Error in measurement is defined as:

Measured value minus true value

True value minus the mean of readings

The standard deviation of readings

The least count of the instrument

Which describes a systematic error?

It follows a definite law, has the same size and sign for repeated readings, and can be corrected

It varies unpredictably from reading to reading

It is a human mistake such as wrong recording

It is removed by taking the mean of many readings

How are random errors handled?

By taking the mean of many readings and describing scatter by standard deviation

By calibrating the instrument once

By repeating the measurement only if a gross error is suspected

Why is measurement ideally done at 20°C?

It is the standard temperature, so temperature differences cause environmental error

It is the temperature at which instruments never wear

Practice · 8 marks

Types and sources of measurement errors

Short answer

Errors are gross (human mistakes), systematic (fixed, predictable: instrumental, environmental, observational) and random (unpredictable variations, treated statistically). Main sources: standard/calibration, workpiece, instrument (backlash, wear, zero error), environment (temperature ≠20°C, vibration), operator (parallax, measuring force), and method (cosine error, alignment).

Explain the different types of errors in measurement and describe the main sources of error in a measuring process.

Error is the difference between the measured value and the true value of the quantity: $e = V_m - V_t$ . Absolute error is $e$ ; relative (percentage) error is $e/V_t \times 100$ .

Types of error

Gross errors: caused by human mistakes such as wrong reading, wrong recording, using the instrument wrongly or forgetting to correct zero error. They can be avoided by care and by repeating the measurement.
Systematic (fixed) errors: they follow a definite law and have the same magnitude and sign for repeated readings under the same conditions, so they can be predicted and corrected.
- Instrumental: worn anvils, wrong calibration, zero error, backlash.
- Environmental: temperature, humidity, pressure, vibration, dust.
- Observational: parallax, wrong estimation of the fraction of a division.
Random (accidental) errors: small variations in repeated readings that cannot be predicted individually, caused by small changes in temperature, friction, operator judgement and so on. They are treated by statistics: the mean of many readings is taken and the scatter is described by standard deviation.

Sources of error

Source	Examples
Standard / calibration	Master or slip gauge worn or not calibrated
Workpiece	Surface roughness, form errors, elastic deformation, out-of-roundness
Instrument	Friction, backlash, hysteresis, zero error, poor resolution, wear of anvils
Environment	Temperature different from the standard $20^\circ$ C, vibration, humidity, dust
Operator	Parallax, unequal measuring force, bad technique, fatigue
Method / contact	Abbe's principle not followed, cosine error, contact pressure, alignment errors

Reducing errors

Measure at standard temperature $20^\circ$ C or allow the work and instrument to soak, apply corrections for known systematic errors, calibrate regularly, use correct measuring force (ratchet), follow Abbe's principle, and take the mean of several readings to reduce random error.

✓ Answer checked by Claude Opus 5.5 (high effort)

Thread errors and effect of pitch error · Metrology, chapter 12
Fringe measurement of flatness error · Metrology, chapter 8
End bar and universal measuring machines · Metrology, chapter 14
Types of measurement errors and minimization · Instrumentation I, chapter 1
Sources of errors in chaining/taping · Surveying I, chapter 2 · asked 4×
Short note: sources of error in levelling · Surveying I, chapter 5
Principles of EDM measuring distances · Surveying I, chapter 2 · asked 12×

All Metrology chapter 2 questions →

Types and sources of measurement errors

Types of error

Sources of error

Reducing errors

Related questions