Q.1 Which of the following best describes a systematic error in a measurement?
Random variation that averages out over many trials
A consistent bias that shifts all measurements in the same direction
An error that occurs only once during a single measurement
An error due to environmental fluctuations
Explanation - Systematic errors produce a consistent offset from the true value, unlike random errors which vary unpredictably. They can be traced to calibration, instrument bias, or methodology.
Correct answer is: A consistent bias that shifts all measurements in the same direction
Q.2 Which of the following is NOT typically considered a source of measurement error?
Instrument calibration drift
Observer bias
Temperature fluctuations
Exact mathematical calculation
Explanation - Accurate mathematical calculations do not introduce errors; they are tools to interpret data. Errors arise from instrument limitations, human factors, or environmental influences.
Correct answer is: Exact mathematical calculation
Q.3 If a voltmeter has an inherent error of ±1 %, what does this mean?
The meter reads 1 % higher than the true value
The meter reads 1 % lower than the true value
The meter may read up to 1 % higher or lower than the true value
The meter’s error changes by 1 % each hour
Explanation - A ±1 % specification indicates the absolute error could be anywhere between +1 % and –1 % of the measured value.
Correct answer is: The meter may read up to 1 % higher or lower than the true value
Q.4 What type of error is caused by a miswired sensor that always reads 0.5 V higher?
Random error
Systematic error
Instrument error
Environmental error
Explanation - A constant offset due to a miswired sensor is a systematic error because it consistently skews all measurements.
Correct answer is: Systematic error
Q.5 Which of the following is a common method to reduce random errors in measurements?
Using a more precise instrument
Averaging multiple measurements
Calibrating the instrument once
Increasing the measurement range
Explanation - Averaging many independent readings reduces random noise because errors tend to cancel out, improving precision.
Correct answer is: Averaging multiple measurements
Q.6 The combined standard uncertainty of a measurement is calculated by combining which of the following?
Only the largest error source
All individual uncertainties added linearly
All individual uncertainties added in quadrature
The average of all error sources
Explanation - The combined standard uncertainty is the square root of the sum of the squares of individual standard uncertainties, assuming they are uncorrelated.
Correct answer is: All individual uncertainties added in quadrature
Q.7 Which formula represents the propagation of uncertainty for a function f(x, y) = x·y?
σ_f = √(σ_x² + σ_y²)
σ_f = √( (σ_x·y)² + (x·σ_y)² )
σ_f = σ_x + σ_y
σ_f = √( (σ_x/x)² + (σ_y/y)² )
Explanation - For multiplication, the absolute uncertainty is the square root of the sum of the squares of each term’s absolute uncertainty multiplied by the other variable.
Correct answer is: σ_f = √( (σ_x·y)² + (x·σ_y)² )
Q.8 The term 'traceability' in metrology refers to:
The ability of a measurement to be transferred between instruments
The link between a measurement result and a reference standard
The accuracy of an instrument over time
The process of eliminating all measurement errors
Explanation - Traceability ensures that a measurement can be related to national or international standards through an unbroken chain of calibrations.
Correct answer is: The link between a measurement result and a reference standard
Q.9 Which of the following is NOT a typical component of a measurement uncertainty budget?
Calibration uncertainty
Random noise contribution
Systematic bias factor
Environmental temperature variation
Explanation - A systematic bias is already accounted for in calibration uncertainty; it is not an additional separate component in a budget.
Correct answer is: Systematic bias factor
Q.10 When calibrating a digital multimeter, the manufacturer specifies a repeatability of ±0.01 % of reading. For a 100 V measurement, what is the worst-case repeatability error?
±0.01 V
±0.10 V
±0.001 V
±1 V
Explanation - 0.01 % of 100 V is 0.01 × 100 = 0.01 V.
Correct answer is: ±0.01 V
Q.11 Which error type is most likely to be reduced by improving the sensor’s temperature compensation?
Random error
Systematic error
Calibration error
Measurement drift
Explanation - Temperature-induced changes cause the sensor output to drift over time, which is a systematic effect mitigated by temperature compensation.
Correct answer is: Measurement drift
Q.12 What does the 'coverage factor' k=2 signify in uncertainty reporting?
Two times the absolute uncertainty for 68% confidence
Two times the absolute uncertainty for 95% confidence
Two times the relative uncertainty for 50% confidence
Two times the absolute uncertainty for 99% confidence
Explanation - In the GUM framework, k=2 approximates a 95% confidence level for a normal distribution.
Correct answer is: Two times the absolute uncertainty for 95% confidence
Q.13 Which of the following is a common consequence of neglecting instrument nonlinearity?
Reduced measurement repeatability
Systematic error that varies with measurement range
Increased random noise
Higher measurement cost
Explanation - Nonlinearity causes the instrument response to deviate from a straight line, producing an error that changes with the input value.
Correct answer is: Systematic error that varies with measurement range
Q.14 In a Wheatstone bridge, what is the primary source of systematic error if one arm has a temperature coefficient of resistance?
Random voltage fluctuations
Offset voltage from the galvanometer
Temperature-dependent resistance change
Bridge imbalance due to mechanical stress
Explanation - Temperature coefficients alter resistance values in a systematic way as temperature varies, biasing the balance point.
Correct answer is: Temperature-dependent resistance change
Q.15 Which of the following best explains 'Type B' uncertainty?
Uncertainty derived from statistical analysis of repeated measurements
Uncertainty derived from the instrument’s calibration certificate
Uncertainty derived from literature or manufacturer specifications
Uncertainty derived from the measurement model equations
Explanation - Type B uncertainties are assigned from non-statistical sources such as manufacturer data or historical experience.
