, zero error, calibration error, loading effect, spring ageing.
• Environmental errors: temperature, humidity, pressure, and magnetic or electric fields around the instrument.
• Observational errors: parallax, and wrong estimation of the pointer position between scale marks.

Minimizing:

• Calibrate against a standard before use and apply correction factors.
• Choose a voltmeter with high input impedance to reduce loading.
• Keep the instrument in a controlled environment; use shielding and temperature compensation.
• Use mirror scales to avoid parallax, or use digital instruments.
• Replace faulty or worn parts, and check the zero before measuring.

3. Random errors

These are small, unpredictable errors that remain after gross and systematic errors are removed. They are caused by unknown variations (noise, small fluctuations) and usually follow a normal (Gaussian) distribution.

Minimizing:

• Take many readings and use the arithmetic mean; the error of the mean falls as 1/√n.
• Apply statistical analysis (standard deviation, probable error).
• Use filtering and averaging, and stable power supplies.

Summary table