Percentage error and Percentage uncertainty
Accuracy as binary concept - Need for measurement , uncertainty of measurement, and accepted value
Resolution of a measuring device is the smallest step or increment or the distance between two divisions.
A physical quantity is specified by the measured value and absolute uncertainty
Absolute uncertainty of a measurement:
Single measurement
For analog meter the absolute uncertainty = half the resolution
For a digital meter the absolute uncertainty = resolution
Improvement of poor resolution by measuring N items at once - -> this will improve the absolute uncertainty
Many measurements
absolute uncertainty = Half the spread or Maximum distance from the mean
The quality of the measurement is specified by percentage uncertainty:
It can be improved if physical quantity is way bigger than the resolution of the meter. At least 10 times.
Choose the smallest possible range consistent with the measured value.
Precision is relevant only for many measurements:
It is about the spread
Half the spread is the absolute uncertainty
Increasing the absolute uncertainty corresponds to decreasing the precision
Accuracy:
Accuracy is the deviation of the mean from the true value
Single measurement [ Measured - True] OVER [ True]
Many measurements [ Mean - True] OVER [ True]
Accuracy can be view as the number of correct significant figures
Sources of random error:
Random error will change the mean
Noise
Real things are never identical. Truly identical are only the elementary particles
Manufacturing process variation
Fluctuation of temperature
Reducing random error:
If there is no systematic error then averaging will improve the mean - consequently the accuracy Averaging improves the accuracy not the precision
Improvement by discarding anomalous readings
Reducing random error by Larger or Longer or Bigger quantities
If measurement is accurate but not precise then there is random error
Types of systematic errors:
Parallax error
Zero error
Miscalibration
Properties of systematic errors:
Systematic errors are directional
Systematic error will shift the mean
If measurement is precise but not accurate then there is systematic error
Dealing with systematic error:
Resetting
Use gradient
Time: Stopwatch Light-gate Data logger for fast measurements
Systematic error: Reaction time
Distance:
Ruler - 0.5mm Vernier calliper - 0.1 mm Micrometre -0.01 mm
Systematic error: Parallax error
Volume of liquid :
Graduated beaker
Mass:
Digital scale Balance
Random error: Variation of earth g - field
Systematic error: Buoyancy force
Temperature:
Thermometer
Systematic error: Time lag of thermometer Leakage of heat Gradient of the temperature
Temperature can affect other physical quantities
Radioactivity:
GM counter
Systematic error: Dead time
Random error: Background radiation
Different types of radiation have different attenuation coefficients
If the thing measured is not a constant, spatial or time variation then performing many measurements leads to better estimation of the range and consequently to the absolute uncertainty.
Range of a meter is about the minimum and maximum value.
Sensitivity or the minimum detectable signal
Error propagation
Parallel and perpendicular lines: set triangle
Vertical line: plumb line / weight on vertical string