Correct answer is: Uncertainty derived from literature or manufacturer specifications
Q.16 If a pressure transducer has a linearity error of ±0.5 % and a hysteresis of ±0.2 %, what is the combined worst-case systematic error?
±0.2 %
±0.5 %
±0.7 %
±1.0 %
Explanation - Worst-case systematic errors add linearly: 0.5 % + 0.2 % = 0.7 %.
Correct answer is: ±0.7 %
Q.17 Which method is commonly used to estimate random error in a set of repeated voltage measurements?
Calculate the mean
Calculate the standard deviation
Use the calibration certificate
Apply temperature correction
Explanation - Random error is characterized by the spread of data, quantified by the standard deviation of repeated measurements.
Correct answer is: Calculate the standard deviation
Q.18 Why is it important to consider the instrument’s resolution when reporting measurement uncertainty?
Resolution determines the speed of measurement
Resolution limits the smallest detectable change and contributes to uncertainty
Resolution is unrelated to uncertainty
Resolution only affects calibration procedures
Explanation - Finite resolution introduces an additional discretization error that must be included in the uncertainty budget.
Correct answer is: Resolution limits the smallest detectable change and contributes to uncertainty
Q.19 The term 'bias' in measurement engineering refers to:
The random spread of measurement results
The systematic deviation from the true value
The time delay in signal processing
The sensitivity of an instrument to temperature
Explanation - Bias is a consistent offset that causes all measurements to be systematically high or low.
Correct answer is: The systematic deviation from the true value
Q.20 Which of the following best describes the 'GUM' in metrology?
Global Uniform Model for Uncertainty
Guide to the Expression of Uncertainty in Measurement
Generic Uncertainty Method
General Use Methodology
Explanation - GUM is the internationally recognized guideline for calculating and reporting measurement uncertainty.
Correct answer is: Guide to the Expression of Uncertainty in Measurement
Q.21 For a capacitance measurement using a bridge, which error source is likely to dominate at high frequencies?
Dielectric loss
Lead inductance
Temperature drift
Mechanical vibration
Explanation - At high frequencies, stray inductance of the leads can significantly affect the bridge balance.
Correct answer is: Lead inductance
Q.22 If a thermocouple’s temperature coefficient of sensitivity is ±0.05 %/°C and the ambient temperature changes by ±2 °C during measurement, what is the induced systematic error?
±0.01 %
±0.10 %
±0.05 %
±0.20 %
Explanation - Error = 0.05 %/°C × 2 °C = 0.10 %.
Correct answer is: ±0.10 %
Q.23 Which statistical distribution is most appropriate for modeling the distribution of a measurement that is affected by many small independent random errors?
Uniform distribution
Exponential distribution
Normal (Gaussian) distribution
Poisson distribution
Explanation - Central Limit Theorem states that the sum of many independent random variables tends to a normal distribution.
Correct answer is: Normal (Gaussian) distribution
Q.24 In uncertainty analysis, what is the purpose of the 'coverage interval'?
To specify the maximum measurement range
To define the confidence level for the stated uncertainty
To adjust the instrument’s calibration curve
To correct systematic errors
Explanation - The coverage interval (U ± k·u) indicates the range within which the true value is expected to lie with a certain confidence level.
Correct answer is: To define the confidence level for the stated uncertainty
Q.25 Which of the following is a consequence of using a high-precision instrument without proper zero adjustment?
Random error increases
Systematic bias appears in all readings
Instrument becomes unstable
Measurement range shrinks
Explanation - Zero offset remains uncorrected, leading to a consistent error in every measurement.
Correct answer is: Systematic bias appears in all readings
Q.26 A data logger records a sensor output every second. The recorded voltage has a standard deviation of 0.02 V. What is the standard uncertainty due to random noise?
0.02 V
0.02 / √12 V
0.02 / √N V
0.02 × √12 V
Explanation - The standard deviation directly represents the standard uncertainty of the noise for each reading.
Correct answer is: 0.02 V
Q.27 The 'error budget' of a measurement system is a:
List of all potential measurement errors with their estimated magnitudes
Summary of all systematic errors only
Summary of all random errors only
A financial plan for purchasing better instruments
Explanation - An error budget quantifies every identified source of uncertainty, both systematic and random.
Correct answer is: List of all potential measurement errors with their estimated magnitudes
Q.28 Which of the following techniques can reduce the effect of instrument drift over time?
Shortening measurement duration
Periodic calibration with traceable standards
Using a higher resolution display
Increasing the sampling frequency
Explanation - Regular calibration realigns the instrument to known references, mitigating long-term drift.
Correct answer is: Periodic calibration with traceable standards
Q.29 When two measurements with uncertainties u1 and u2 are combined by subtraction, what is the combined standard uncertainty?
√(u1² + u2²)
u1 + u2
|u1 – u2|
max(u1, u2)
Explanation - For independent measurements, uncertainties combine in quadrature regardless of whether the operation is addition or subtraction.
Correct answer is: √(u1² + u2²)
Q.30 What is the impact of a sensor’s 'hysteresis' on measurement accuracy?
It introduces random noise
It causes a time delay
It produces a systematic offset depending on the direction of change
It reduces the sensor’s sensitivity
Explanation - Hysteresis means the sensor’s output depends on its previous state, leading to systematic errors.
Correct answer is: It produces a systematic offset depending on the direction of change
Q.31 In a temperature measurement chain, why is it essential to consider the thermal expansion of the sensor leads?
Because it affects the sensor’s electrical resistance
Because it changes the sensor’s mechanical stability
Because it influences the calibration frequency
Because it alters the sensor’s electromagnetic interference profile
Explanation - Thermal expansion can change lead lengths, impacting resistance and thus the measurement reading.
Correct answer is: Because it affects the sensor’s electrical resistance