# Uncertainty and Errors

Uncertainty and Errors
Accuracy is concerned with how close a reading is to its true value.
Precision is determined by the size of the random error and can be controlled by the experimenter.
Errors
In Physics when physical quantities are measured, exactness is impossible,
Errors are the difference between the measured result and the true or actual value. They occur because of
imperfections in the measuring instruments and human mistakes.
Types of errors
Random error –
 Error has equal chance of causing measured value, vM to be greater than or less than true value, vT.
 Caused by poor judgement or slightly uncontrolled fluctuating conditions
 E.g parallax error
Random errors can be reduced by:
2. Taking average reading of several values
3. Plotting a best fit straight line graph
Systematic error –
 Error causes measured value, vM to be either greater than or less than true value, vT by the same amount
each time a measurement is taken.
 Caused by inaccuracy in the measuring system
 E.g. zero error, poorly calibrated scale
Systematic error may be reduced by:
1. Determining the offset value of the error and adding or subtracting this value from measured
3. Re-calibration of the measuring instrument
Calculating errors
= measured value, vM - true value, vT (must be in the same units)
Absolute error, EA
௩ ି௩
Proportonal error EP = ಾ ೅
Percentage Error, E% =
௩೅
௩ಾ ି௩೅
௩೅
x 100
Note that vT is determined experimentally usually by taking several values over a period of time.
Uncertainty
Uncertainty indicates the range of values within which a measurement is likely to lie.
Combining Uncertainties
The rules are:
1. For quantities which are added or subtracted to give a final result, add the actual uncertainties
2. For quantities which are multiplied together or divided to give a final result, add the fractional
uncertainties
3. For quantities which are multiplied together or divided to give a final result and contain indices, add the
fractional uncertainties and multiply the corresponding fractional uncertainty by its index
Example:-
Percentage Uncertainty Example